• *Photon detection efficiency* (PDE), i.e., the ability to detect photons. This is the ratio between the number of detected photons and the photons arriving at the detector. PDE is calculated as the product of: (i) the quantum efficiency (QE) and (ii) the avalanche triggering probability (PT). The latter is the probability that photo-generated carriers can reach the high-field

• The noise is typically divided into "primary" noise and correlated noise. The primary noise represents all the avalanche pulses due to thermally generated carriers (or generated by tunneling or field-assisted thermal generation). The *dark count rate* (DCR) is typically in the

• The correlated noise for a SPAD is represented by the *afterpulsing.* During the avalanche, a large amount of carriers flows through the depleted region and some of them can be trapped in deep-levels (traps), being subsequently released with a delay, causing retriggering of another spurious avalanche, not related to photon absorption but to a previous avalanche, thus "correlated noise." The time distribution of carrier release follows normally an exponential (or multiexponential) distribution. Its time constant depends on temperature, being slower at low temperatures. The afterpulsing probability depends on the SPAD itself, on the

• The *dead-time* is the time interval after an avalanche, where the SPAD is not sensitive to another photon. This interval is necessary to recharge the SPAD and to let the traps to release the carriers without triggering a spurious avalanche. This is typically in the order of tens of nanosecond. Differently from active quenching, with passive quenching, the recharge is exponential, and thus it is not easy to identify a precise dead-time. The recharge time-constant

• The time resolution of the SPAD, i.e., the ability of precise time-tag the photon arrival time, is another important parameter. The "*timing jitter*" or "*single-photon time resolution*" (SPTR) quantifies the time spread between the photon arrival and the pulse detection by the frontend electronics. This spread is due to the different absorption position and the statistical avalanche buildup time. It is in the order of a few tens of picoseconds [15]. To measure the timing jitter, it can be used a pulsed laser, attenuated to single-photon level. Using TCSPC

and it is well-defined.

**3.1. SPAD parameters**

parameters identifying the performance:

44 Photon Counting - Fundamentals and Applications

order of 10–1000 counts per second.

quenching circuit, and on the dead-time.

can be used as a parameter.

region and trigger a self-sustaining detectable avalanche.

Some applications require detecting single photons with a wavelength in the near-infrared (NIR) range, above 1000 nm, for example when using laser emitting in the telecom wavelengths, at 1310 nm and 1550 nm. There are SPADs made by semiconductor materials different from silicon. In particular, there has been recently a development of SPADs made with III/V materials like InGaAs/InP [17, 18] or InGaAs/InAlAs [19] or InGaAsP/InP [20]. InGaAs/ InP SPADs are used to detect photons at 1550 nm. They are based on a separate absorption, grading, charge and multiplication (SAGCM) heterostructure as shown in **Figure 4**. The absorption layer is made of InGaAs and the multiplication layer is of InP. Between them, there

**Figure 3.** Representation of two photon absorption cases in the depleted region and in the neutral region beneath it (a) and examples of the relative timing histograms (b). At λ = 400 nm, all the photons are absorbed in the depleted region, whereas at 850 nm, they are absorbed mostly in the neutral region, creating the tail.

**Figure 4.** Schematic cross-section of an InGaAs/InP SPAD, with different layers (a). Comparison of photon detection efficiency (PDE) of some silicon SPADs and InGaAs SPADs (b): "thin" silicon SPAD [23], "thick" silicon SPAD [23], the FBK RGB technology (SiPM PDE divided by the FF) [25] and the typical state-of-the-art InGaAs/InP SPADs [24].

is one or more layers of InGaAsP, called "grading layer." This is needed to smooth the heterobarrier in the valence band between the InGaAs and the InP layers. On the top of it, there is a "charge layer" that shapes the electric field profile.

lifetime imaging microscopy (FLIM), Raman spectroscopy, time-resolved near-infrared spectroscopy, and consumer applications like three-dimensional (3-D) imaging based on time-of-flight [26]. In particular, fluorescence microscopy is an established technique for the analysis of biological processes and relies on the measurement of the fluorescence intensity upon an excitation [22] at different wavelengths. Fluorescent light emission can occur in a variety of temporal scales, from nanoseconds upward. Its lifetime measurements add valuable information and require a specific kind of detectors, like a SPAD array with timetagging circuitry per pixel. In the same way, 3D imaging, based on time-of-flight (TOF), is an application that is rapidly emerging in many fields [26], to have a three-dimensional image of the scene or to measure the distance from the objects. 3D imaging can be obtained by means of direct TOF or indirect TOF. The first one is based on the direct detection of the

High Sensitivity Photodetector for Photon-Counting Applications

http://dx.doi.org/10.5772/intechopen.71940

47

The first approach to have SPAD pixels with time-tagging capabilities is the addition of a time-to-digital converter (TDC) in each pixel [27]. The SPAD array will have in each pixel the photon-number information as well as the time-of arrival information (typically of the first photon), as shown, for example, in **Figure 5(a)**. Devices realized with this approach, showed good performance in many biological and 3D-ranging applications. However, the TDC generally occupies a significant part of the pixel area, reducing the fill factor (FF). There are also special implementations without the TDC, but performing distance measurements with indirect

In general, to improve the FF in a CMOS implementation, it is necessary to reduce the read-out circuitry occupation and complexity. The SPAD structure has to be placed very close to the readout electronics, but being electrically isolated with proper implants, as shown in **Figure 5(b)**. To minimize the pixel circuitry, it is possible to implement just the time-to-amplitude conversion

**Figure 5.** Example of 32 × 32 SPAD array, where each pixel contains a SPAD, the quenching circuitry, counters, and the time-to-digital converter (TDC) [27] (a). Example of possible SPAD CMOS implementation with read-out electronics isolated inside the deep p-well (b) [28]. Example of analog time-gated SPAD pixel, with a reduced electronics-complexity

time-of-flight (iToF) method, by using three different counters per pixel [4].

time-of-arrival of the reflected light pulse.

to obtain a higher FF (c) [5].

InGaAs has an energy gap of about 0.75 eV [17]. The PDE of InGaAs/InP SPAD is typically around 40% between 1000 nm and 1550 nm (see **Figure 4(b)**), being limited by the thickness of the absorption layer. This cannot be too high in order to limit the noise. The primary noise is typically higher in InGaAs/InP SPADs compared to silicon ones. The technology of the III/V material is commonly less mature. The main noise source is thermal generation in the InGaAs layer down to about 225 K, whereas at lower temperatures, it is trap-assisted-tunneling in the multiplication layer. The afterpulsing probability is also higher in InGaAs/InP SPADs, compared to silicon. The typical dead-time can be in the order of few microseconds. However, despite these limitations, InGaAs/InP SPADs have been used in several applications. Advantages such as good PDE, compactness, and low power consumption make this a competitive solution for NIR single-photon counting. They are typically used inside compact modules and cooled at 230 K (or lower) to decrease the primary noise [24].

The high afterpulsing probability can be a limiting factor in several applications. Some solutions have been proposed that aim to reduce the amount of charge flowing per each avalanche. The first is based on very fast quenching circuit, reducing the bias at the SPAD quickly once an avalanche is detected [21]. Another solution is based on fast gating the detector, for example, using sinusoidal signals with a frequency of few gigahertz: the bias at the SPAD is modulated and, once an avalanche is triggered, it can last at maximum for the duration of half a gating period [18]. This technique is called *sinusoidal gating*. Another approach is based on the integration of a quenching resistor directly on the SPAD, very close to the active area. This approach limits the overall capacitance at the node between the SPAD and the quenching resistor, thus the avalanche charge. Some implementations of this kind of detector are called negative-feedback avalanche diode (NFAD) [18].

## **4. SPAD array and low-light imagers**

SPADs can be arranged in arrays, 1D or 2D, manufactured in custom process or CMOS process. SPAD array in CMOS process has the advantage of having all the quenching, control and read-out electronics in each pixel. Unfortunately, usually with the CMOS process, the SPAD performance is not as good as with a custom process, due to the non-optimized implants and electric fields. In particular, they have a higher DCR.

SPAD arrays are one of the solutions for low-light-level imaging [4, 5]. With such technology, it is possible to have a sensitivity down to the single-photon level, working in photoncounting mode. With the proper in-pixel circuitry, each pixel counts the number of photons detected in the integrating period. This information is stored and then downloaded, to build an image. Scientific imaging applications often require such low level of sensitivity, typically with the addition of time-resolving capabilities. As few examples: fluorescence lifetime imaging microscopy (FLIM), Raman spectroscopy, time-resolved near-infrared spectroscopy, and consumer applications like three-dimensional (3-D) imaging based on time-of-flight [26]. In particular, fluorescence microscopy is an established technique for the analysis of biological processes and relies on the measurement of the fluorescence intensity upon an excitation [22] at different wavelengths. Fluorescent light emission can occur in a variety of temporal scales, from nanoseconds upward. Its lifetime measurements add valuable information and require a specific kind of detectors, like a SPAD array with timetagging circuitry per pixel. In the same way, 3D imaging, based on time-of-flight (TOF), is an application that is rapidly emerging in many fields [26], to have a three-dimensional image of the scene or to measure the distance from the objects. 3D imaging can be obtained by means of direct TOF or indirect TOF. The first one is based on the direct detection of the time-of-arrival of the reflected light pulse.

is one or more layers of InGaAsP, called "grading layer." This is needed to smooth the heterobarrier in the valence band between the InGaAs and the InP layers. On the top of it, there is a

InGaAs has an energy gap of about 0.75 eV [17]. The PDE of InGaAs/InP SPAD is typically around 40% between 1000 nm and 1550 nm (see **Figure 4(b)**), being limited by the thickness of the absorption layer. This cannot be too high in order to limit the noise. The primary noise is typically higher in InGaAs/InP SPADs compared to silicon ones. The technology of the III/V material is commonly less mature. The main noise source is thermal generation in the InGaAs layer down to about 225 K, whereas at lower temperatures, it is trap-assisted-tunneling in the multiplication layer. The afterpulsing probability is also higher in InGaAs/InP SPADs, compared to silicon. The typical dead-time can be in the order of few microseconds. However, despite these limitations, InGaAs/InP SPADs have been used in several applications. Advantages such as good PDE, compactness, and low power consumption make this a competitive solution for NIR single-photon counting. They are typically used inside compact

The high afterpulsing probability can be a limiting factor in several applications. Some solutions have been proposed that aim to reduce the amount of charge flowing per each avalanche. The first is based on very fast quenching circuit, reducing the bias at the SPAD quickly once an avalanche is detected [21]. Another solution is based on fast gating the detector, for example, using sinusoidal signals with a frequency of few gigahertz: the bias at the SPAD is modulated and, once an avalanche is triggered, it can last at maximum for the duration of half a gating period [18]. This technique is called *sinusoidal gating*. Another approach is based on the integration of a quenching resistor directly on the SPAD, very close to the active area. This approach limits the overall capacitance at the node between the SPAD and the quenching resistor, thus the avalanche charge. Some implementations of this kind of detector are called

SPADs can be arranged in arrays, 1D or 2D, manufactured in custom process or CMOS process. SPAD array in CMOS process has the advantage of having all the quenching, control and read-out electronics in each pixel. Unfortunately, usually with the CMOS process, the SPAD performance is not as good as with a custom process, due to the non-optimized implants and

SPAD arrays are one of the solutions for low-light-level imaging [4, 5]. With such technology, it is possible to have a sensitivity down to the single-photon level, working in photoncounting mode. With the proper in-pixel circuitry, each pixel counts the number of photons detected in the integrating period. This information is stored and then downloaded, to build an image. Scientific imaging applications often require such low level of sensitivity, typically with the addition of time-resolving capabilities. As few examples: fluorescence

modules and cooled at 230 K (or lower) to decrease the primary noise [24].

"charge layer" that shapes the electric field profile.

46 Photon Counting - Fundamentals and Applications

negative-feedback avalanche diode (NFAD) [18].

**4. SPAD array and low-light imagers**

electric fields. In particular, they have a higher DCR.

The first approach to have SPAD pixels with time-tagging capabilities is the addition of a time-to-digital converter (TDC) in each pixel [27]. The SPAD array will have in each pixel the photon-number information as well as the time-of arrival information (typically of the first photon), as shown, for example, in **Figure 5(a)**. Devices realized with this approach, showed good performance in many biological and 3D-ranging applications. However, the TDC generally occupies a significant part of the pixel area, reducing the fill factor (FF). There are also special implementations without the TDC, but performing distance measurements with indirect time-of-flight (iToF) method, by using three different counters per pixel [4].

In general, to improve the FF in a CMOS implementation, it is necessary to reduce the read-out circuitry occupation and complexity. The SPAD structure has to be placed very close to the readout electronics, but being electrically isolated with proper implants, as shown in **Figure 5(b)**. To minimize the pixel circuitry, it is possible to implement just the time-to-amplitude conversion

**Figure 5.** Example of 32 × 32 SPAD array, where each pixel contains a SPAD, the quenching circuitry, counters, and the time-to-digital converter (TDC) [27] (a). Example of possible SPAD CMOS implementation with read-out electronics isolated inside the deep p-well (b) [28]. Example of analog time-gated SPAD pixel, with a reduced electronics-complexity to obtain a higher FF (c) [5].

(TAC) in pixel [29, 30], or using an all-analog approach [5, 28], by means just of few transistors and capacitances. **Figure 5(c)** shows an example of analog time-gated SPAD pixel, based on analog time-gating and analog counter [5].

detectors, such as compactness, ruggedness, ease of use, low operational voltage, and insensitivity to magnetic fields [32]. One of the most common applications is the detection of fast scintillation light in particle detectors that are used in nuclear medicine [32, 38] and in high-energy physics experiments [33, 34]. In these applications, SiPMs are coupled with scintillator crystals, which convert high-energy particle, X or gamma ray into visible or NUV light, being detected

heights) is shown in **Figure 7a**. SiPMs allowed significant advancements in positron-emission tomography (PET) [35] and other medical applications, especially due to their excellent time resolution [37]. This made possible to develop PET scanners with improved performance as

**Figure 6.** Example of silicon photomultiplier chip (SiPM), with back contact and common top PAD (a). Example of SiPM signal, acquired with oscilloscope in persistence mode (b). Typical circuit for the readout of a SiPM, with transimpedance amplifier (c) with the SiPM equivalent circuit, composed by quenching resistor (RQ), quenching capacitance (CQ), i.e., parasitic capacitance of the quenching resistor through the SPAD, and the metal grid equivalent capacitance (CGRID). Example of digital SiPM with TDC per each subpixel [38] (d) and schematic of dSiPM with one global TDC (e).

