# A Single-Photon-compatible Telecom-C-Band Quantum Memory in a Hot Atomic Gas

S. E. Thomas1, S. Sagona-Stophel1, Z. Schofield2, I. A. Walmsley1, P. M.
Ledingham2<EMAIL_ADDRESS>1QOLS, Department of Physics, Imperial
College London, London SW7 2BW, UK
2Department of Physics and Astronomy, University of Southampton, Southampton
SO17 1BJ, UK

(27th August 2024)

###### Abstract

The efficient storage and on-demand retrieval of quantum optical states that
are compatible with the telecommunications C-band is a requirement for future
terrestrial-based quantum optical networking. Spectrum in the C-band minimises
optical fiber-propagation losses, and broad optical bandwidth facilitates
high-speed networking protocols. Here we report on a telecommunication
wavelength and bandwidth compatible quantum memory. Using the Off-Resonant
Cascaded Absorption protocol in hot 87Rb vapour, we demonstrate a total memory
efficiency of $20.90(1)\,\%$ with a Doppler-limited storage time of
$1.10(2)\,$ns. We characterise the memory performance with weak coherent
states, demonstrating signal-to-noise ratios greater than unity for mean
photon number inputs above $4.5(6)\times 10^{-6}$ per pulse.

Introduction – Quantum light-matter interfaces are a critical component for
quantum repeating Briegel1998 ; Gisin2007  technology and therefore building
large-scale quantum networks Ladd2010 ; Komar2014 ; Wehner2018 . Such
interfaces allow for a quantum memory Heshami2016 , a device capable of
storing true single photons with both high fidelity and efficiency, with on-
demand retrieval after a sufficiently long storage time. Besides these
important attributes, compatibility with wavelengths in the telecommunications
C-band, as well as GHz operational bandwidth, is of crucial importance to
allow high repetition rate quantum photonic operations in low-loss optical
fiber networks.

Significant progress has been made realising telecom quantum optical memories
across different material platforms. Atomic-based systems require an optical
transition in the telecom range, with cryogenically-cooled trivalent erbium
ions in solid-state hosts a popular choice Sun2005 . Protocols including the
Atomic Frequency Comb (AFC) Lauritzen2011 ; Craiciu2019 ; Stuart2021 , stark-
modulated AFC Craiciu21 ; Liu2022 , controlled-reversible inhomogeneous
broadening Lauritzen2010  and revival of silenced echo Dajczgewand2014  have
been performed in erbium doped Y2SiO5, which include realisations in nano-
photonic structures Craiciu2019 ; Craiciu21 . Other hosts have been explored,
with demonstrations of AFC in erbium-doped optical fiber Jin2015 ; Wei2022
and lithium niobate waveguides Askarani2019 . Further, frequency conversion
via non-linear processes have been used to interface telecom light with
quantum memories, including four-wave mixing in cold atomic clouds Radnaev2010
; Ding2012  and non-linear crystals Maring2014 ; Luo2022 . Furthermore, opto-
mechanical interactions have enabled telecom light storage in optical fiber
Zhu2007 , chalcogenide glass chips Merklein2017  and in nanofabricated
mechanical resonators Wallucks2020 .

Despite these impressive advances, the combination of on-demand read-out with
high signal-to-noise ratio (SNR) remains elusive. Erbium-based systems suffer
poor optical pumping leading to high absorbing backgrounds that limit the
overall memory efficiency Lauritzen2010 , requiring magnetic fields of the
order of $7\,$T and a $2\,$K temperature to overcome Stuart2021 . Frequency
conversion adds layers of inefficiency and in the case of non-linear crystals,
adds noise via pump-induced Raman scattering and spurious spontaneous
parametric down-conversion Pelc2011 . Opto-mechanical systems need to overcome
the challenge of reaching the mechanical quantum ground state to remove
thermal-phononic-mode induced noise Shandilya2021 . In this work, we
circumvent these problems and demonstrate an ultra-low-noise, high bandwidth
quantum memory using a telecom transition in hot rubidium vapour.

