11institutetext:  1Physics Division, Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA; 2Department of Physics, University of California San
Diego, San Diego, CA 92093, USA; 3STAR Cryoelectronics, Santa Fe, NM 87508,
USA; 4Department of Physics, University of California Berkeley, Berkeley CA,
94720, USA; 5 National Institute of Standards and Technology, Boulder, CO
80305, USA; 6 High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki 305-0801, Japan; 7 Electrical and Computer Engineering Department,
Princeton University, Princeton, NJ 08540, USA; 8 Physics Department, McGill
University, Montreal, QC H3A 0G4, Canada
11email<EMAIL_ADDRESS>
# Low Noise Frequency-Domain Multiplexing of TES Bolometers Using Sub-kelvin
SQUIDs

T. Elleflot1 A. Suzuki1 K. Arnold2 C. Bebek1 R. H. Cantor3 K. T. Crowley4 J.
Groh5 T. de Haan6 A. Hornsby4 J. Joseph1 A. T. Lee1,4 T. Liu7 J. Montgomery8
M. Russell2 Q. Yu4

###### Abstract

Digital Frequency-Domain Multiplexing (DfMux) is a technique that uses MHz
superconducting resonators and Superconducting Quantum Interference Device
(SQUID) arrays to read out sets of Transition Edge Sensors. DfMux has been
used by several Cosmic Microwave Background experiments, including most
recently POLARBEAR-2 and SPT-3G with multiplexing factors as high as 68, and
is the baseline readout technology for the planned satellite mission
_LiteBIRD_. Here, we present recent work focused on improving DfMux readout
noise, reducing parasitic impedance, and improving sensor operation. We have
achieved a substantial reduction in stray impedance by integrating the
sensors, resonators, and SQUID array onto a single carrier board operated at
250 $\mathrm{mK}$. This also drastically simplifies the packaging of the
cryogenic components and leads to better-controlled crosstalk. We demonstrate
a low readout noise level of 8.6 $$\mathrm{pA}$/$\mathrm{Hz}$^{1/2}$, which
was made possible by operating the SQUID array at a reduced temperature and
with a low dynamic impedance. This is a factor of two improvement compared to
the achieved readout noise level in currently operating Cosmic Microwave
Background experiments using DfMux and represents a critical step toward
maturation of the technology for the next generation of instruments.

###### Keywords:

Frequency-domain multiplexing, transition edge sensors, readout electronics,
Cosmic Microwave Background

††journal: Journal of Low Temperature Physics

##  1 Introduction

Digital Frequency-Domain Multiplexing (DfMux) 1, 2, 3 is a TES multiplexing
technique, in which sets of $\sim$1 $\mathrm{\SIUnitSymbolOhm}$ TES bolometers
are placed in series with superconducting LC resonators 4 that define unique
$\mathcal{O}$(1) $\mathrm{MHz}$ bias frequencies. A voltage bias is applied to
each detector at the resonance frequency of its associated LC resonator and
the resulting current is actively nulled. Residual current is amplified by a
cryogenic SQUID array and room temperature electronics and used to rapidly
update the nulling current 5. DfMux has been deployed in many Cosmic Microwave
Background (CMB) experiments, including most recently POLARBEAR-2 and SPT-3G
with multiplexing factors as high as 68 6. DfMux is also the baseline readout
technology for the planned CMB satellite mission _LiteBIRD_ 7.

Here, we present recent work aimed at reducing readout noise and parasitic
impedance, and improving readout packaging8, 9. In section 2, we describe the
hardware used for these measurements, including a technology demonstrator
circuit board called the Cold Integrated Multiplexing Module (CIMM). The CIMM
moves all cryogenic readout components onto a single circuit board that is
cooled to 250 $\mathrm{mK}$, reducing parasitic impedances that generate
crosstalk and detector instability and simplifying the readout packaging. In
section 3, we present results from measurements performed using the CIMM,
which include a factor of two reduction in readout noise and factor of five
reduction in parasitic resistance compared to currently operating CMB DfMux
systems. We conclude in Section 4.