**Figure 7.** Picture of a test SiPM with several scintillator crystals (to be mounted on the top of it) (a). Example of setup for the measurement of coincidence resolving time (CRT), with two SiPMs with crystals detecting two coincident gamma

SiPMs (c).

rays (b). Example of a SiPM TILE with 6 × 6 element of 4 × 4 mm2

SiPM with some scintillator crystals (with different

High Sensitivity Photodetector for Photon-Counting Applications

http://dx.doi.org/10.5772/intechopen.71940

49

by the SiPM. An example of 4 × 4 mm2

An alternative implementation of low-level imager is the so-called "quanta image sensor" (QIS) [31]. This is based on the concept of extending the sensitivity of a "classical" image sensor, which is not based on avalanche multiplication process. The pixel is composed of a pinned photodiode (PPD), collecting the photo-generated charge, which then is transferred to a small floating diffusion (FD). FD has a small dimension and its capacitance is very small, thus the conversion gain between charge and voltage amplitude is very high, enough to measure a single photo-electron. In a single-bit QIS, the output after each acquisition is a binary bit plane, where each bit represents the presence or absence of at least one photoelectron. A series of bit planes has to be generated, with a high-speed readout, eventually being able to create an image.

## **5. Silicon photomultiplier**

Silicon photomultipliers (SiPMs) are arrays of many single-photon avalanche diodes (SPADs), all connected in parallel [25, 32, 43]. Each SPAD is called microcell (or cell) and has a square area with a side between 10 μm and 100 μm, whereas the overall SiPM active area can be typically between 1 × 1 mm2 and 10 × 10 mm2 . This is one of the main advantages of SiPM over other SPDs: they can have big active area, but preserving the good performance of the single SPAD, with the additional advantage of being photon-number resolved (i.e., being able to count the number of photons arriving at the detector simultaneously, with a high dynamic range). These characteristics are becoming more and more important in a large number of applications [33–37] (**Figure 6**).

The silicon photomultipliers can be divided into: (i) analog SiPM [25] (see (**Figure 6a**), (**Figure 6b**), and (**Figure 6c**)) and (ii) digital SiPM [37, 38] (see (**Figure 6d**) and (**Figure 6e**)). In analog SiPM (aSiPM), the microcell, composing the array, is just made of a SPAD and a quenching resistor. The output current is the sum of the currents from the triggered cells in the array; thus, the output (amplitude or charge) is proportional to the number of detected photons (see (**Figure 6b**)). In digital SiPM (dSiPM), each microcell is typically composed by a SPAD and a more-complex quenching circuit (see (**Figure 6d**)). The cell provides a digital output to the internal dSiPM circuitry, which eventually digitally sumup the signals from the microcells and can contain a time-to-digital converter (TDC) (see (**Figure 6e**)) to time-stamp the photons arrival times [37, 38]. In dSiPM, the signals are digital starting from the single microcell, thus less affected by the front-end noise. However, due to the more complex quenching and due to the presence of the control circuitry, the fill factor is lower as well as the photon detection efficiency.

#### **5.1. SiPM applications**

SiPMs have obtained a growing attention as alternative to the traditional photomultiplier tubes in the detection of low photon fluxes due to a number of advantages typical of solid-state detectors, such as compactness, ruggedness, ease of use, low operational voltage, and insensitivity to magnetic fields [32]. One of the most common applications is the detection of fast scintillation light in particle detectors that are used in nuclear medicine [32, 38] and in high-energy physics experiments [33, 34]. In these applications, SiPMs are coupled with scintillator crystals, which convert high-energy particle, X or gamma ray into visible or NUV light, being detected by the SiPM. An example of 4 × 4 mm2 SiPM with some scintillator crystals (with different heights) is shown in **Figure 7a**. SiPMs allowed significant advancements in positron-emission tomography (PET) [35] and other medical applications, especially due to their excellent time resolution [37]. This made possible to develop PET scanners with improved performance as

(TAC) in pixel [29, 30], or using an all-analog approach [5, 28], by means just of few transistors and capacitances. **Figure 5(c)** shows an example of analog time-gated SPAD pixel, based on

An alternative implementation of low-level imager is the so-called "quanta image sensor" (QIS) [31]. This is based on the concept of extending the sensitivity of a "classical" image sensor, which is not based on avalanche multiplication process. The pixel is composed of a pinned photodiode (PPD), collecting the photo-generated charge, which then is transferred to a small floating diffusion (FD). FD has a small dimension and its capacitance is very small, thus the conversion gain between charge and voltage amplitude is very high, enough to measure a single photo-electron. In a single-bit QIS, the output after each acquisition is a binary bit plane, where each bit represents the presence or absence of at least one photoelectron. A series of bit planes has to be generated, with a high-speed readout, eventually being able to create an image.

Silicon photomultipliers (SiPMs) are arrays of many single-photon avalanche diodes (SPADs), all connected in parallel [25, 32, 43]. Each SPAD is called microcell (or cell) and has a square area with a side between 10 μm and 100 μm, whereas the overall SiPM active area can be typi-

other SPDs: they can have big active area, but preserving the good performance of the single SPAD, with the additional advantage of being photon-number resolved (i.e., being able to count the number of photons arriving at the detector simultaneously, with a high dynamic range). These characteristics are becoming more and more important in a large number of

The silicon photomultipliers can be divided into: (i) analog SiPM [25] (see (**Figure 6a**), (**Figure 6b**), and (**Figure 6c**)) and (ii) digital SiPM [37, 38] (see (**Figure 6d**) and (**Figure 6e**)). In analog SiPM (aSiPM), the microcell, composing the array, is just made of a SPAD and a quenching resistor. The output current is the sum of the currents from the triggered cells in the array; thus, the output (amplitude or charge) is proportional to the number of detected photons (see (**Figure 6b**)). In digital SiPM (dSiPM), each microcell is typically composed by a SPAD and a more-complex quenching circuit (see (**Figure 6d**)). The cell provides a digital output to the internal dSiPM circuitry, which eventually digitally sumup the signals from the microcells and can contain a time-to-digital converter (TDC) (see (**Figure 6e**)) to time-stamp the photons arrival times [37, 38]. In dSiPM, the signals are digital starting from the single microcell, thus less affected by the front-end noise. However, due to the more complex quenching and due to the presence of the control circuitry, the

SiPMs have obtained a growing attention as alternative to the traditional photomultiplier tubes in the detection of low photon fluxes due to a number of advantages typical of solid-state

. This is one of the main advantages of SiPM over

and 10 × 10 mm2

fill factor is lower as well as the photon detection efficiency.

analog time-gating and analog counter [5].

48 Photon Counting - Fundamentals and Applications

**5. Silicon photomultiplier**

cally between 1 × 1 mm2

**5.1. SiPM applications**

applications [33–37] (**Figure 6**).

**Figure 6.** Example of silicon photomultiplier chip (SiPM), with back contact and common top PAD (a). Example of SiPM signal, acquired with oscilloscope in persistence mode (b). Typical circuit for the readout of a SiPM, with transimpedance amplifier (c) with the SiPM equivalent circuit, composed by quenching resistor (RQ), quenching capacitance (CQ), i.e., parasitic capacitance of the quenching resistor through the SPAD, and the metal grid equivalent capacitance (CGRID). Example of digital SiPM with TDC per each subpixel [38] (d) and schematic of dSiPM with one global TDC (e).

**Figure 7.** Picture of a test SiPM with several scintillator crystals (to be mounted on the top of it) (a). Example of setup for the measurement of coincidence resolving time (CRT), with two SiPMs with crystals detecting two coincident gamma rays (b). Example of a SiPM TILE with 6 × 6 element of 4 × 4 mm2 SiPMs (c).

regards the time-of-flight (TOF) technique, which significantly improves image quality. In these applications, SiPMs are typically grouped in TILEs, to cover areas of few centimeters squared. An example is shown in **Figure 7c**.

SiPMs are also becoming an interesting choice in other applications based on single-photon or few-photon detection. For example: (i) light detection and ranging (LIDAR) [39], where many cells with good detection efficiency are highly desirable, (ii) optical spectroscopy [40], where high detection efficiency and big sensitive areas are very useful, (iii) fluorescence detection, (iv) flow cytometry, (v) Cherenkov detection for physics experiments [36], etc.

#### **5.2. From SPAD to SiPM**

Moving from a single SPAD to a silicon photomultiplier, there are some additional parameters and other noise sources that have to be considered.

The integrated quenching resistor also reduces the amplitude of the *single-cell signal.* Considering the SiPM equivalent circuit, when the avalanche switch is closed, the bias at the internal node (between SPAD and quenching resistor) is lowered, discharging CD and CQ. Then, it is recharged through RQ. However, the detectable signal is only the current that flows through the anode and cathode pins of the SiPM. The SiPM signal is composed by a fast peak (capacitive coupling through CQ) and a slower component, due to the recharge current through RQ. Both are "filtered" by the presence of CGRID. The bigger the SiPM the larger is CGRID, thus the

**Figure 8.** Representation of SiPM cross-section and of correlated noise source (a) [43] and typical oscilloscope persistence

High Sensitivity Photodetector for Photon-Counting Applications

http://dx.doi.org/10.5772/intechopen.71940

51

PDE is one of the most important parameter for a SiPM. It has been significantly improved over the last years. One possible improvement is having the PDE spectrally peaked in the region of interest of the specific application, for example, in the blue or in the green wavelength region. An Examples are the RGB [25] and NUV [43] technologies from FBK, made with p-on-n junction or n-on-p junction type. Another improvement is the increment of the cell FF, which can be obtained reducing the *border region*, i.e., the not-sensitive region between

The signal coming out from the SiPM is the superposition of many pulses, either in light or in dark. Depending on the application, it is possible to measure directly the current level produced by the SiPM, or count the avalanche pulses (photon-counting mode). If the count rate is low, the pulses are clearly distinguishable, but increasing the count rate, they start to overlap, making the counting more difficult. To avoid this situation, some techniques have been

• *High-pass filtering or pole-zero cancellation*. At the front-end level, it is possible to filter the

• *DLED (delayed leading-edge discrimination) method* [44]. This method consists of subtracting

from the signal its delayed replica, creating some sort of high-pass filtering.

higher is the filtering effect on the signal [42].

trace showing the direct and delayed crosstalk and afterpulsing events (b).

signal to remove the slow tails of the signals.

one cell and the neighboring one.

**5.3. Front-end and read-out**

developed:

**Figure 8.** Representation of SiPM cross-section and of correlated noise source (a) [43] and typical oscilloscope persistence trace showing the direct and delayed crosstalk and afterpulsing events (b).

The integrated quenching resistor also reduces the amplitude of the *single-cell signal.* Considering the SiPM equivalent circuit, when the avalanche switch is closed, the bias at the internal node (between SPAD and quenching resistor) is lowered, discharging CD and CQ. Then, it is recharged through RQ. However, the detectable signal is only the current that flows through the anode and cathode pins of the SiPM. The SiPM signal is composed by a fast peak (capacitive coupling through CQ) and a slower component, due to the recharge current through RQ. Both are "filtered" by the presence of CGRID. The bigger the SiPM the larger is CGRID, thus the higher is the filtering effect on the signal [42].

PDE is one of the most important parameter for a SiPM. It has been significantly improved over the last years. One possible improvement is having the PDE spectrally peaked in the region of interest of the specific application, for example, in the blue or in the green wavelength region. An Examples are the RGB [25] and NUV [43] technologies from FBK, made with p-on-n junction or n-on-p junction type. Another improvement is the increment of the cell FF, which can be obtained reducing the *border region*, i.e., the not-sensitive region between one cell and the neighboring one.

#### **5.3. Front-end and read-out**

regards the time-of-flight (TOF) technique, which significantly improves image quality. In these applications, SiPMs are typically grouped in TILEs, to cover areas of few centimeters

SiPMs are also becoming an interesting choice in other applications based on single-photon or few-photon detection. For example: (i) light detection and ranging (LIDAR) [39], where many cells with good detection efficiency are highly desirable, (ii) optical spectroscopy [40], where high detection efficiency and big sensitive areas are very useful, (iii) fluorescence detection, (iv) flow cytometry, (v) Cherenkov detection for physics experiments [36],

Moving from a single SPAD to a silicon photomultiplier, there are some additional param-

• The *fill factor* of the cell has to be included in the photon detection efficiency (PDE) calculation. The cell FF is the ratio between the sensitive area and the total area of the cell. Nowa-

• *Optical crosstalk* between the cells is an additional source of correlated noise [43]. During the avalanche in one cell, not only the carriers can be trapped but also the secondary photons are produced [3]. Being emitted isotopically, some can reach the neighboring cells, triggering another spurious avalanche. They can be absorbed in the depleted region or in the neutral region. In the former case, there is a *direct crosstalk* (DiCT) (see **Figure 8**), giving an instantaneous triggering of the neighboring cell. In the latter case, the crosstalk event happen delayed in time (typically few nanoseconds or tens of nanoseconds), creating a *delayed crosstalk* (DeCT). The direct crosstalk produces a current pulse that has twice the amplitude

• Another source of correlated noise is the *diffused afterpulsing*, as shown in **Figure 8**. The secondary photon can be reabsorbed in the same cell, and the photo-generated carrier can diffuse and reach the depleted region with a certain delay, producing an afterpulsing. • An important parameter for SiPMs is the *gain* of the cell, i.e., the number of carriers produced in response to a single photo-generated carrier. The presence of an integrated resistor right above each cell reduces the amount of carriers flowing per each avalanche and reduces the amount of carriers flowing per each avalanche and makes this quantity well

• Finally, the *single-photon time resolution* (SPTR) [42] is important for SiPMs. Differently from SPAD, SPTR of analog SiPM is mainly limited by the effect of electronic noise from the front-end circuit and by the transit-time spread. The former is the effect of the baseline fluctuation due to the noise: given a limited signal slope, the baseline variation induces a threshold crossing time variation, thus worsening the time resolution. The latter is the effect

of different lengths of the path connecting the cells to the common PAD.

and 106

, similarly to a photomultiplier tubes.

squared. An example is shown in **Figure 7c**.