Protocol – We use the off-resonant cascaded absorption (ORCA) Kaczmarek2018
protocol for our demonstration. ORCA comprises two counter-propagating optical
fields that are two-photon resonant with an optical ladder transition of an
atomic ensemble while being detuned from the intermediate transition by
$\Delta$ (Fig. 1), giving rise to absorption of the beams by exciting the
atoms in the ensemble. The intense control pulse dresses the atomic system
providing a broad virtual state to which the signal field couples efficiently,
so that it may be completely absorbed. For large enough intermediate detuning,
the absorption bandwidth is determined by the bandwidth of the control pulse.
The input pulse excites a superposition of atoms in the ensemble of the
$|\textrm{g}\rangle-|\textrm{s}\rangle$ transition. The state of the atomic
ensemble after absorption of the signal is of the form
$\frac{1}{\sqrt{N}}\sum_{j=1}^{N}e^{i(\vec{k}_{s}-\vec{k}_{c})\cdot\vec{v}_{j}t}\ket{g_{1},\dots,s_{j},\dots,g_{N}}$
where $\ket{g(s)_{j}}$ labels the ground (storage) state of the
$j^{\mathrm{th}}$ atom, $N$ is the total number of atoms, $\vec{k}_{s(c)}$ is
the input (control) pulse wave vector, $\vec{v}_{j}$ is the velocity of the
$j^{\mathrm{th}}$ atom. The collective dipole moment will emit light upon the
application of a second control pulse after a storage time $T$, allowing the
signal to be read out and completing the memory operation.

The main benefits of ORCA are threefold. Firstly, the optical fields can be at
significantly different wavelengths, depending on the chosen atomic species
and on the levels used. This makes it simple to filter the strong control from
the single-photon-level signal. Secondly, the storage state is a doubly-
excited one and so has no atomic population under normal operational
conditions. This simplifies the approach by not needing any initialisation of
the atomic ensemble with optical pumping fields, and eliminates spontaneous
emission noise associated with inefficient optical pumping. Finally, four-wave
mixing type noise is eliminated. For example, in Lambda-based approaches, the
strong control is able to efficiently Raman scatter from the populated ground
state, spontaneously emitting a photon and leaving spurious excitations in the
storage state that are subsequently read-out into the same spatial-spectral-
temporal mode as that of the desired signal Thomas2019 . Equivalent processes
with a ladder system are not possible. In the case of a non-degenerate ladder
system, there is no two-control-photon process that can populate the storage
state and so the ORCA protocol is inherently noise-free in this respect.

ORCA has been achieved in hot atomic vapours demonstrating low-noise operation
over GHz bandwidth allowing for high SNR for single-photon-level inputs
Finkelstein2018 , recall of heralded single photons Kaczmarek2018 , and can be
used as a time-nonstationary coherent spectral-temporal filter to improve
indistinguishably of single photon sources Gao2019 . Here we extend the ORCA
protocol to store light in the telecom C-band for the first time.

Figure 1: Left Panel: Telecom ORCA level scheme. Right Panel: Experimental
Set-up. DM: Dichroic Mirror; ND: Neutral density filters; RF: Arbitrary
Waveform Generator; SNSPD: Superconducting Nanowire Single Photon Detectors;
U-MZI: Unbalanced Mach–Zehnder interferometer.

Experimental Set-up – See Fig. 1. An ensemble of rubidium atoms in a cell of
length $8\,$cm is heated to around $120^{\circ}$C yielding more than $10^{9}$
atoms into the vapour phase. With spectroscopy we estimate the vapour to
contain $96.9\,\%$ of the isotope 87Rb. The ladder system used for this
demonstration is depicted in the left panel of Fig. 1. We utilise the doubly-
excited $4$D5/2 state as the storage state $|s\rangle$, that connects to the
ground state $|g\rangle$ ($5$P1/2, F$=2$) via a two-photon process with the
telecommunication C-band compatible wavelength $1529.3\,$nm (signal) and the
Rb D2 line at $780.3\,$nm (control). The signal (control) field is blue-
(red-) detuned from the intermediate level $|e\rangle$ ($5$P3/2,
F${}^{\prime}=\\{1,2,3\\}$) by $\Delta=6\,$GHz.