Figure 1: (Color figure online) Left: Schematic of DfMux circuit with
cryogenic components in gray shaded box. Inductance between points _P1_ and
_P2_ is a source of bias frequency-dependent readout noise6. We minimize off-
chip parasitic inductance by putting points _P1_ and _P2_ on the SQUID chip
itself. Right: Photograph of CIMM printed circuit board with readout
components labelled.

##  2 Implementation

This work was done using a technology demonstrator circuit board called the
CIMM, described previously in8. In contrast with deployed Dfmux systems, in
which the cryogenic readout components are spread across two cryogenic
temperature stages 10, the CIMM holds all cryogenic readout components on a
single printed circuite board at 250 $\mathrm{mK}$. This dramatically reduces
the parasitic impedance associated with the electrical connection between the
SQUID and resonators, which is a source of crosstalk1, 11, and relaxes the
requirements on the $\mathcal{O}$(1) $\mathrm{m}$ cable that spans the 4
$\mathrm{K}$ to 250 $\mathrm{mK}$ temperature differential, allowing us to use
commercial twisted pair cable instead of the custom low-inductance cables used
in deployed instruments.

Due to a subtlety of the SQUID feedback scheme used, the inductance of the
SQUID array input coil and parasitic series inductance provide a mechanism for
bias frequency-dependent readout noise6, 11. We designed the CIMM such that
only on-chip impedances contribute to this effect (see Fig. 1). We chose to
use an SA13ax SQUID array because of its low input inductance of 70
$\mathrm{nH}$12. The SA13ax has several other favorable characteristics as
well, including high transimpedance ($Z_{t}=dV/dI_{in}$ where $V$ is the
voltage across the array and $I_{in}$ is the current through the input coil)
at 4 $\mathrm{K}$ of $Z_{t}\sim$700 $\mathrm{\SIUnitSymbolOhm}$ and variable
dynamic impedance ($R_{dyn}=dV/dI_{SQ}$ where $I_{SQ}$ is the current through
the SQUID array). The SA13ax is also used in the SPT-3G and PB-2 receivers at
a temperature of 4 $\mathrm{K}$.

The CIMM also holds one LC resonator chip and up to five TES chips, allowing
us to operate 40 detectors. The TES bias is provided by a 4.2 $\mathrm{nH}$
controlled inductance circuit board trace. The use of a reactive bias element
reduces power dissipation on the sub-kelvin stage and provides a small
reduction in readout noise.

Magnetic shielding was provided by several layers of high magnetic
permeability foil (Metglas 2705M). Care was taken to ensure that no
ferromagnetic materials were used in the fabrication of the circuit board. The
assembly was installed on the sub-kelvin stage of a cryostat cooled with a
pulse tube cryocooler and a helium adsorption cooler with a base temperature
of 250 $\mathrm{mK}$. The connection from the CIMM to the room temperature
electronics is made with twisted pair cable.

##  3 Results

###  3.1 SQUID Performance

We measured flux modulation curves at several temperatures between 4
$\mathrm{K}$ and 250 $\mathrm{mK}$. The modulation curves were smooth at 4
$\mathrm{K}$, but irregularities developed on the rising slope of curve
at/below 800 $\mathrm{mK}$. The SA13ax array has significantly different
dynamic impedance values on the rising and falling slope of the modulation
curve, with $R_{dyn}\sim$300 $\mathrm{\SIUnitSymbolOhm}$ on the rising slope
$R_{dyn}\sim$700 $\mathrm{\SIUnitSymbolOhm}$ on the falling slope (in the
polarity that we have chosen). Operating the array with low $R_{dyn}$ is
crucial to achieving the required reduction in readout noise and these
irregularities would prevent us from doing so. These irregularities are also
thought to be associated with excess SQUID noise. Others have demonstrated
reduced SQUID noise by using an RC snubber in parallel with the SQUID input
coil 13. We found that shunting the input coil with a cryogenic resistor
completely removed the irregularities at all accessible temperatures (see Fig.
2). The resistor and input inductance of the SQUID input coil form a low-pass
filter. We chose the shunt resistance value such that the cutoff frequency of
the filter is well above our readout bandwidth. During CIMM operation, the
shunt resistor is at a temperature of 250 $\mathrm{mK}$ and its Johnson noise
makes a negligible contribution to the total readout noise.