50 Photon Counting - Fundamentals and Applications

eters and other noise sources that have to be considered.

defined. The gain is typically between few 105

days, typical FF for analog SiPMs are between 40 and 80%.

etc.

**5.2. From SPAD to SiPM**

of a single-cell event.

The signal coming out from the SiPM is the superposition of many pulses, either in light or in dark. Depending on the application, it is possible to measure directly the current level produced by the SiPM, or count the avalanche pulses (photon-counting mode). If the count rate is low, the pulses are clearly distinguishable, but increasing the count rate, they start to overlap, making the counting more difficult. To avoid this situation, some techniques have been developed:

• At the device level, one producer added a third output, called *fast-output* [45]. In the SiPM, there is a capacitive pick-up in each microcell, connected between the internal nodes and a common output. This produces a faster signal which is used for timing purpose.

a good photon-number resolution. **Figure 9c** shows a typical charge spectrum obtained with

High Sensitivity Photodetector for Photon-Counting Applications

http://dx.doi.org/10.5772/intechopen.71940

53

The recent efforts to increase the PDE lead to an enhanced FF [48, 49, 54], meaning a smaller border region between cells. This gives a higher optical crosstalk. One efficient way to limit the correlated noise is to reduce the cell gain, giving a smaller amount of carriers flowing, thus smaller probability of trapping and emitting secondary photons. A lower gain can be obtained by means of small cells [54]. However, reducing the cell pitch normally means smaller FF, thus lower PDE. To have both smaller cells and a good PDE, the border structure of the cell

SiPM with small cells also have other advantages: a higher cell density and a shorter recovery time due to the smaller diode capacitance. Both these features increase the dynamic range of the SiPM, which for some applications is very important. Few examples are: (i) for calorimetry in high-energy physics experiments with high luminosity, (ii) in LIDAR and (iii) for prompt gamma imaging in proton therapy [55]. Short recovery time means reduced pile-up of the avalanche pulses, thus higher maximum count rate. Another interesting feature of SiPMs with small cell is their improved radiation hardness. The smaller is the cell size the lower is the performance degradation caused by the effects of radiations. Indeed, with a lower gain there is a smaller correlated noise, thus the noisy cells that have an increased primary dark count rate (DCR) due to radiation damage produce a lower number of correlated pulses, reducing the total overall DCR of the SiPM. With a lower total DCR and reduced gain, the SiPM has a smaller power consumption, even when damaged by radiation. Furthermore, due to the higher number of cells with a lower correlated noise, even after radiation damages there are a larger number of cells ready to be triggered by a light signal, thus a smaller PDE reduction.

One interesting example of SiPM with small cells is the so-called "high density" (HD) SiPM technology, developed in FBK [48, 54]. In HD technology, there are deep trenches (few micrometers deep), with high aspect ratio between the cells to electrically isolate them (as shown in **Figure 10**). The border region at the edge of each active area in the cells have been reduced to less than 2 μm, making possible to have a high FF of about 80% for a 30-μm cellpitch SiPM and more than 50% for a 12-μm cell-pitch SiPM. For the FBK previous non-HD technology, the FF was about 60% for a 40-μm pitch SiPM [41]. The gain decreases as the cell

SiPM, at 5 V of excess bias. Due to the small active area and the trench isolation, the direct crosstalk probability is around 9% for 15 μm cell-pitch SiPM, which have a FF of 62%, whereas it was about 35% for non-HD SiPM with 40 μm cell-pitch (FF of 60%). The PDE, in HD technology, with n-on-p junction is peaked at 550 nm, reaching values of ~40% at 4 V of excess bias, and ~50% at 10 V of excess bias, for the 30 μm pitch SiPM-HD, and 25% for the 12 μm

for the 30-μm pitch SiPM and 3 × 105

for the 12-μm pitch

a 40-μm cell-pitch SiPM [43].

**5.5. SiPM with small cells**

has to be redesigned [48].

*5.5.1. High density silicon photomultipliers*

pitch reduces: it is about 2.4 × 106

pitch SiPM-HD (see **Figure 10**).

Another problem is how to distinguish the primary events from the correlated noise. Direct crosstalk events are easily distinguishable: they produce pulses with higher amplitudes, but afterpulsing and delayed crosstalk events are mixed within the primary ones. One efficient way is to evaluate the inter-time between the events, with a method described in Ref. [46], and used in Ref. [47]. This method is based on the collection of a train of many events, filtering and peak-detection. For each event, the inter-time and the amplitude (normalized to single-cell amplitude) are extracted. Plotting the amplitude vs. inter-time and the histogram of the inter-times, it creates a plot like in **Figure 9(a)**. By fitting the events with high inter-times, with an exponential function, it is possible to identify and distinguish the primary events.

#### **5.4. SiPM performance**

The performance of SiPMs has been significantly improved over the last years [48–52]. Producers pushed the technology limits to obtain a higher PDE, now at levels of 50–60% (peak), with FF around 70–80%. In particular, some examples are: PDE of 34% at 400 nm, with 15 μm cell pitch [48], PDE of 49% at 420 nm, with cell size of 35 μm [51], PDE of 43% at 400 nm, with cell pitch of 25 μm [50], and PDE of 33% at 520 nm, with a cell pitch of 50 μm [52]. The primary noise has been reduced, being now at the level of 50–100 kcps/mm2 [48–52] at T = 20°C (see **Figure 9b**). The correlated noise has also been reduced due to: (i) an improvement in the silicon materials [43] and (ii) a better cell-to-cell isolation with trenches [46, 49, 53]. In particular, some examples are: CT probability of 10%, at 8 V of excess bias, with 15 μm cell pitch [48], which increases to 35%, with 7 V of excess bias when the cell pitch is 30 μm, or CT probability of just 3% in a 50 μm cell, with 3 V of excess bias, due to better cell isolation [49]. The reduction of the correlated noise and the uniformity of gain between cells give the SiPMs

**Figure 9.** Example of amplitude vs. inter-time plot (a) and of inter-time histogram (b) [46]. Typical primary dark count rate of a SiPM, at different temperatures (c) [43] and charge spectrum (d).

a good photon-number resolution. **Figure 9c** shows a typical charge spectrum obtained with a 40-μm cell-pitch SiPM [43].

#### **5.5. SiPM with small cells**

• At the device level, one producer added a third output, called *fast-output* [45]. In the SiPM, there is a capacitive pick-up in each microcell, connected between the internal nodes and a

Another problem is how to distinguish the primary events from the correlated noise. Direct crosstalk events are easily distinguishable: they produce pulses with higher amplitudes, but afterpulsing and delayed crosstalk events are mixed within the primary ones. One efficient way is to evaluate the inter-time between the events, with a method described in Ref. [46], and used in Ref. [47]. This method is based on the collection of a train of many events, filtering and peak-detection. For each event, the inter-time and the amplitude (normalized to single-cell amplitude) are extracted. Plotting the amplitude vs. inter-time and the histogram of the inter-times, it creates a plot like in **Figure 9(a)**. By fitting the events with high inter-times, with an exponential function, it is possible to identify and distinguish the

The performance of SiPMs has been significantly improved over the last years [48–52]. Producers pushed the technology limits to obtain a higher PDE, now at levels of 50–60% (peak), with FF around 70–80%. In particular, some examples are: PDE of 34% at 400 nm, with 15 μm cell pitch [48], PDE of 49% at 420 nm, with cell size of 35 μm [51], PDE of 43% at 400 nm, with cell pitch of 25 μm [50], and PDE of 33% at 520 nm, with a cell pitch of 50 μm

at T = 20°C (see **Figure 9b**). The correlated noise has also been reduced due to: (i) an improvement in the silicon materials [43] and (ii) a better cell-to-cell isolation with trenches [46, 49, 53]. In particular, some examples are: CT probability of 10%, at 8 V of excess bias, with 15 μm cell pitch [48], which increases to 35%, with 7 V of excess bias when the cell pitch is 30 μm, or CT probability of just 3% in a 50 μm cell, with 3 V of excess bias, due to better cell isolation [49]. The reduction of the correlated noise and the uniformity of gain between cells give the SiPMs

**Figure 9.** Example of amplitude vs. inter-time plot (a) and of inter-time histogram (b) [46]. Typical primary dark count

rate of a SiPM, at different temperatures (c) [43] and charge spectrum (d).

[48–52]

[52]. The primary noise has been reduced, being now at the level of 50–100 kcps/mm2

common output. This produces a faster signal which is used for timing purpose.

primary events.

**5.4. SiPM performance**

52 Photon Counting - Fundamentals and Applications

The recent efforts to increase the PDE lead to an enhanced FF [48, 49, 54], meaning a smaller border region between cells. This gives a higher optical crosstalk. One efficient way to limit the correlated noise is to reduce the cell gain, giving a smaller amount of carriers flowing, thus smaller probability of trapping and emitting secondary photons. A lower gain can be obtained by means of small cells [54]. However, reducing the cell pitch normally means smaller FF, thus lower PDE. To have both smaller cells and a good PDE, the border structure of the cell has to be redesigned [48].

SiPM with small cells also have other advantages: a higher cell density and a shorter recovery time due to the smaller diode capacitance. Both these features increase the dynamic range of the SiPM, which for some applications is very important. Few examples are: (i) for calorimetry in high-energy physics experiments with high luminosity, (ii) in LIDAR and (iii) for prompt gamma imaging in proton therapy [55]. Short recovery time means reduced pile-up of the avalanche pulses, thus higher maximum count rate. Another interesting feature of SiPMs with small cell is their improved radiation hardness. The smaller is the cell size the lower is the performance degradation caused by the effects of radiations. Indeed, with a lower gain there is a smaller correlated noise, thus the noisy cells that have an increased primary dark count rate (DCR) due to radiation damage produce a lower number of correlated pulses, reducing the total overall DCR of the SiPM. With a lower total DCR and reduced gain, the SiPM has a smaller power consumption, even when damaged by radiation. Furthermore, due to the higher number of cells with a lower correlated noise, even after radiation damages there are a larger number of cells ready to be triggered by a light signal, thus a smaller PDE reduction.

#### *5.5.1. High density silicon photomultipliers*

One interesting example of SiPM with small cells is the so-called "high density" (HD) SiPM technology, developed in FBK [48, 54]. In HD technology, there are deep trenches (few micrometers deep), with high aspect ratio between the cells to electrically isolate them (as shown in **Figure 10**). The border region at the edge of each active area in the cells have been reduced to less than 2 μm, making possible to have a high FF of about 80% for a 30-μm cellpitch SiPM and more than 50% for a 12-μm cell-pitch SiPM. For the FBK previous non-HD technology, the FF was about 60% for a 40-μm pitch SiPM [41]. The gain decreases as the cell pitch reduces: it is about 2.4 × 106 for the 30-μm pitch SiPM and 3 × 105 for the 12-μm pitch SiPM, at 5 V of excess bias. Due to the small active area and the trench isolation, the direct crosstalk probability is around 9% for 15 μm cell-pitch SiPM, which have a FF of 62%, whereas it was about 35% for non-HD SiPM with 40 μm cell-pitch (FF of 60%). The PDE, in HD technology, with n-on-p junction is peaked at 550 nm, reaching values of ~40% at 4 V of excess bias, and ~50% at 10 V of excess bias, for the 30 μm pitch SiPM-HD, and 25% for the 12 μm pitch SiPM-HD (see **Figure 10**).

performance of small cells, and it is more and more important as the cell pitch decreases. To reduce this issue, a new version of the cell has been designed, with modified doping profile. The new version has a wider high-field region and a reduced lateral depletion

**Figure 11.** SEM image of 10-μm cell ultra-high density SIPM (a), showing active areas, metal and polysilicon resistors. Nominal FF of UHD, HD and non-HD technologies from FBK (b). Typical single-cell signals of UHD SiPMs (c).

UHD SiPM with new structure have a higher PDE: an UHD SiPM with 7.5 μm pitch reaches a PDE of about 30% in the peak, with 6 V of excess bias at a wavelength of 470 nm, whereas a 10-μm pitch SiPM have a PDE peak of ~40% in the same conditions. SiPM with 5 μm cell pitch reaches a PDE higher than 15%. Due to the small cell capacitance, the signals from UHD SiPMs are very fast, in the order of few nanoseconds FWHM, as shown in **Figure 11**.

ture, it is higher. This is probably due to an increased electric field; but, this technology is relatively new and there is room for improvement. The gain of the cells, thus the crosstalk probability, is low (even without absorbing material in the trenches). In a 7.5 μm cell, the

**Figure 12.** TCAD simulations of electric fields inside a 10-μm pitch and a 7.5-μm pitch microcells of the ultra-high

, at 6 V of excess bias, and the direct crosstalk probability is smaller

High Sensitivity Photodetector for Photon-Counting Applications

http://dx.doi.org/10.5772/intechopen.71940

55

, but in the new struc-

The noise of UHD SiPM is generally in the order of 100 kcps/mm<sup>2</sup>

underneath the junction.

gain is about 2 × 105

density SiPMs, with depleted region highlighted.

than 5%.

**Figure 10.** Schematic representation of RGB-HD SiPM structure (a). SEM image of a 12-μm cell pitch SiPM with details of the single microcell (b). Measured performance of high density SiPMs: gain (c), direct crosstalk probability (d), and PDE vs. wavelength (e) of RGB-HD and one NUV-HD (e).

#### *5.5.2. Ultra-high density silicon photomultipliers*

The HD technology has been further improved developing the "ultra-high density" (UHD) technology [56]. UHD SiPMs have very small cells and high cell density. All the feature size of the manufacturing process have been reduced (e.g., contact dimension, resistor width, etc.). The cells have a circular active area, to avoid corners with smaller electric field, and they are arranged in a honeycomb configuration (see **Figure 11**). The border region is now less than 1 μm. UHD SiPMs have been produced with cell pitch between 5 μm and 12.5 μm. With a pitch of 5 μm, the FF is about 40%, and it is higher than 70% for the 12.5-μm cell-pitch SiPM. The cell density is between 7400 cell/mm2 and 46,190 cells/mm2 . Moreover, very small cells mean low gain, low correlated noise, and very fast recovery time.