Control pulses of a few nJ energy are delivered by a mode-locked Titanium
Sapphire laser (Spectra Physics Tsunami) at a repetition rate of $80\,$MHz.
The pulse bandwidth is approximately $1\,$GHz. An unbalanced Mach–Zehnder
interferometer (U-MZI) splits an individual pulse into the read-in and read-
out pulses, separated by time $T$. We use polarising beamsplitters to
construct the U-MZI, with a half waveplate before used to adjust the energy
into each of the pulses. The output of the U-MZI is polarized by a half
waveplate and PBS (not shown), to ensure that the read-in and read-out control
pulses have the same polarization. Dichroic mirrors are used to overlap and
separate the control and the signal mode, and we monitor the average power of
the control pulses with a power meter (Thorlabs). The signal is generated from
a CW telecom laser (Santec) that is passed through an intensity modulator
(iXBlue) driven by a fast arbitrary waveform generator (Tektronix) to generate
Gaussian pulses of around $300\,$ps duration synchronised to the repetition
rate of the control pulse laser and delivered at a rate of $10\,$MHz. Neutral
density filters are used to reduce the intensity of the pulses to the single-
photon level. High transmission band- and long-pass filters are placed before
the detection fiber to provide 14 orders of magnitude suppression of
background light at the control pulse wavelength. Photons are detected with
superconducting nanowire single photon detectors (Photon Spot) together with a
time-to-digital converter (Swabian) to produce start-stop histograms.

Figure 2: (a) Storage and retrieval of telecom light. The solid lines are the
start-stop histograms for the signal at input (red), at the memory output
(purple) and the noise without signal (light blue) - the timing resolution of
the TDC is $1\,$ps and the measurement time for each data set is $120\,$s. The
dashed lines show Gaussian fits to the measured signal. The shaded areas
indicate the read-in and read-out integration windows of $500\,$ps width. The
storage time in this case is $660\,$ps. (b) Read-out efficiency vs storage
time. Pink circles are the data which are fit with a Gaussian function of
control delay (grey dashed line). For this data, the measurement time per data
point is $10\,$s and integration window as before.

Memory Performance – Fig. 2 shows a plot of storage and recall of telecom
light for the highest measured storage efficiency. We implement Gaussian fits
to these traces and use these fits to calculate photon number and
efficiencies. We use an input pulse with an average number of photons per
pulse of $\mu_{\textrm{in}}=0.084(10)$. The mean photon number was estimated
by integrating the counts over a $500\,$ps integration window centred on the
$350\,$ps FWHM pulse at $t=0$, then dividing out detection loss
$(\eta_{\textrm{det}}=80(8)\,\%)$ and transmission from the input of the cell
to the detector $(\eta_{\textrm{trans}}=56(4)\,\%)$, and finally normalising
by the number of trials in the $120$s total measurement time. Two control
pulses, with a time separation of $660\,$ps, are applied to read in and read
out the signal to the memory, with respective energies of $0.57(4)\,$nJ and
$3.6(3)\,$nJ. When photons are successfully stored, they are measured in the
time-region called the “read-out window” – while photons that are not
successfully stored pass through undelayed by the memory in the “read-in
window”. We define the read-in efficiency as the ratio of counts remaining in
the read-in window when the control is applied to when it is not – in this
case it is $\eta_{\textrm{read-in}}\,=\,69.13(1)\,\%$. We see clear retrieved
signal in the read-out window, defined as the $500\,$ps window centred at
$t=660\,$ps. The total memory efficiency, defined as the ratio of read-out to
input counts, is measured to be $\eta_{\textrm{mem}}=20.90(1)\,\%$, resulting
in read-out efficiency of $\eta_{\textrm{read-out}}\,=\,30.23(1)\,\%$. The
total throughput efficiency for the input at the front of the cell to being
stored, retrieved and detected is
$\eta_{\text{mem}}\eta_{\text{trans}}\eta_{\text{det}}=9.4(1.2)\%$.

Storage Dynamics – Fig. 2 shows the read-out memory efficiency as a function
of read-out delay after the storage. Performed under similar conditions to
Fig. 2, we measure an average read-in efficiency of $\eta_{\textrm{read-
in}}=78(2)\,\%$ and infer the read-out efficiency at zero storage time from
the fit to be $\eta_{\textrm{read-out}}=50(2)\,\%$. The read-in and read-out
efficiencies are not matched. Forward retrieval (i.e the retrieved signal
propagates in the same direction as the input) results in re-absorption of the
signal toward the exit of the cell, reducing the maximum efficiency for fixed
control pulse energy. Backward retrieval can, in principle, avoid this
Surmacz2008 .