SQUID tuning is the process by which a current bias and flux bias is applied
to the SQUID in order to achieve an optimum between readout noise and
linearity. Tuning is usually performed using an automated routine, but can
also be performed manually. We performed the automated SQUID tuning routine at
several temperatures between 4 $\mathrm{K}$ and 250 $\mathrm{mK}$ and found
that the transimpedance, $Z_{t}=dV/dI_{in}$, and dynamic impedance,
$R_{dyn}=dV/dI_{SQUID}$, increased by 60% and 20% over this temperature range,
respectively. We also investigated the achievable range of $Z_{t}$ and
$R_{dyn}$ values by manually tuning the SQUID to eleven different bias points
while holding the CIMM at a constant temperature of 250 $\mathrm{mK}$ (Fig.
4). Using manual tuning, it is possible to increase $Z_{t}$ by nearly a factor
of two relative to the automated routine. But since $R_{dyn}$ is strongly
correlated with $Z_{t}$, the expected improvement in readout noise from manual
tuning is less than a factor of two. The impact of SQUID tuning on readout
noise will be discussed more in Section 3.3.

Figure 2: (Color figure online) Left: The modulation curve for an SA13ax SQUID
array measured at 250 $\mathrm{mK}$ with and without a 5
$\mathrm{\SIUnitSymbolOhm}$ shunt resistor in parallel with its input coil.
Right: Transimpedance of an SA13ax SQUID array as a function of temperature.
The array was tuned using an automated tuning algorithm that optimizes between
$Z_{t}$ and linearity.

###  3.2 TES Operation

We verified TES operation by simultaneously lowering the voltage biases
applied to a set of TES bolometers such that they cooled through their
superconducting transitions. This was done by first heating the CIMM above the
critical temperature of the sensors ($\sim$450 $\mathrm{mK}$) and applying a
large voltage bias of $\sim$10 $\mathrm{\SIUnitSymbolMicro V}$ using the
CIMM’s inductive bias element. We then cooled the CIMM to its base temperature
and then incrementally decreased the voltage biases while measuring the
resulting current. The results are shown in Fig 3. A total of 30 bolometers
were electrically connected and we successfully operated 28. There are broad
stable regions on many channels. Several channels become unstable at high
fractional resistance and we suspect that this is due to a mismatch between
the detector and electrical bandwidths, rather than instability due to
parasitic impedance. The residual resistance measured after the detector is
superconducting14, 15 contributes to crosstalk and detector instability at low
operating resistance. The measured values have a median of 60
$\mathrm{m\SIUnitSymbolOhm}$, which is a reduction by about a factor of five
compared to currently deployed systems.

Figure 3: (Color figure online) A set of TES bolometers are cooled through
their superconducting transition by lowering the applied voltage biases. The
TES bolometers used had varied normal resistance and saturation power.

###  3.3 Readout Noise

Power absorbed by a bolometer is transduced into an amplitude-modulation of
the narrow-band SQUID feedback current associated with the bolometer’s bias
frequency 5. In the absence of signals and detector noise, we can take the
demodulated signal as a measurement of readout noise. To perform this
measurement, we replaced the TES sensors with 1 $\mathrm{\SIUnitSymbolOhm}$
resistors, which do not have a superconducting transition in the relevant
temperature range and do not have sensitivity to optical power. The resistors
contribute Johnson noise to the measurement, which we conservatively estimated
by assuming a low electron temperature of 250 $\mathrm{mK}$ and a resistance
of 1 $\mathrm{\SIUnitSymbolOhm}$. This is removed when analyzing readout noise
data, though it only accounts for about 10% of the total measured noise.