The realization of very small cell sizes poses different challenges not only in the design and in the microfabrication process, but also due to intrinsic problems. The "border region" at the edge of the high-field region is no longer negligible but starts to play a very important role. **Figure 12** shows the TCAD simulation of electric field inside a 10 μm SiPM cell. The effective region, where the electric field is high, is smaller than the nominal one (defined by layout). Moreover, the depleted region close to the trench extends laterally toward the center of the cell. This makes the carriers photo-generated in that region to drift laterally toward the peripheral region, instead of drifting vertically, thus they are not detected. These effects are collectively called "border effect." This issue worsens the

**Figure 11.** SEM image of 10-μm cell ultra-high density SIPM (a), showing active areas, metal and polysilicon resistors. Nominal FF of UHD, HD and non-HD technologies from FBK (b). Typical single-cell signals of UHD SiPMs (c).

performance of small cells, and it is more and more important as the cell pitch decreases. To reduce this issue, a new version of the cell has been designed, with modified doping profile. The new version has a wider high-field region and a reduced lateral depletion underneath the junction.

UHD SiPM with new structure have a higher PDE: an UHD SiPM with 7.5 μm pitch reaches a PDE of about 30% in the peak, with 6 V of excess bias at a wavelength of 470 nm, whereas a 10-μm pitch SiPM have a PDE peak of ~40% in the same conditions. SiPM with 5 μm cell pitch reaches a PDE higher than 15%. Due to the small cell capacitance, the signals from UHD SiPMs are very fast, in the order of few nanoseconds FWHM, as shown in **Figure 11**. The noise of UHD SiPM is generally in the order of 100 kcps/mm<sup>2</sup> , but in the new structure, it is higher. This is probably due to an increased electric field; but, this technology is relatively new and there is room for improvement. The gain of the cells, thus the crosstalk probability, is low (even without absorbing material in the trenches). In a 7.5 μm cell, the gain is about 2 × 105 , at 6 V of excess bias, and the direct crosstalk probability is smaller than 5%.

*5.5.2. Ultra-high density silicon photomultipliers*

PDE vs. wavelength (e) of RGB-HD and one NUV-HD (e).

54 Photon Counting - Fundamentals and Applications

cells/mm2

recovery time.

The HD technology has been further improved developing the "ultra-high density" (UHD) technology [56]. UHD SiPMs have very small cells and high cell density. All the feature size of the manufacturing process have been reduced (e.g., contact dimension, resistor width, etc.). The cells have a circular active area, to avoid corners with smaller electric field, and they are arranged in a honeycomb configuration (see **Figure 11**). The border region is now less than 1 μm. UHD SiPMs have been produced with cell pitch between 5 μm and 12.5 μm. With a pitch of 5 μm, the FF is about 40%, and it is higher than

**Figure 10.** Schematic representation of RGB-HD SiPM structure (a). SEM image of a 12-μm cell pitch SiPM with details of the single microcell (b). Measured performance of high density SiPMs: gain (c), direct crosstalk probability (d), and

The realization of very small cell sizes poses different challenges not only in the design and in the microfabrication process, but also due to intrinsic problems. The "border region" at the edge of the high-field region is no longer negligible but starts to play a very important role. **Figure 12** shows the TCAD simulation of electric field inside a 10 μm SiPM cell. The effective region, where the electric field is high, is smaller than the nominal one (defined by layout). Moreover, the depleted region close to the trench extends laterally toward the center of the cell. This makes the carriers photo-generated in that region to drift laterally toward the peripheral region, instead of drifting vertically, thus they are not detected. These effects are collectively called "border effect." This issue worsens the

. Moreover, very small cells mean low gain, low correlated noise, and very fast

and 46,190

70% for the 12.5-μm cell-pitch SiPM. The cell density is between 7400 cell/mm2

**Figure 12.** TCAD simulations of electric fields inside a 10-μm pitch and a 7.5-μm pitch microcells of the ultra-high density SiPMs, with depleted region highlighted.

## **6. Conclusions**

We have reviewed some of the most interesting photodetectors technologies for photon counting. Solid-state solution, like single-photon avalanche diodes (SPADs), is able to reach high detection efficiencies and good time resolution, in the order of few tens of picoseconds. SPAD can be made in silicon or III/V materials, for the detection in the NIR wavelength range. Building a silicon SPAD in CMOS technology, it is possible to integrate some electronics into each pixel, to count the photons and to time-tag them. An array of such kind of SPAD pixels can be exploited to create low-light imagers. SPAD imagers are nowadays used in several biomedical applications (e.g., FLIM, Raman spectroscopy, etc.) and in 3D ranging. This technology is continuously evolving with a pixel density getting higher due to the CMOS technology development. Another interesting detector based on SPAD arrays is the silicon photomultiplier (SiPM). Here, all the SPADs are connected in parallel, in analog or digital way. It has single-photon sensitivity but, differently from single-SPADs, it is able to reach big active areas (few millimeters squared) and it is able to count the number of photons arriving simultaneously with good photon-number resolution. SiPM performance has been significantly improved over the last years, reaching a high FF and a high detection efficiency. This promising technology is now starting to be used not only in the typical applications (e.g., nuclear medicine and physics experiments) but also in biomedical and 3D ranging applications. SiPM technologies are evolving in the direction of smaller cells (SPADs), which is advantageous for SiPM performance, but it requires improvements in the manufacturing processes. For example, there are new technologies for SiPMs with cell-pitches smaller than 10 μm, down to 5 μm. This provides a higher cell density and a larger dynamic range. Some mixed solutions are also emerging, with imagers made by an array of many mini-SiPMs. This allows to have imaging capabilities but with a high dynamic range per pixel.

[2] Hamamatsu Photonics KK. R3809U-50 datasheet [Internet]. Available from: http://www.

High Sensitivity Photodetector for Photon-Counting Applications

http://dx.doi.org/10.5772/intechopen.71940

57

[3] Cova S, Ghioni M, Lacaita AL, Samori C, Zappa F. Avalanche photodiodes and quench-

[4] Bronzi D, Villa F, Tisa S, Tosi A, Zappa F, Durini D, Weyers S, Brockherde W. 100 000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging. IEEE

[5] Perenzoni M, Massari N, Perenzoni D, Gasparini L, Stoppa D. A 160 × 120 pixel analogcounting single-photon imager with time-gating and self-referenced column-parallel A/D conversion for fluorescence lifetime imaging. Journal of Solid State Circuit.

[6] Michalet X, Colyer RA, Scalia G, Ingargiola A, Lin R, Millaud JE, Weiss S, Siegmund OHW, Tremsin AS, Vallerga JV, Cheng A, Levi M, Aharoni D, Arisaka K, Villa F, Guerrieri F, Panzeri F, Rech I, Gulinatti A, Zappa F, Ghioni M, Cova S. Development of new photon-counting detectors for single-molecule fluorescence microscopy. Philosophical

[7] Jeon EJ, Kim JY, Kim YD, Ma KJ, Nam JT. Magnetic field effects on the photocathode uniformity of Hamamatsu R7081 photomultiplier tubes. Nuclear Instrument and Methods

[8] Sansoni L et al. A two-channel, spectrally degenerate polarization entangled source on

[9] Dauler EA, Stevens MJ, Baek B, Molnar RJ, Hamilton SA, Mirin RP, Nam SW, Berggren KK. Measuring intensity correlations with a two-element superconducting nanowire single-

[10] Marsili F, Verma VB, Stern JA, Harrington S, Lita AE, Gerrits T, Vayshenker I, Baek B, Shaw MD, Mirin RP, Nam SW. Detecting single infrared photons with 93% system efficiency. Nature Photonics Letters. 2013;**7**:210-214. DOI: 10.1038/NPHOTON.2013.13

[11] Redaelli L, Bulgarini G, Dobrovolskiy S, Dorenbos SN, Zwiller V, Monroy E, Gérard JM. Design of broadband high-efficiency superconducting-nanowire single photon detectors. Superconductor Science and Technology. 2016;**29**(6). DOI: 10.1088/0953-2048/

[12] Lita AE, Miller AJ, Nam SW. Counting near-infrared single-photons with 95% efficiency.

[13] Zhao Q-Y et al. Single-photon imager based on a superconducting nanowire delay line.

Nature Photonics. 2017;**11**:247-251. DOI: 10.1038/NPHOTON.2017.35

chip. NPJ Quantum Information. 2017;**3**(5). DOI: 10.1038/s41534-016-0005-z

hamamatsu.com/eu/en/product [Accessed: Sep 2017]

Transactions of the Royal Society B. 2012;**368**

photon detector. Physical Review A. 2008;**78**(5)

in Physics Research A. 2013;**697**:46-51

2016;**51**(1)

29/6/065016

Optics Express. 2008;**16**(5)

ing circuits for single photon-detection. Applied Optics. 1996;**32**(2)

Journal of Selected Topics in Quantum Electronics. 2014;**20**(6)

## **Author details**

Fabio Acerbi\* and Matteo Perenzoni

\*Address all correspondence to<EMAIL_ADDRESS>
Fondazione Bruno Kessler (FBK), Trento, Italy

## **References**

[1] Hamamatsu editor. Photomultiplier Tubes—Basics and Applications. 3rd ed. https:// www.hamamatsu.com/resources

[2] Hamamatsu Photonics KK. R3809U-50 datasheet [Internet]. Available from: http://www. hamamatsu.com/eu/en/product [Accessed: Sep 2017]

**6. Conclusions**

56 Photon Counting - Fundamentals and Applications

**Author details**

**References**

Fabio Acerbi\* and Matteo Perenzoni

\*Address all correspondence to<EMAIL_ADDRESS>
Fondazione Bruno Kessler (FBK), Trento, Italy

www.hamamatsu.com/resources

bilities but with a high dynamic range per pixel.

We have reviewed some of the most interesting photodetectors technologies for photon counting. Solid-state solution, like single-photon avalanche diodes (SPADs), is able to reach high detection efficiencies and good time resolution, in the order of few tens of picoseconds. SPAD can be made in silicon or III/V materials, for the detection in the NIR wavelength range. Building a silicon SPAD in CMOS technology, it is possible to integrate some electronics into each pixel, to count the photons and to time-tag them. An array of such kind of SPAD pixels can be exploited to create low-light imagers. SPAD imagers are nowadays used in several biomedical applications (e.g., FLIM, Raman spectroscopy, etc.) and in 3D ranging. This technology is continuously evolving with a pixel density getting higher due to the CMOS technology development. Another interesting detector based on SPAD arrays is the silicon photomultiplier (SiPM). Here, all the SPADs are connected in parallel, in analog or digital way. It has single-photon sensitivity but, differently from single-SPADs, it is able to reach big active areas (few millimeters squared) and it is able to count the number of photons arriving simultaneously with good photon-number resolution. SiPM performance has been significantly improved over the last years, reaching a high FF and a high detection efficiency. This promising technology is now starting to be used not only in the typical applications (e.g., nuclear medicine and physics experiments) but also in biomedical and 3D ranging applications. SiPM technologies are evolving in the direction of smaller cells (SPADs), which is advantageous for SiPM performance, but it requires improvements in the manufacturing processes. For example, there are new technologies for SiPMs with cell-pitches smaller than 10 μm, down to 5 μm. This provides a higher cell density and a larger dynamic range. Some mixed solutions are also emerging, with imagers made by an array of many mini-SiPMs. This allows to have imaging capa-

[1] Hamamatsu editor. Photomultiplier Tubes—Basics and Applications. 3rd ed. https://

[14] Gallivanoni A, Rech I, Ghioni M. Progress in quenching circuits for single photon avalanche diodes. IEEE Transaction on Nuclear Science. 2010;**57**(6):3815-3826

[27] Villa F et al. CMOS imager with 1024 SPADs and TDCs for single-photon timing and 3-D time-of-flight. IEEE Journal of Selected Topics in Quantum Electronics. 2014;**20**(6). DOI:

High Sensitivity Photodetector for Photon-Counting Applications

http://dx.doi.org/10.5772/intechopen.71940

59

[28] Pancheri L, Massari N, Stoppa D. SPAD image sensor with analog counting pixel for time-resolved fluorescence detection. IEEE Transactions on Electron Devices. 2013;

[29] Stoppa D, et al. A 32 × 32-pixel array with in-pixel photon counting and arrival time measurement in the analog domain. In: Proc. of ESSCIRC 2009; Athens, Greece. 2009 [30] Parmesan L, et al. A 256 × 256 SPAD array with in-pixel time to amplitude conversion for fluorescence lifetime imaging microscopy. In: Proc. of the international Image Workshop

[31] Fossum ER. The quanta image sensor: every photon counts. Sensors. 2016;**16**:1260. DOI:

[32] Renker D. Geiger-mode avalanche photodiodes history, properties and problems.

[33] Sefkow F. The CALICE tile hadron calorimeter prototype with SiPM read-out: Design, construction and first test beam results. In: IEEE, editor. Nuclear Science Symposium Conference Record, 2007. NSS '07; 26 Oct–3 Nov 2007; 2007. DOI: 0.1109/NSSMIC.