The characteristic lifetime of $1.10(2)\,$ns is extracted from a Gaussian fit.
The lifetime is limited by inhomogenous Doppler broadening of the atoms
causing dephasing of the atomic polarization. Atom $j$ constituting the
collective dipole moment between the ground and storage state has a net
wavevector $e^{i(\vec{k}_{s}-\vec{k}_{c})\cdot\vec{v}_{j}t}$ where
$(\vec{k}_{s}-\vec{k}_{c})\cdot\vec{v}_{j}$ is the Doppler shift for the
$j^{\textrm{th}}$ atom. Given the broad Maxwell-Boltzmann distribution of
velocities of the atomic vapour, each atom accumulates a different phase
thereby reducing the collective dipole moment. The spatial wavelength of the
collective orbital-wave excitation is around $1.6\,\mu$m, a distance traversed
by an atom in the hot vapour in a few nanoseconds. The storage time is also
reduced by the interference of multiple pathways through different hyperfine
states with characteristic timescales of $\sim 10$ns Kaczmarek2018 . The
natural lifetime of the storage state provides the ultimate limit of
$\sim\,90\,$ns Theodosiou1984 ; Safronova2004 . The timescale we have measured
here is consistent with that expected from Doppler dephasing Main2021
suggesting strongly that this is the main limitation for our storage time.

Control Dependence – The data presented in Fig. 2 show the optimised output
efficiency. The ORCA memory efficiency varies with the total energy in the
control pulses, and is shown for a read-out to read-in ratio,
$\mathcal{R}\,=\,E_{\textrm{R}_{\textrm{out}}}/E_{\textrm{R}_{\textrm{in}}}$
of $\mathcal{R}\,=\,3.3(1)$ in Fig. 3. Note that this is a different condition
for Fig. 2 with $\mathcal{R}\,=\,6.4(1)$, allowing for more pulse energy for
the read-in process (and so less for the read-out). The read-in efficiency
quickly increases and then begins to decrease when the read-in pulse energy is
near $0.7\,$nJ. This decrease is the consequence of the AC-Stark effect by
which the atomic resonances are frequency-shifted by the control pulse. The
effect scales as $\Omega^{2}/\Delta$ where $\Omega$ is the Rabi frequency of
the control field, and so higher control pulse energies result in shifts large
enough to move the optical fields out of two-photon resonance and reduce the
efficiency. One approach to prevent this is to optimise the spectral-temporal
mode of the control pulse for a given pulse energy Nunn2007 ; Gorshkov2007 .
This effect is not seen on the read-out efficiency because the optical mode
that is read out will frequency shift with the atoms.

Noise Performance – A critical requirement for any quantum memory is that the
output SNR be sufficiently high to retain the input quantum state upon
readout. In Fig. 4 we assess the SNR by quantifying the average number of
photons per pulse in the input, the retrieved output, and the noise floor
(when the input signal is blocked but the control pulses are switched on) for
$\mathcal{R}\,=\,6.4$. We measure the noise floor to be less than $10^{-6}$
photons per cycle. There is a slight linear increase of the noise as a
function of control pulse energy which we attribute to either leakage of the
control pulse or leakage of one-photon scattering events of the control with
the atoms. In spite of this we observe an SNR of around 4 orders of magnitude
for every control pulse energy tested using $\mu_{\textrm{in}}$ at about
$0.1$. For the data in Fig. 2 with input photon number $0.084$ we measure the
SNR to be $1.9(1)\,\times\,10^{4}$.

A useful metric to compare the performance of quantum memories is the ratio of
the noise counts on the output to the total memory efficiency:
$\mu_{1}=N/\eta_{\textrm{mem}}$ Gundogan2015 . This parameter $\mu_{1}$ is
essentially the number of photons per pulse on average at the input of the
quantum memory that gives an SNR = 1 at the output. For the data in Fig. 2 we
measure the noise to be $N=9(1)\times 10^{-7}$ photons per pulse over the
integration window of $500\,$ps. This leads to $\mu_{1}$ = $4.5(6)\times
10^{-6}$ which is approximately one order of magnitude improvement compared to
the previous ORCA demonstrations Kaczmarek2018 ; Finkelstein2018 ; Gao2019 ,
and to our knowledge the lowest reported for atom-based quantum memories.