Since the SQUID array used can be operated with low or high $R_{dyn}$, we were
able to check the impact of $R_{dyn}$ on readout noise. The SQUID dynamic
impedance impacts readout noise in two ways: it converts the input current
noise of the first stage amplifier into a voltage noise at the output of the
SQUID, and it forms a low-pass filter with the capacitance of the cryogenic
wiring between the SQUID and 300 $\mathrm{K}$ amplifier 11. The latter effect
was not expected to be important for this measurement because we are using a
short length of cryogenic wiring with capacitance of $\sim$30 pF, resulting in
a cutoff frequency of 8 MHz and 16 MHz for high $R_{dyn}$ and low $R_{dyn}$
tuning, respectively, both of which are well above our readout bandwidth.
Comparing the readout noise from high and low $R_{dyn}$ SQUID tuning, we
measured a noise reduction of 6-8 $$\mathrm{pA}$/$\mathrm{Hz}$^{1/2}$ with low
$R_{dyn}$ tuning across the range of bias frequencies, which matched our
expectations from the current noise of the room temperature amplifier.

Figure 4: (Color figure online) Measured values of $Z_{t}$ and $R_{dyn}$ (top)
and readout noise (bottom) at 250 $\mathrm{mK}$ with several different values
of current bias applied to the SQUID array.

Next, we looked at the effect of optimizing SQUID tuning on readout noise. We
measured readout noise while the CIMM was cooled to 250 $\mathrm{mK}$ for
eleven different manual SQUID tunings. Despite the change in $Z_{t}$ and
$R_{dyn}$ by a factor of about two over the range of current biases, we
measure only a $\sim$10% change in median readout noise. This is likely due to
the correlation between $Z_{t}$ and $R_{dyn}$ and the fact that they decrease
and increase readout noise, respectively. There is a broad minimum in readout
noise, which indicates that there is flexibility in optimizing SQUID linearity
without significantly affecting readout noise performance. The lowest achieved
median noise level is 8.6 $$\mathrm{pA}$/$\mathrm{Hz}$^{1/2}$. This represents
a factor of two reduction in readout noise compared to currently observing CMB
experiments using DfMux. The bias frequency dependence of the readout noise is
also greatly suppressed. We measure an increase in noise by about 15% at our
highest bias frequencies, which should be compared to a $\sim$100% increase in
noise in deployed CMB DfMux systems.

We refer the measured readout noise to the input of a _LiteBIRD_ -like
bolometer by assuming a 1 $\mathrm{\SIUnitSymbolOhm}$ TES operating resistance
and a conservative 1 $\mathrm{pW}$ electrical bias power16. In all observing
bands, the measured readout noise is below the projected _LiteBIRD_
sensitivity17.

Figure 5: Measured readout noise as a function of bias frequency for 36
channels. The median value is 8.6 $$\mathrm{pA}$/$\mathrm{Hz}$^{1/2}$. The
slight increase in noise with frequency is likely due to an effect related to
the SQUID feedback6 and is suppressed significantly compared to deployed
instruments.

##  4 Conclusions

We have demonstrated several improvements to TES multiplexing using DfMux
readout, including a substantial reduction in readout noise and operation of
many TES bolometers under an inductive bias. The reduction in readout noise is
a crucial step toward future applications of DfMux readout. The noise
reduction was achieved by operating the SQUID array at lower temperature and
with low dynamic impedance tuning. Additionally, parasitic impedances which
are known to affect the frequency dependence on the readout noise have been
significantly reduced by the circuit board design. The decrease in residual
superconducting resistance in the TES bias circuit will allow for TES
operation at lower resistance, resulting in higher responsivity and a further
suppression of readout noise compared to deployed CMB DfMux systems. The
improvements made to the cryogenic architecture significantly relax the
constraints on the cryogenic cables, making the cryogenic packaging more
robust and much simpler to procure. We are developing a version of the CIMM
that is compatible with the POLARBEAR-2 receivers and we hope to deploy
several CIMM modules in the near future. The datasets generated during and/or
analysed during the current study are available from the corresponding author
on reasonable request.

###### Acknowledgements.

This work was supported by Early Career Research Program, Office of Science,
of the U.S. Department of Energy. Many of the figures were made using
matplotlib 18 and PGF/TikZ 19. Analyses were conducted using python scientific
packages 20, 21.

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