[34] Berra A, et al. Shashlink calorimeters with embedded SiPMs for longitudinal segmenta-

[35] Townsted DW. Multimodality imaging of structure and function. Physics in Medicine

[36] Gamal A, Paul B, Michael C, Roland H, Johann M, Herbert O, Ken S. Application of Geiger-mode photosensors in Cherenkov detectors. Nuclear Instruments and Methods

[37] Gundacker S, Auffray E, Jarron P, Meyer T, Lecoq P. On the comparison of analog and digital SiPM readout in terms of expected timing performance. Nuclear Instruments and

[38] Braga LHC et al. A fully digital 8 16 SiPM Array for PET applications with per-pixel TDCs and real-time energy output. IEEE Journal of Solid-State Circuits. 2014;**49**(1):

[39] Son KT, Lee CC. Multiple-target laser range finding receiver using a silicon photomultiplier array. IEEE Transactions on Instrumentation and Measurement. 2010;**59**:

[40] Dalla Mora A et al. Fast silicon photomultiplier improves signal harvesting and reduces

complexity in time domain diffuse optics. Optics Express. 2015;**23**(11)

10.1109/JSTQE.2014.2342197

2015; Vaals, The Nederlands. 2015

Nuclear Instruments and Methods A. 2006;**567**:48-56

tions. IEEE Transaction on Nuclear Science. 2017;**64**(4)

in Physics Research Section A. 2011;**639**(1):107-110

Methods in Physics Research A. 2015;**787**:6-11

**60**(10):3442-3449

10.3390/s16081260

2007.4436327

301-314

3005-3011

and Biology. 2008;**53**:R1-R39

[27] Villa F et al. CMOS imager with 1024 SPADs and TDCs for single-photon timing and 3-D time-of-flight. IEEE Journal of Selected Topics in Quantum Electronics. 2014;**20**(6). DOI: 10.1109/JSTQE.2014.2342197

[14] Gallivanoni A, Rech I, Ghioni M. Progress in quenching circuits for single photon ava-

[15] Ghioni M, Gulinatti A, Rech I, Zappa F, Cova S. Progress in silicon single-photon avalanche diodes. IEEE Journal of Selected Topics in Quantum Electronics. 2007;**13**(4):

[16] Contini D et al. Effects of time-gated detection in diffuse optical imaging at short sourcedetector separation. Journal of Physics D: Applied Physics. 2015;**48**. DOI: 10.1088/0022-

[17] Acerbi F, Anti M, Tosi A, Zappa F. Design criteria for InGaAs/InP single-photon avalanche

[18] Zhang J, Itzler MA, Zbinden H, Pan J-w. Advances in InGaAs/InP single-photon detector systems dor quantum communications. Light: Science & Applications. 2015;**4**(e286).

[19] Meng X et al. InGaAs/InAlAs single photon avalanche diode for 1550 nm photons. Royal

[20] Jiang X, Itzler MA, Ben-Michael R, Slomkowski K. InGaAsP–InP avalanche photodiodes for single photon detection. IEEE Journal of Selected Topics in Quantum Electronics.

[21] Acerbi F, Frera AD, Tosi A, Zappa F. Fast active quenching circuit for reducing avalanche charge and afterpulsing in InGaAs/InP single-photon avalanche diode. IEEE Journal of Quantum Electronics. 2013;**49**(7):563-569. DOI: 10.1109/JQE.2013.

[22] Wang XF, Periasamy A, Herman B, Coleman DM. Fluorescence lifetime imaging microscopy (FLIM): Instrumentation and application. Critical Reviews in Analytical Chemistry.

[23] Michalet X et al. Development of new photon-counting detectors for single-molecule fluorescence microscopy. Philosophical Transactions of the Royal Society B: Biological

[24] Micro photon devices. InGaAs SPAD freerunning datasheet [Internet]. Available from: www.micro-photon-devices.com/Docs/Datasheet/InGaAs\_Datasheet\_freerunning.pdf

[25] Serra N, Ferri A, Gola A, Pro T, Tarolli A, Zorzi N, Piemonte C. Characterization of new FBK SiPM technology for visible light detection. Journal of Instrumentation. 2013;**8**(P03019).

[26] Remondino F, Stoppa D. TOF Range-Imaging Cameras. Heidelberg, Germany: Springer;

Society Open Science. 2016;**3**(3):150584. DOI: 10.1098/rsos.150584

2007;**13**(4):895-905. DOI: 10.1109/JSTQE.2007.903001

Sciences. 2013;**368**(1611). DOI: 10.1098/rstb.2012.0035

lanche diodes. IEEE Transaction on Nuclear Science. 2010;**57**(6):3815-3826

852-862

2260726

1992;**23**(5):369-395

[Accessed: Sep. 2017]

2013

DOI: 10.1088/1748-0221/8/03/P03019

3727/48/4/045401

58 Photon Counting - Fundamentals and Applications

DOI: 10.1038/lsa.2015.59

diode. IEEE Photonics Journal. 2013;**5**:6800209

[41] Seifert S et al. Simulation of silicon photomultiplier signals. IEEE Transaction on Nuclear Scince. 2009;**56**(6):3726-3733

[55] Regazzoni V et al. Characterization of high density SiPM non-linearity and energy resolution for prompt gamma imaging applications. Journal of Instrumentation. 2017;**12**

High Sensitivity Photodetector for Photon-Counting Applications

http://dx.doi.org/10.5772/intechopen.71940

61

[56] Acerbi F et al. High efficiency, ultra high-density silicon photomultipliers. IEEE Journal

of Selected Topics in Quantum Electronics; March-April 2018;**24**(2)

(P07001)

[55] Regazzoni V et al. Characterization of high density SiPM non-linearity and energy resolution for prompt gamma imaging applications. Journal of Instrumentation. 2017;**12** (P07001)

[41] Seifert S et al. Simulation of silicon photomultiplier signals. IEEE Transaction on Nuclear

[42] Acerbi F et al. Characterization of single-photon time resolution: From single SPAD to silicon photomultiplier. IEEE Transaction on Nuclear Science. 2014;**61**(5):2678-2686. DOI:

[43] Acerbi F et al. NUV silicon photomultipliers with high detection efficiency and reduced delayed correlated-noise. IEEE Transaction on Nuclear Science. 2015;**62**(3):

[44] Gola A, Piemonte C, Tarolli A. The DLED algorithm for timing measurements on large area SiPMs coupled to scintillators. IEEE Transactions on Nuclear Science. 2012;

[45] Yeom JY et al. Fast timing silicon photomultipliers for scintillation detectors. IEEE

[46] Piemonte C, et al. Development of an automatic procedure for the characterization of silicon photomultipliers. In: Nuclear Science Symposium and Medical Imaging Conference

[47] Otte AN, Garcia D, Nguyen T, Purushotham D. Characterization of three high efficiency and blue sensitive silicon photomultipliers. Nuclear Instruments and Methods in

[48] Piemonte C et al. Performance of NUV-HD silicon photomultiplier technology. IEEE

[49] Hamamatsu. MPPC (Multi-Pixel Photon Counters)—S13360 Series [Internet]. Available

[50] Ketek. SiPM WB Series [Internet]. Available from: https://www.ketek.net/sipm/sipm-

[51] SensL. J-Series Family [Internet]. Available from: http://sensl.com/products/j-series/

[52] Excelitas. C30742-11 Series [Internet]. Available from: http://www.excelitas.com/

[53] Sul W-S, Lee C-H, Cho G-S. Influence of guard-ring structure on the dark count rates of silicon photomultipliers. IEEE Electron Device Letters. 2013;**34**(3):336-338. DOI: 10.1109/

[54] Piemonte C et al. Characterization of the first FBK high-density cell silicon photomultiplier technology. IEEE Transactions on Electron Devices. 2013;**60**(8):2567-2573

Downloads/DTS\_C30742-11-050\_Series\_SiPM.pdf [Accessed: Sep. 2017]

Photonics Technology Letters. 2013;**25**(15):1309-1312

Transaction on Electron Devices. 2016;**63**(3):1111-1116

from: www.hamamatsu.com/resources [Accessed: Sep. 2017]

(NSS/MIC), 2012 IEEE; 27 Oct-3 Nov 2012

products/wb-series/ [Accessed: Sep. 2017]

[Accessed: Sep. 2017]

LED.2012.2236296

Physics Research A. 2017;**846**:106-125

Scince. 2009;**56**(6):3726-3733

60 Photon Counting - Fundamentals and Applications

10.1109/TNS.2014.2347131

1318-1325

**59**(2):358-365

[56] Acerbi F et al. High efficiency, ultra high-density silicon photomultipliers. IEEE Journal of Selected Topics in Quantum Electronics; March-April 2018;**24**(2)

**Section 2**

**Fundamentals**

**Section 2**

## **Fundamentals**

**Chapter 3**

Provisional chapter

**Quantum Non-Demolition Measurement of Photons**

DOI: 10.5772/intechopen.72871

According to Heisenberg's uncertainty principle, measurement of a quantum observable introduces noise to this observable and thus limits the available precision of measurement. Quantum non-demolition measurements are designed to circumvent this limitation and have been demonstrated in detecting the photon flux of classical light beam. Quantum non-demolition measurement of a single photon is the ultimate goal because it is of great interest in fundamental physics and also a powerful tool for applications in quantum information processing. This chapter presents a brief introduction of the history and a review of the progress in quantum non-demolition measurement of light. In particular, a detailed description is presented for two works toward cavity-free schemes of quantum non-demolition measurement of single photons. Afterward, an outlook of

Keywords: QND measurement, single photon, four-wave mixing, Rabi oscillation

Measurement of observables is at the very heart of quantum measurement. In the classical macroscopic world, measurement of a classical object can be conducted without introducing perturbation to the detected object. Repeating measurement of a classical object can improve the precision to arbitrarily accurate. Counterintuitively, the measurement of an observable of a quantum object cannot be arbitrarily precise in the microscopic world according to the well-known Heisenberg's uncertainty principle [1], which roots in the wave nature of quantum mechanics. For non-commuting operators, A and B, described as physical quantities in the quantum formalism, a very precise measurement of A, resulting in a very small uncertainty ΔA, will be associated with a large value of uncertainty, ΔB, in B. Measuring a quantum object will inevitably cause perturbation in the measured object. This perturbation due to measurement is called as the "measurement back action." This quantum back action, in turn, enlarges uncertainty of the observables. As a result, it limits the available precision in a series of repeated measurements. Then a natural question is what is the limitation of sensitivity in measurement set by quantum mechanics.

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. What is quantum non-demolition measurement?

Quantum Non-Demolition Measurement of Photons

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72871

the future in this direction is given.

Keyu Xia

Keyu Xia

Abstract

#### **Quantum Non-Demolition Measurement of Photons** Quantum Non-Demolition Measurement of Photons

DOI: 10.5772/intechopen.72871

#### Keyu Xia Keyu Xia

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72871

#### Abstract

According to Heisenberg's uncertainty principle, measurement of a quantum observable introduces noise to this observable and thus limits the available precision of measurement. Quantum non-demolition measurements are designed to circumvent this limitation and have been demonstrated in detecting the photon flux of classical light beam. Quantum non-demolition measurement of a single photon is the ultimate goal because it is of great interest in fundamental physics and also a powerful tool for applications in quantum information processing. This chapter presents a brief introduction of the history and a review of the progress in quantum non-demolition measurement of light. In particular, a detailed description is presented for two works toward cavity-free schemes of quantum non-demolition measurement of single photons. Afterward, an outlook of the future in this direction is given.

Keywords: QND measurement, single photon, four-wave mixing, Rabi oscillation

#### 1. What is quantum non-demolition measurement?

Measurement of observables is at the very heart of quantum measurement. In the classical macroscopic world, measurement of a classical object can be conducted without introducing perturbation to the detected object. Repeating measurement of a classical object can improve the precision to arbitrarily accurate. Counterintuitively, the measurement of an observable of a quantum object cannot be arbitrarily precise in the microscopic world according to the well-known Heisenberg's uncertainty principle [1], which roots in the wave nature of quantum mechanics. For non-commuting operators, A and B, described as physical quantities in the quantum formalism, a very precise measurement of A, resulting in a very small uncertainty ΔA, will be associated with a large value of uncertainty, ΔB, in B. Measuring a quantum object will inevitably cause perturbation in the measured object. This perturbation due to measurement is called as the "measurement back action." This quantum back action, in turn, enlarges uncertainty of the observables. As a result, it limits the available precision in a series of repeated measurements. Then a natural question is what is the limitation of sensitivity in measurement set by quantum mechanics.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

distribution, and eproduction in any medium, provided the original work is properly cited.

In response to this question, Braginsky and Vorontsov introduced in the 1970s the concept of "quantum non-demolition measurement" (QND) to evade the unwanted quantum back action in measurement [2]. Through studying the detectable minimum force on a quantum oscillator, they concluded that "Nondestructive recording of the n-quantum state of an oscillator is possible in principle." Their measurement strategy opened a door for circumventing the issue of back action in quantum measurement. Thorne, Drever, Caves, Zimmermann, Sandberg, Unruh, and others developed the concept of QND measurement further [3–5]. The key point in the QND measurement is to keep the back-action noise confined to the unwanted observable quadrature, without being coupled back onto the quantity to be measured.

Although a great number of efforts have been made in various systems, quantum optics is particularly well suited for implementing QND measurement. The reason is threefold: (1) there are optical sources with very good quality; (2) photon detectors can be extremely sensitive, even being able to detect a single photon; and (3) a quantum system can be initialized with very high accuracy. The photon number and phase are two complementary observables of quantum light. They are associated with non-commuting operators. It means that QND measurement of photon number of a quantum field will inevitably add quantum noise to the phase quadrature. If only, in principle, the photon number of field remains unchanged during measurement, the measurement is QND. Of course, the real implementation of experiment may be imperfect, and this imperfection can cause noise to the variable of interest.

converting these light impulses to signals which can be recognized by the optic nerve. In doing

Quantum Non-Demolition Measurement of Photons http://dx.doi.org/10.5772/intechopen.72871 67

Semiconductor photon detector is a sensitive man-made photodetector, which is made by using semiconductor materials. Two principal classes of semiconductor photodetectors are in common use: thermal detectors and photoelectric detectors. Thermal detectors convert photon energy into heat. Most thermal detectors are rather inefficient and relatively slow. Therefore, photoelectric detectors are widely used for optics. The operation of photoelectric detectors is based on the photoeffect. Similar to eyes, the detector absorbs photons from light, generating electronic current pulse which can be measured. The semiconductor photon detector is the most used photodetector in industry. The most common semiconductor-based devices are single-photon avalanche diode (SPAD) detectors and can reach sensitivity at the single photon level. The SPAD detector is reversely biased above the avalanche breakdown voltage in the Geiger mode. When a photon is captured by this SPAD detector, the absorbed photon generates an electron-hole pair which causes a self-sustaining avalanche, rapidly generating a

Figure 2. Schematic diagram for semiconductor photon detectors (from www.single-photon.com).

so, eyes convert light into bioelectric signals.