Figure 3: ORCA memory vs pulse energy. Plot shows read-in efficiency (orange
circles), read-out efficiency (red triangles) and total memory efficiency
(purple squares) for different energies in read-in and read-out control pulses
for $\mathcal{R}=3.3(1)$. For this data, the measurement time per data point
is $10\,$s and integration window $500\,$ps.

We can infer the quantum performance this memory could achieve. The second-
order coherence of a retrieved single photon (which has ideally
$\mu_{\textrm{in}}=1$ and $g^{(2)}_{\textrm{in}}=0$) is given by
$g^{(2)}_{\textrm{out}}=2/(\mu_{\textrm{in}}/\mu_{\textrm{1}}+1)$ Thomas2019 ,
under the assumption that the noise is thermal and is created independently of
the memory process, so that the output can be treated as an incoherent
admixture of signal and noise. Our ORCA memory would retrieve the photon with
$g^{(2)}\leavevmode\nobreak\ =\leavevmode\nobreak\ 9(1)\,\times\,10^{-6}$.
Furthermore, the output fidelity for single-photon storage follows
$F=(\mu_{\textrm{in}}+\mu_{\textrm{1}})/(\mu_{\textrm{in}}+2\mu_{\textrm{1}})$
Gundogan2015 . The retrieved qubit fidelity of the ORCA memory would be at the
$99.9996\,\%$ level.

Figure 4: The average photon number per integration bin for the input (red
cricles), memory (purple squares) and noise (light blue diamonds) as a
function of control pulse energy. For this data, $\mathcal{R}\,=\,6.4(1)$, the
measurement time per data point is $10\,$s and integration window $500\,$ps.

Discussion – Our telecommunication-wavelength ORCA quantum memory has
demonstrated exceptional SNR performance over a GHz bandwidth. This opens the
possibility of interfacing with single-photon sources based on parametric-down
conversion or four-wave mixing with modest spectral filtering to match our
memory bandwidth, as well as to InGaAs quantum dot photon sources
Kolatschek2021 ; Lettner2021  the bandwidths of which are well-matched to our
device. Total memory efficiencies approaching unity should be achieved with
optimal temporal-spectral mode shaping of the control pulse Kaczmarek2018 ;
Gao2019 ; Guo2019 . For some applications, the limitation of our memory is the
Doppler-induced storage time, as discussed previously. Magneto-optical
trapping of the ensemble would eliminate atomic motion, albeit with the
additional complexity of ultrahigh-vacuum chambers. An alternate approach to
eliminate the dephasing is to perform velocity-selective optical pumping (VSP)
to target atoms with a narrow spread of velocities Main2021  or even tailor
atomic frequency comb structures for rephasing Main2021b . These trapped and
VSP approaches however sacrifice significant atom numbers and therefore total
memory efficiency. An approach that utilises all atoms is to apply additional
optical fields that compensate the dephasing by means of a controlled dynamic
AC-Stark shift Finkelstein2021 , or using additional optical fields to map to
an auxiliary state in order to facilitate a backward read out that would
automatically undo the accumulated phase Moiseev2001 . With Doppler-dephasing
eliminated, the storage time would be limited to the decay time of the $4$D5/2
state, of around $90\,$ns. Overcoming this would require additional fields to
map to longer-lived states, e.g. a higher-lying Rydberg state, or to ground
state.

Conclusion – We present a GHz-bandwidth quantum memory for telecom C-band
light. We demonstrate a total efficiency of $20.90(1)\,\%$ and a lifetime of
$1.10(2)\,$ns. The noise performance is unprecedented with a measured SNR of
$1.9(1)\,\times\,10^{4}$ for $\mu_{\textrm{in}}=0.084$, allowing for input
states with an average photon number as low as $4.5(6)\times 10^{-6}$ to yield
SNR = 1. We discuss avenues for further improvements on both storage time and
efficiency, which would fulfil a critical requirement for future quantum
technologies.

Acknowledgements – This work was supported by: Engineering and Physical
Sciences Research Council via the Quantum Computing and Simulation Hub
(T001062); Horizon 2020 research and innovation program under Grant Agreement
No.899814 (Qurope). PML acknowledges a UKRI Future Leaders Fellowship Grant
Reference MR/V023845/1.

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