Figure 1. Sketch for seeing photons with eyes (from www.nkcf.org).

measurable current pulse (Figure 2).

Throughout this chapter, we focus on the measurement of light according to the principle of quantum optics. In particular, we introduce the measurement of photon number of a light beam. In the conventional "direct" measurement, the light is absorbed. Therefore, the measurement completely changes the observable of photon number and causes a very large back action onto the light beam. In a QND measurement of photon number, it is required that the amount of photon number is measured without changing. Of course, the measurement still adds perturbation to the light. However, the perturbation is only confined to the phase of the photon but is not added to the photon flux of interest in measurement. In a restricted mathematical language, the condition for QND measurement is that h i As <sup>i</sup> <sup>¼</sup> h i As <sup>i</sup>þ<sup>1</sup> and h i <sup>Δ</sup>As <sup>i</sup> <sup>¼</sup> h i <sup>Δ</sup>As <sup>i</sup>þ<sup>1</sup> for two successive detections of observable As.

#### 2. Classical measurement by absorbing photons

In the classical world, measurement of light always absorbs photons and then gets energy from them. In this way, the photon carried by a light beam disappears and is destroyed completely. This type of photon detector includes eyes, photoelectric converter, semiconductor photon detector, superconducting photon detector, and so on.

Eyes are photon detectors we use most often (Figure 1). It converts the energy of light into electric current and stimulates the nerve. Photons of light enter the eye through the cornea, that is the clear front "window" of the eye. Then light is bent by the cornea, passes freely through the pupil, the opening in the center of the iris, the eye's natural crystalline lens, and then is focused into a sharp point on the retina. The retina is responsible for capturing all of the light rays, processing them into light impulses through millions of tiny eye nerve endings, and then

Figure 1. Sketch for seeing photons with eyes (from www.nkcf.org).

In response to this question, Braginsky and Vorontsov introduced in the 1970s the concept of "quantum non-demolition measurement" (QND) to evade the unwanted quantum back action in measurement [2]. Through studying the detectable minimum force on a quantum oscillator, they concluded that "Nondestructive recording of the n-quantum state of an oscillator is possible in principle." Their measurement strategy opened a door for circumventing the issue of back action in quantum measurement. Thorne, Drever, Caves, Zimmermann, Sandberg, Unruh, and others developed the concept of QND measurement further [3–5]. The key point in the QND measurement is to keep the back-action noise confined to the unwanted observ-

Although a great number of efforts have been made in various systems, quantum optics is particularly well suited for implementing QND measurement. The reason is threefold: (1) there are optical sources with very good quality; (2) photon detectors can be extremely sensitive, even being able to detect a single photon; and (3) a quantum system can be initialized with very high accuracy. The photon number and phase are two complementary observables of quantum light. They are associated with non-commuting operators. It means that QND measurement of photon number of a quantum field will inevitably add quantum noise to the phase quadrature. If only, in principle, the photon number of field remains unchanged during measurement, the measurement is QND. Of course, the real implementation of experiment

Throughout this chapter, we focus on the measurement of light according to the principle of quantum optics. In particular, we introduce the measurement of photon number of a light beam. In the conventional "direct" measurement, the light is absorbed. Therefore, the measurement completely changes the observable of photon number and causes a very large back action onto the light beam. In a QND measurement of photon number, it is required that the amount of photon number is measured without changing. Of course, the measurement still adds perturbation to the light. However, the perturbation is only confined to the phase of the photon but is not added to the photon flux of interest in measurement. In a restricted mathematical language, the condition for QND measurement is that h i As <sup>i</sup> <sup>¼</sup> h i As <sup>i</sup>þ<sup>1</sup> and h i <sup>Δ</sup>As <sup>i</sup> <sup>¼</sup> h i <sup>Δ</sup>As <sup>i</sup>þ<sup>1</sup>

In the classical world, measurement of light always absorbs photons and then gets energy from them. In this way, the photon carried by a light beam disappears and is destroyed completely. This type of photon detector includes eyes, photoelectric converter, semiconductor

Eyes are photon detectors we use most often (Figure 1). It converts the energy of light into electric current and stimulates the nerve. Photons of light enter the eye through the cornea, that is the clear front "window" of the eye. Then light is bent by the cornea, passes freely through the pupil, the opening in the center of the iris, the eye's natural crystalline lens, and then is focused into a sharp point on the retina. The retina is responsible for capturing all of the light rays, processing them into light impulses through millions of tiny eye nerve endings, and then

able quadrature, without being coupled back onto the quantity to be measured.

may be imperfect, and this imperfection can cause noise to the variable of interest.

for two successive detections of observable As.

66 Photon Counting - Fundamentals and Applications

2. Classical measurement by absorbing photons

photon detector, superconducting photon detector, and so on.

converting these light impulses to signals which can be recognized by the optic nerve. In doing so, eyes convert light into bioelectric signals.

Semiconductor photon detector is a sensitive man-made photodetector, which is made by using semiconductor materials. Two principal classes of semiconductor photodetectors are in common use: thermal detectors and photoelectric detectors. Thermal detectors convert photon energy into heat. Most thermal detectors are rather inefficient and relatively slow. Therefore, photoelectric detectors are widely used for optics. The operation of photoelectric detectors is based on the photoeffect. Similar to eyes, the detector absorbs photons from light, generating electronic current pulse which can be measured. The semiconductor photon detector is the most used photodetector in industry. The most common semiconductor-based devices are single-photon avalanche diode (SPAD) detectors and can reach sensitivity at the single photon level. The SPAD detector is reversely biased above the avalanche breakdown voltage in the Geiger mode. When a photon is captured by this SPAD detector, the absorbed photon generates an electron-hole pair which causes a self-sustaining avalanche, rapidly generating a measurable current pulse (Figure 2).

Figure 2. Schematic diagram for semiconductor photon detectors (from www.single-photon.com).

Superconducting nanowires have been used to detect single photons. It exploits a different principle in comparison with eyes and semiconductor photon detectors. It is designed in this way [6, 7]: a patterned superconducting nanowire is cooled below the transition temperature of the superconducting material. The superconducting nanowire is biased by an external current slightly smaller than the critical current at the operating temperature. When a single photon hits the nanowire, it creates a transient normal spot in the resistive state. As a result of loss of superconductivity, a nonzero voltage is induced between two terminals of the nanowire. Measuring this induced voltage can tell the arrival of the single photon. To date, superconducting single photon detectors have achieved a detection efficiency of more than 90% [8, 9].

The abovementioned are three representatives of photon detectors. All of them destroy photons in signals.

#### 3. Measuring light intensity without absorption

QND measurement of light needs to keep the quantum average of the observable and its uncertainty unchanged after detection. In general quantum measurement, the observable of a signal system, As, is measured by detecting the change of observable, Am, of a "meter" system. The concept can be explained by describing the measurement as a joint Hamiltonian [10]

$$H = H\_s + H\_M + H\_{I\prime} \tag{1}$$

length L. Due to the cross-Kerr optical nonlinearity, the refractive index of medium is dependent on the intensity, Is ∝ ns, of the signal field. Its change is proportional to ns and subse-

Δf<sup>M</sup> is proportional to the photon number of signal field. Measuring Δf<sup>M</sup> can determine the

The concept of QND measurement based on the cross-Kerr effect has been demonstrated in experiments for classical light including many photons [12]. However, QND measurement at the single photon level is still a challenging problem. The difficulty is twofold. Technically, the nonlinearity of normal materials is too weak to induce a large phase shift per photon. Although the cross-Kerr nonlinearity can be improved by orders by using atom system, typically, a single photon can only cause an mrad scale phase shift [13]. It is worth noting two recent experiments in cross-phase modulation [14, 15], which demonstrated the pi phase shift at the single photon level via the cross-Kerr nonlinearity of atoms. At first sight, the methods may be able to apply to QND measurement of single photons. Actually, they are yet to meet

In the first work [14], by storing a single photon in a cloud of Rydberg atoms, Tiarks et al. achieved a π phase shift imprinted onto a probe field including only 0.9 photon. However, the efficiency of storing and retrieving signal photon is very low, that is only 0.2. The signal photon suffers a big loss and has a small possibility to survive after inducing the phase shift. In this,

Alternatively, Liu et al. used a double-Λ system to induce a giant cross-Kerr nonlinearity to achieve the π phase shift per photon [15]. In their configuration, the signal and the probe fields, each including eight photons, share a common ground state, while they couple to their individual dark states created by other two control fields. As a result, a giant cross-Kerr nonlinearity between them is created. A π cross-phase shift is induced at the single photon level. However, the reported scheme is still classical but has yet to reach the quantum regime

Figure 3. Configuration for the QND measurement of the signal photon number via cross-Kerr nonlinearity [10].

this scheme cannot be used for QND measurement of single photons.

<sup>M</sup> � fM, to the probe field. Obviously, this phase shift

Quantum Non-Demolition Measurement of Photons http://dx.doi.org/10.5772/intechopen.72871 69

quently causes a phase shift, Δf<sup>M</sup> ¼ f<sup>0</sup>

the criteria of QND measurement.

intensity of the signal field without absorbing its photon.

where Hs is the unperturbed Hamiltonian of the signal system to be measured, HM is that of the meter system, and HI describes the way in which the meter measures the signal. The motion for As and AM under measurement is

$$-i\hbar \frac{dA\_s}{dt} = [H\_s, A\_s] + [H\_I, A\_s]\_\prime \tag{2}$$

$$-i\hbar \frac{dA\_M}{dt} = [H\_s, A\_M] + [H\_I, A\_M]. \tag{3}$$

QND measurement requires (i) Hs; As ½ �¼ 0, which is normally satisfied; (ii) HI; As ½ �¼ 0; and (iii) HI ½ � ; AM 6¼ 0. The second condition guarantees that the back action is isolated from As. The third one implies that a measurement can induce change in the meter system.

It is quite straightforward to get the cross-Kerr effect in mind for QND measurement of photon flux, ns <sup>¼</sup> <sup>A</sup>† <sup>s</sup>As, of light beam [10, 11]. The Hamiltonian describing the cross-Kerr interaction is as follows:

$$H\_I = \chi A\_s^\dagger A\_s A\_M^\dagger A\_{M\nu} \tag{4}$$

where χ is the strength of nonlinear interaction. Obviously, HI; As ½ �¼ 0 is met.

The condition HI ½ � ; AM 6¼ 0 holds if the phase of probe field is measured. The intuitive picture of QND measurement of photon flux, ns, with the cross-Kerr effect can be well explained in Figure 3. The signal and probe laser fields co-propagate in a Kerr nonlinear medium with length L. Due to the cross-Kerr optical nonlinearity, the refractive index of medium is dependent on the intensity, Is ∝ ns, of the signal field. Its change is proportional to ns and subsequently causes a phase shift, Δf<sup>M</sup> ¼ f<sup>0</sup> <sup>M</sup> � fM, to the probe field. Obviously, this phase shift Δf<sup>M</sup> is proportional to the photon number of signal field. Measuring Δf<sup>M</sup> can determine the intensity of the signal field without absorbing its photon.

Superconducting nanowires have been used to detect single photons. It exploits a different principle in comparison with eyes and semiconductor photon detectors. It is designed in this way [6, 7]: a patterned superconducting nanowire is cooled below the transition temperature of the superconducting material. The superconducting nanowire is biased by an external current slightly smaller than the critical current at the operating temperature. When a single photon hits the nanowire, it creates a transient normal spot in the resistive state. As a result of loss of superconductivity, a nonzero voltage is induced between two terminals of the nanowire. Measuring this induced voltage can tell the arrival of the single photon. To date, superconducting

The abovementioned are three representatives of photon detectors. All of them destroy pho-

QND measurement of light needs to keep the quantum average of the observable and its uncertainty unchanged after detection. In general quantum measurement, the observable of a signal system, As, is measured by detecting the change of observable, Am, of a "meter" system. The concept can be explained by describing the measurement as a joint Hamiltonian [10]

where Hs is the unperturbed Hamiltonian of the signal system to be measured, HM is that of the meter system, and HI describes the way in which the meter measures the signal. The

QND measurement requires (i) Hs; As ½ �¼ 0, which is normally satisfied; (ii) HI; As ½ �¼ 0; and (iii) HI ½ � ; AM 6¼ 0. The second condition guarantees that the back action is isolated from As. The

It is quite straightforward to get the cross-Kerr effect in mind for QND measurement of photon

sAsA†

The condition HI ½ � ; AM 6¼ 0 holds if the phase of probe field is measured. The intuitive picture of QND measurement of photon flux, ns, with the cross-Kerr effect can be well explained in Figure 3. The signal and probe laser fields co-propagate in a Kerr nonlinear medium with

<sup>s</sup>As, of light beam [10, 11]. The Hamiltonian describing the cross-Kerr interaction is

�i<sup>ℏ</sup> dAs

�i<sup>ℏ</sup> dAM

third one implies that a measurement can induce change in the meter system.

HI <sup>¼</sup> <sup>χ</sup>A†

where χ is the strength of nonlinear interaction. Obviously, HI; As ½ �¼ 0 is met.

H ¼ Hs þ HM þ HI, (1)

dt <sup>¼</sup> Hs; As ½ �þ HI; As ½ �, (2)

dt <sup>¼</sup> Hs ½ �þ ; AM HI ½ � ; AM : (3)

<sup>M</sup>AM, (4)

single photon detectors have achieved a detection efficiency of more than 90% [8, 9].

3. Measuring light intensity without absorption

motion for As and AM under measurement is

tons in signals.

68 Photon Counting - Fundamentals and Applications

flux, ns <sup>¼</sup> <sup>A</sup>†

as follows:

The concept of QND measurement based on the cross-Kerr effect has been demonstrated in experiments for classical light including many photons [12]. However, QND measurement at the single photon level is still a challenging problem. The difficulty is twofold. Technically, the nonlinearity of normal materials is too weak to induce a large phase shift per photon. Although the cross-Kerr nonlinearity can be improved by orders by using atom system, typically, a single photon can only cause an mrad scale phase shift [13]. It is worth noting two recent experiments in cross-phase modulation [14, 15], which demonstrated the pi phase shift at the single photon level via the cross-Kerr nonlinearity of atoms. At first sight, the methods may be able to apply to QND measurement of single photons. Actually, they are yet to meet the criteria of QND measurement.

In the first work [14], by storing a single photon in a cloud of Rydberg atoms, Tiarks et al. achieved a π phase shift imprinted onto a probe field including only 0.9 photon. However, the efficiency of storing and retrieving signal photon is very low, that is only 0.2. The signal photon suffers a big loss and has a small possibility to survive after inducing the phase shift. In this, this scheme cannot be used for QND measurement of single photons.

Alternatively, Liu et al. used a double-Λ system to induce a giant cross-Kerr nonlinearity to achieve the π phase shift per photon [15]. In their configuration, the signal and the probe fields, each including eight photons, share a common ground state, while they couple to their individual dark states created by other two control fields. As a result, a giant cross-Kerr nonlinearity between them is created. A π cross-phase shift is induced at the single photon level. However, the reported scheme is still classical but has yet to reach the quantum regime

Figure 3. Configuration for the QND measurement of the signal photon number via cross-Kerr nonlinearity [10].

for detecting a single photon in a QND way. There are two prerequisites in this scheme. First, to ensure the atoms are transparent, the probe field needs to be known. Other than the optimal phase, the absorption is considerable. But this phase is unknown for a signal photon to be detected. It means a large loss for the signal photon to be detected. Second, the phase shift is obtained in the steady state where the probe field is classically treated as a constant field. This is not the case for a single photon as it is a quantum field. Therefore, it is hard to do genuine QND measurement at the single photon level.

with jgi \$ jei. It is designed to cause a full Rabi oscillation if the cavity includes one photon and results in a π phase shift to jgi yielding �Cg gi þ Ci j jii. While in the empty-cavity case, the atomic state is unchanged. In short, the atomic coherent changes its phase by π if there is one photon in C. R2 mixes the atomic state again, probing after C the superposition phase shift. The final atomic population can be detected with a state-selective detector. The probability of finding the atom in jgi is a cosine function of the phase shift and thus gives information about the phase shift. In this way, Haroche et al. implemented the QND measurement of a single mw

5. Cavity-free schemes for non-demolition measurement of single photons

The concept of QND measurement and its realization in measuring classical light intensity have been introduced earlier. QND measurement of single photons is the ultimate goal. Single "static" photon in cavity has been detected nondestructively. Measuring "moving" single photons without destroying it is still far to be achieved. Two important progresses toward this

As mentioned earlier, although the optical cross-Kerr effect has been proposed for implementing intensity QND measurement of light, detection of light at the single photon level in a QND way is still a challenging task. In the cross-Kerr-based proposals [10], the signal photon changes the refractive index nI of medium. The change of nI causes a phase shift of the co-propagating probe photon. The interaction between the signal and probe photons is "Ising" type. Its application for single-photon QND measurement is questionable at the fundamental level [16–19]. A "Rabi" type photon-photon interaction created from four-wave mixing (FWM) was proposed for a photon-photon controlled quantum phase gate [24]. The proposal treated the moving fields as a single mode and suggested equal group velocity for both the signal and probe pulses. The work did not circumvent the issues raised in [16–19]. Instead, Xia and his coworker studied this type of photon-photon interaction for QND measurement of a single photon taking into account the quantum nonlocality [26]. In the proposal, the four-wave mixing occurs in an optical nonlinear medium. One of the light modes in four-wave mixing is a strong coherent laser. This coherent laser is used to coherent pump the nonlinear process and perform an effective three-wave mixing process involving the signal mode, as, the probe mode, ap, and an auxiliary mode, aa. The

photon.

pump field Ec.

direction are presented in the following.

5.1. QND measurement via Rabi-type photon-photon interaction

Hamiltonian describing the interaction among these three modes takes the form

<sup>2</sup> aaa† pa†

<sup>s</sup> <sup>þ</sup> g Eð Þ<sup>c</sup> <sup>2</sup> <sup>a</sup>†

where g Eð Þ<sup>c</sup> indicates the nonlinear coupling strength that can be tuned by the intensity of the

To induce a Rabi-type interaction, the auxiliary mode is initially in a vacuum state. The signal field has at most one photon. The probe field is assumed to be weak that, to a good approxi-

<sup>a</sup> apas, (5)

Quantum Non-Demolition Measurement of Photons http://dx.doi.org/10.5772/intechopen.72871 71

with α<sup>p</sup> ∨ ≪ 1.

 ≈ 0<sup>p</sup> þ α<sup>p</sup> 1<sup>p</sup>

HI <sup>¼</sup> g Eð Þ<sup>c</sup>

mation, it can be considered as the superposition state of α<sup>p</sup>

At the fundamental level, the cross-Kerr-based QND measurement is found invalid when a continuous spatiotemporal multimode model [16] or a finite response time [17–19] is considered. In this sense, although many important progresses have been achieved, QND detection of a moving single photon still needs proposals.

## 4. Non-demolition measurement of photons with cavities

With the progress of cavity electrodynamics, in particular the ultrastrong coupling between a microwave cavity and an artificial atom, QND measurement of single mw photons have been realized via qubit-photon CNOT gate [20], ac Stark effect [21–23], and the intrinsic phase shift in Rabi oscillation [24]. Photon blockade has been demonstrated as a new effect to implement QND measurement of a single optical photon trapped in a high-quality optical cavity [25].

The first breakthrough of QND measurement of single photons was accomplished by Haroche et al. exploiting the intrinsic π phase shift after a full Rabi oscillation of an atom [24]. The principle can be understood using the schematic diagram as shown in Figure 4. The atom is first prepared in Rydberg state with the ground state jgi, the excited state jei, and an auxiliary state jii by B. R1 and R2 conduct the Ramsey interferometer measurement. R1 drives the Rydberg atom into a superposition state of Cg gi þ Ci j jii. The mw cavity C induces a phase shift dependent on the photon number in it. It is off resonance with jgi \$ jii, but on resonance

Figure 4. Schematic diagram for QND measurement of a single microwave photon via the intrinsic phase shift of a full Rabi oscillation [24].

with jgi \$ jei. It is designed to cause a full Rabi oscillation if the cavity includes one photon and results in a π phase shift to jgi yielding �Cg gi þ Ci j jii. While in the empty-cavity case, the atomic state is unchanged. In short, the atomic coherent changes its phase by π if there is one photon in C. R2 mixes the atomic state again, probing after C the superposition phase shift. The final atomic population can be detected with a state-selective detector. The probability of finding the atom in jgi is a cosine function of the phase shift and thus gives information about the phase shift. In this way, Haroche et al. implemented the QND measurement of a single mw photon.

## 5. Cavity-free schemes for non-demolition measurement of single photons

The concept of QND measurement and its realization in measuring classical light intensity have been introduced earlier. QND measurement of single photons is the ultimate goal. Single "static" photon in cavity has been detected nondestructively. Measuring "moving" single photons without destroying it is still far to be achieved. Two important progresses toward this direction are presented in the following.

#### 5.1. QND measurement via Rabi-type photon-photon interaction

for detecting a single photon in a QND way. There are two prerequisites in this scheme. First, to ensure the atoms are transparent, the probe field needs to be known. Other than the optimal phase, the absorption is considerable. But this phase is unknown for a signal photon to be detected. It means a large loss for the signal photon to be detected. Second, the phase shift is obtained in the steady state where the probe field is classically treated as a constant field. This is not the case for a single photon as it is a quantum field. Therefore, it is hard to do genuine

At the fundamental level, the cross-Kerr-based QND measurement is found invalid when a continuous spatiotemporal multimode model [16] or a finite response time [17–19] is considered. In this sense, although many important progresses have been achieved, QND detection

With the progress of cavity electrodynamics, in particular the ultrastrong coupling between a microwave cavity and an artificial atom, QND measurement of single mw photons have been realized via qubit-photon CNOT gate [20], ac Stark effect [21–23], and the intrinsic phase shift in Rabi oscillation [24]. Photon blockade has been demonstrated as a new effect to implement QND measurement of a single optical photon trapped in a high-quality optical cavity [25].

The first breakthrough of QND measurement of single photons was accomplished by Haroche et al. exploiting the intrinsic π phase shift after a full Rabi oscillation of an atom [24]. The principle can be understood using the schematic diagram as shown in Figure 4. The atom is first prepared in Rydberg state with the ground state jgi, the excited state jei, and an auxiliary state jii by B. R1 and R2 conduct the Ramsey interferometer measurement. R1 drives the Rydberg atom into a superposition state of Cg gi þ Ci j jii. The mw cavity C induces a phase shift dependent on the photon number in it. It is off resonance with jgi \$ jii, but on resonance

Figure 4. Schematic diagram for QND measurement of a single microwave photon via the intrinsic phase shift of a full

QND measurement at the single photon level.

70 Photon Counting - Fundamentals and Applications

of a moving single photon still needs proposals.

Rabi oscillation [24].

4. Non-demolition measurement of photons with cavities

As mentioned earlier, although the optical cross-Kerr effect has been proposed for implementing intensity QND measurement of light, detection of light at the single photon level in a QND way is still a challenging task. In the cross-Kerr-based proposals [10], the signal photon changes the refractive index nI of medium. The change of nI causes a phase shift of the co-propagating probe photon. The interaction between the signal and probe photons is "Ising" type. Its application for single-photon QND measurement is questionable at the fundamental level [16–19]. A "Rabi" type photon-photon interaction created from four-wave mixing (FWM) was proposed for a photon-photon controlled quantum phase gate [24]. The proposal treated the moving fields as a single mode and suggested equal group velocity for both the signal and probe pulses. The work did not circumvent the issues raised in [16–19]. Instead, Xia and his coworker studied this type of photon-photon interaction for QND measurement of a single photon taking into account the quantum nonlocality [26]. In the proposal, the four-wave mixing occurs in an optical nonlinear medium. One of the light modes in four-wave mixing is a strong coherent laser. This coherent laser is used to coherent pump the nonlinear process and perform an effective three-wave mixing process involving the signal mode, as, the probe mode, ap, and an auxiliary mode, aa. The Hamiltonian describing the interaction among these three modes takes the form

$$H\_I = \frac{g(E\_c)}{2} a\_a a\_p^\dagger a\_s^\dagger + \frac{g(E\_c)}{2} a\_a^\dagger a\_p a\_{s\prime} \tag{5}$$

where g Eð Þ<sup>c</sup> indicates the nonlinear coupling strength that can be tuned by the intensity of the pump field Ec.

To induce a Rabi-type interaction, the auxiliary mode is initially in a vacuum state. The signal field has at most one photon. The probe field is assumed to be weak that, to a good approximation, it can be considered as the superposition state of α<sup>p</sup> ≈ 0<sup>p</sup> þ α<sup>p</sup> 1<sup>p</sup> with α<sup>p</sup> ∨ ≪ 1. Here, the probe field is truncated up to 1<sup>p</sup> . Focusing on the space spanned by the associated state of the probe and auxiliary modes, as shown in Figure 5(a), these two modes form a laddertype quantum system. The ground state is 0p; 0<sup>a</sup> , and the first and second excited states are 1p; 0<sup>a</sup> and 0p; <sup>1</sup><sup>a</sup> , respectively. The incoming signal photon will drive the transition between 1p; 0<sup>a</sup> and 0p; <sup>1</sup><sup>a</sup> . This photon-driven transition between photonic states is a photonic counterpart of atomic Rabi oscillation. For a weak probe field α<sup>p</sup> , the initial state is 0p; 0<sup>a</sup> þ α<sup>p</sup> 1p; 0<sup>a</sup> . Similar to the Rabi oscillation in atoms, the state 1p; 0<sup>a</sup> will suffer a <sup>π</sup> phase shift after a full Rabi oscillation. As a result, the probe field passing through the medium becomes 0<sup>p</sup> � α<sup>p</sup> 1<sup>p</sup> ≈ �α<sup>p</sup> . Effectively, the probe field is shifted by phase of π. The concept is depicted in Figure 5(b). Such full Rabi oscillation can be conducted by controlling the pump field intensity or the length of nonlinear medium.

To determine the phase shift of the probe field, a strong local bias is overlapped on the transmitted probe field via a highly reflective beam splitter. By properly choosing the bias field, the transmitted probe field presented to the detector is displaced by �α<sup>p</sup> , yielding �2α<sup>p</sup> in the presence of a single signal photon or 0<sup>j</sup> <sup>i</sup> in the absence of signal field. Simply observing the photon "click" on the single-photon detector can determine whether a single signal photon passes through the medium without destroying it. This accomplishes the QND measurement of a single signal photon. Of course, this measurement will cause disturbance in the phase of signal field. However, the photon flux is concerned, and the noise added to the phase quadrature is not unwanted.

In the presence of a single signal photon, the field presented to the detector is �2α<sup>p</sup>

Figure 6. Wigner functions of the transmitted and detected states for a probe field with α<sup>p</sup>

detection of signal photon. The resulted error probability is given by Perr α<sup>p</sup>

. The black dashed lines at gz ¼ 2π are the guides to eye [26].

state �2α<sup>p</sup>

αp 2

signal input [26].

error. An optimal trade-off is α<sup>p</sup>

case, even an ideal photon detector can have a "dark count," that is, no detection, because the

signal (probe) state after interacting (a Full Rabi oscillation) for the length of the media; (c) detected state of probe field presented to detector. The concentric circles show the Wigner function contours of the detection field in the absence of

decreases exponentially as the intensity of probe field increases. However, the fidelity of transmitted signal field decreases as well. Therefore, a weak probe field is preferable for achieving a high fidelity, while a relative strong probe field is required to reduce the detection

reduce the error probability and improve the fidelity, a cascade configuration is needed. In such configuration, the transmitted signal field of the former QND measurement is fed into the latter. The transmitted probe field is detected in each measurement. For an N-cascade configuration, the error probability decreases exponentially as a function of N, but the fidelity

Figure 7. Evolution of the occupation (a), the fidelity (b) and the detection error probability (c) for different probe field,

includes a small occupation in vacuum state 0<sup>j</sup> <sup>i</sup>. This dark count causes error in

<sup>2</sup> <sup>¼</sup> <sup>0</sup>:6, yielding Perr <sup>¼</sup> <sup>0</sup>:09 and a fidelity of 0.9 (Figure 7). To

Quantum Non-Demolition Measurement of Photons http://dx.doi.org/10.5772/intechopen.72871

. In this

73

�<sup>4</sup>j j <sup>α</sup><sup>p</sup> 2 . It

≈ e

<sup>2</sup> <sup>¼</sup> <sup>0</sup>:6. In (a) [(b)] transmitted

To evaluate the performance of the QND measurement, only one investigates the response of system to the initial case of a single signal photon input, 1j <sup>s</sup>i, and a weak probe field, α<sup>p</sup> . Numerical simulation of corresponding quantum Langevin equation shows the transmitted signal and probe fields, and the displaced field presented to the detector for the input 1j <sup>s</sup>i and αp , as shown in Figure 6. It is found that the transmitted signal field keeps its initial state with a very high fidelity, while the transmitted probe field on the detector, shifted by a phase of π due to the presence of signal photon, can be well distinguished from the transmission without phase shift in the absence of signal photon.

Figure 5. Schematic for detection of a single moving photon. (a) Configuration for QND detection of a single moving photon via four-wave mixing in a nonlinear medium. (b) Level diagram describing the interaction between the signal, auxiliary, and probe photons [26].

Here, the probe field is truncated up to 1<sup>p</sup>

72 Photon Counting - Fundamentals and Applications

1p; 0<sup>a</sup>

1p; 0<sup>a</sup>

0p; 0<sup>a</sup>

�2α<sup>p</sup>

αp

becomes 0<sup>p</sup>

and 0p; <sup>1</sup><sup>a</sup>

and 0p; <sup>1</sup><sup>a</sup>

þ α<sup>p</sup> 1p; 0<sup>a</sup>

> � α<sup>p</sup> 1<sup>p</sup> ≈ �α<sup>p</sup>

phase quadrature is not unwanted.

auxiliary, and probe photons [26].

type quantum system. The ground state is 0p; 0<sup>a</sup>

field intensity or the length of nonlinear medium.

without phase shift in the absence of signal photon.

terpart of atomic Rabi oscillation. For a weak probe field α<sup>p</sup>

. Similar to the Rabi oscillation in atoms, the state 1p; 0<sup>a</sup>

. Focusing on the space spanned by the associated

, and the first and second excited states are

, the initial state is

will suffer a <sup>π</sup> phase

, yielding

.

state of the probe and auxiliary modes, as shown in Figure 5(a), these two modes form a ladder-

shift after a full Rabi oscillation. As a result, the probe field passing through the medium

is depicted in Figure 5(b). Such full Rabi oscillation can be conducted by controlling the pump

To determine the phase shift of the probe field, a strong local bias is overlapped on the transmitted probe field via a highly reflective beam splitter. By properly choosing the bias

 in the presence of a single signal photon or 0<sup>j</sup> <sup>i</sup> in the absence of signal field. Simply observing the photon "click" on the single-photon detector can determine whether a single signal photon passes through the medium without destroying it. This accomplishes the QND measurement of a single signal photon. Of course, this measurement will cause disturbance in the phase of signal field. However, the photon flux is concerned, and the noise added to the

To evaluate the performance of the QND measurement, only one investigates the response of system to the initial case of a single signal photon input, 1j <sup>s</sup>i, and a weak probe field, α<sup>p</sup>

Numerical simulation of corresponding quantum Langevin equation shows the transmitted signal and probe fields, and the displaced field presented to the detector for the input 1j <sup>s</sup>i and

 , as shown in Figure 6. It is found that the transmitted signal field keeps its initial state with a very high fidelity, while the transmitted probe field on the detector, shifted by a phase of π due to the presence of signal photon, can be well distinguished from the transmission

Figure 5. Schematic for detection of a single moving photon. (a) Configuration for QND detection of a single moving photon via four-wave mixing in a nonlinear medium. (b) Level diagram describing the interaction between the signal,

field, the transmitted probe field presented to the detector is displaced by �α<sup>p</sup>

, respectively. The incoming signal photon will drive the transition between

. This photon-driven transition between photonic states is a photonic coun-

. Effectively, the probe field is shifted by phase of π. The concept

Figure 6. Wigner functions of the transmitted and detected states for a probe field with α<sup>p</sup> <sup>2</sup> <sup>¼</sup> <sup>0</sup>:6. In (a) [(b)] transmitted signal (probe) state after interacting (a Full Rabi oscillation) for the length of the media; (c) detected state of probe field presented to detector. The concentric circles show the Wigner function contours of the detection field in the absence of signal input [26].

In the presence of a single signal photon, the field presented to the detector is �2α<sup>p</sup> . In this case, even an ideal photon detector can have a "dark count," that is, no detection, because the state �2α<sup>p</sup> includes a small occupation in vacuum state 0<sup>j</sup> <sup>i</sup>. This dark count causes error in detection of signal photon. The resulted error probability is given by Perr α<sup>p</sup> ≈ e �<sup>4</sup>j j <sup>α</sup><sup>p</sup> 2 . It decreases exponentially as the intensity of probe field increases. However, the fidelity of transmitted signal field decreases as well. Therefore, a weak probe field is preferable for achieving a high fidelity, while a relative strong probe field is required to reduce the detection error. An optimal trade-off is α<sup>p</sup> <sup>2</sup> <sup>¼</sup> <sup>0</sup>:6, yielding Perr <sup>¼</sup> <sup>0</sup>:09 and a fidelity of 0.9 (Figure 7). To reduce the error probability and improve the fidelity, a cascade configuration is needed. In such configuration, the transmitted signal field of the former QND measurement is fed into the latter. The transmitted probe field is detected in each measurement. For an N-cascade configuration, the error probability decreases exponentially as a function of N, but the fidelity

Figure 7. Evolution of the occupation (a), the fidelity (b) and the detection error probability (c) for different probe field, αp 2 . The black dashed lines at gz ¼ 2π are the guides to eye [26].

decreases linearly. A four-cascade detection unit can already achieve <sup>F</sup><sup>4</sup> P4 err > 23:75 for a very weak probe field of α<sup>p</sup> � � � � <sup>2</sup> <sup>¼</sup> <sup>0</sup>:2.

pi phase shift, see Figure 8(a). To circumvent this issue raised by the nonlocality of single photon pulse, the probe field pulse is delayed with respect to the signal field pulse but propagates at a higher velocity. To do so, the signal mode can be slowed down via the electromagnetically induced transparency (EIT) technique. In such an arrangement, the probe field pulse scans over the signal field pulse. No matter where the probe and signal photons appear within the pulses, they will interact with each other once. It can be seen from Figure 8(b) that a π phase shift can be clearly induced after the probe pulse passes through the entire signal pulse. The fidelity is very high about unity. Another advantage of this arrangement over the former is that the phase shift

Quantum Non-Demolition Measurement of Photons http://dx.doi.org/10.5772/intechopen.72871 75

By comparing two models, it can be seen that when the probe field has at most one photon, a unit fidelity for the transmitted signal mode is achieved. If the probe contains higher Fock states, then interaction with these high Fock states of probe mode prevents to achieve perfect

Rubidium vapor embedded in a hollow-core photonic crystal fiber [12] or a hollow antiresonant reflecting optical waveguide [29] can be a good experimental implementation for this QND measurement scheme. This setup, to a good approximation, can be modeled as a 1D nonlinear medium. The four-wave mixing can be effectively conducted using a diamond-level configuration as shown in Figure 9. The signal field can be slowed via EIT with the fifth level, 4d<sup>3</sup>=2.

Figure 8. Evolution of the wave function ∅ps for (a) the same propagating speeds vp ¼ vs ¼ 1 and delay and (b) different

Figure 9. Configuration for four-wave mixing realized in Rb atomic vapor in hollow waveguides. The signal field is

will not change once the probe field passes the signal field, see Figure 8(b).

non-demolition of the signal mode.

speeds vp > vs and different delays [26].

slowed via EIT by a strong coupling between levels of 5P<sup>1</sup>=<sup>2</sup> and 4d<sup>3</sup>=2.

The measured photon and the probe photon are "moving" pulse-shaped wavefunctions. The quantum Langevin equation describes the motion of system in the single mode regime, in which both the signal and the probe photons are treated as a single mode. In the real experiment, they are moving pulse including continuous spatiotemporal modes and can be confined in a one-dimensional (1D) waveguide. Therefore, a model accounting for the interaction of continuous spatiotemporal modes is required. The method developed by Fan et al. can model the interaction of the signal and probe photons in 1D real space [27]. In the Fan's method, the photons are the wavefunctions of quantum fields propagating in 1D real space. The probability density of photon appearing at certain time (position) is the squared absolute value of wavefunctions. For the purpose of single-photon QND measurement, only one needs the fidelity and phase shift of a photon-pair input state 1p; 1<sup>s</sup> � � � after propagating a certain distance. Starting from the vacuum auxiliary field, it can be excited during the propagation of the probe and signal fields. One can define an associate wavefunction ∅ps t; zp; zs � � for the state 1p; 1<sup>s</sup> � � � , and the wavefunction ∅að Þ t; za for the state 1j <sup>a</sup>i. These wavefunctions imply that the photons 1p � � � and 1<sup>j</sup> <sup>s</sup><sup>i</sup> ( 1<sup>j</sup> <sup>a</sup>i) appear(s) at zp and zs (za) at time t with probability density of <sup>∅</sup>ps <sup>t</sup>; zp; zs � � � � � � 2 (j j <sup>∅</sup>að Þ <sup>t</sup>; za <sup>2</sup> ). The nonlinear medium can be assumed to possess a spatial nonlocal response distribution with an interaction length of σ that f <sup>g</sup> za; zp; zs � � <sup>¼</sup> <sup>1</sup>ffiffiffiffiffiffi πσ<sup>3</sup> <sup>p</sup> <sup>e</sup> � ð Þ za�zp 2 =2σ<sup>2</sup> � � e � ð Þ za�zs <sup>2</sup> <sup>=</sup>2σ<sup>2</sup> ½ �. Following Fan's treatment, the evolution of the photonic wavefunctions is governed by the partial differential equations [27, 28]

$$\frac{\partial \mathfrak{Q}\_{ps}}{\partial t} = -\upsilon\_p \frac{\partial \mathfrak{Q}\_{ps}}{\partial z\_p} - \upsilon\_s \frac{\partial \mathfrak{Q}\_{ps}}{\partial z\_s} - \frac{ig\_0}{2} \int\_0^L f\_g \left( z\_d, z\_p, z\_s \right) \mathfrak{Q}\_d dz\_{a\nu} \tag{6}$$

$$\frac{\partial \mathfrak{Q}\_{a}}{\partial t} = -\upsilon\_{a} \frac{\partial \mathfrak{Q}\_{a}}{\partial z\_{p}} - \frac{ig\_{0}}{2} \int\_{0}^{L} f\_{\mathcal{g}} \left(z\_{a}, z\_{p}, z\_{s}\right) \mathfrak{Q}\_{\mathbb{R}^{3}} dz\_{p} dz\_{s} \tag{7}$$

where g<sup>0</sup> is the coupling amplitude, va(vp, vs) is the group velocity of the auxiliary (probe, signal) field in the 1D waveguide. g<sup>0</sup> is not important because the coupling strength in experiment can be tuned via the pump laser intensity. The photon pulses are assumed to be long enough that the group velocity of each mode is constant in time, and the perfect phase and energy matching are satisfied.

Solving Eqs. (2) and (3)) can simulate the evolution of the fields in medium. Without loss of generality, a Gaussian input is applied. For a single-photon pulse which is a quantum field, the photon can appear everywhere within the pulse with a probability density determined by the wave packet. This is the nonlocal nature of a single photon pulse. When the probe and signal fields propagate at the same group velocity in the medium as previous schemes, they have no necessity to interact with each other. Actually, with a large probability, they propagate independently as they never meet each other. The signal photon couples the probe photon only if they appear at the same position. As a result, only the central part of ∅ps reverses its sign, implying a

pi phase shift, see Figure 8(a). To circumvent this issue raised by the nonlocality of single photon pulse, the probe field pulse is delayed with respect to the signal field pulse but propagates at a higher velocity. To do so, the signal mode can be slowed down via the electromagnetically induced transparency (EIT) technique. In such an arrangement, the probe field pulse scans over the signal field pulse. No matter where the probe and signal photons appear within the pulses, they will interact with each other once. It can be seen from Figure 8(b) that a π phase shift can be clearly induced after the probe pulse passes through the entire signal pulse. The fidelity is very high about unity. Another advantage of this arrangement over the former is that the phase shift will not change once the probe field passes the signal field, see Figure 8(b).

decreases linearly. A four-cascade detection unit can already achieve <sup>F</sup><sup>4</sup>

The measured photon and the probe photon are "moving" pulse-shaped wavefunctions. The quantum Langevin equation describes the motion of system in the single mode regime, in which both the signal and the probe photons are treated as a single mode. In the real experiment, they are moving pulse including continuous spatiotemporal modes and can be confined in a one-dimensional (1D) waveguide. Therefore, a model accounting for the interaction of continuous spatiotemporal modes is required. The method developed by Fan et al. can model the interaction of the signal and probe photons in 1D real space [27]. In the Fan's method, the photons are the wavefunctions of quantum fields propagating in 1D real space. The probability density of photon appearing at certain time (position) is the squared absolute value of wavefunctions. For the purpose of single-photon QND measurement, only one needs the

Starting from the vacuum auxiliary field, it can be excited during the propagation of the probe

and the wavefunction ∅að Þ t; za for the state 1j <sup>a</sup>i. These wavefunctions imply that the photons

Following Fan's treatment, the evolution of the photonic wavefunctions is governed by the

where g<sup>0</sup> is the coupling amplitude, va(vp, vs) is the group velocity of the auxiliary (probe, signal) field in the 1D waveguide. g<sup>0</sup> is not important because the coupling strength in experiment can be tuned via the pump laser intensity. The photon pulses are assumed to be long enough that the group velocity of each mode is constant in time, and the perfect phase and