Time-walk and jitter correction in SNSPDs at high count rates Andrew Mueller Applied Physics California Institute of Technology 1200 E California Blvd Pasadena CA USA and

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Time-walk and jitter correction in SNSPDs at high count rates

Andrew Mueller∗

Applied Physics, California Institute of Technology, 1200 E California Blvd, Pasadena, CA, USA and

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA, USA

Emma E. Wollman, Boris Korzh, Andrew D. Beyer, Ryan Rogalin, and Matthew D. Shaw

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA, USA

Lautaro Narvaez and Maria Spiropulu

Division of Physics, Mathematics and Astronomy, California Institute of Technology, 1200 E California Blvd., Pasadena, CA 91125, USA

(*amueller@caltech.edu)

(Dated: October 5, 2022)

Superconducting nanowire single-photon detectors (SNSPDs) are a leading detector type for time correlated

single photon counting, especially in the near-infrared. When operated at high count rates, SNSPDs exhibit

increased timing jitter caused by internal device properties and features of the RF ampliﬁcation chain. Varia-

tions in RF pulse height and shape lead to variations in the latency of timing measurements. To compensate

for this, we demonstrate a calibration method that correlates delays in detection events with the time elapsed

between pulses. The increase in jitter at high rates can be largely canceled in software by applying corrections

derived from the calibration process. We demonstrate our method with a single-pixel tungsten silicide SNSPD

and show it decreases high count rate jitter. The technique is especially effective at removing a long tail that

appears in the instrument response function at high count rates. At a count rate of 11.4 MCounts/s we reduce

the full width at one percent maximum level (FW1%M) by 45%. The method therefore enables certain quantum

communication protocols that are rate-limited by the (FW1%M) metric to operate almost twice as fast.

Over the last decade, SNSPDs have advanced rapidly to be-

come essential components in many optical systems and tech-

nologies, owing to their high efﬁciency (>90%)[1, 2], fast

reset times (<1 ns) [3] and scalability to kilopixel arrays [4].

The timing jitter of SNSPDs is also best-in-class – values as

low as 3 ps have been demonstrated in short nanowires [5],

and new high-efﬁciency designs exhibit sub-10 ps jitter [6, 7].

SNSPD jitter increases with count rate due to properties of

the nanowire reset process and features of the readout circuit.

The effect bears resemblance to time walk observed in silicon

avalanche diodes and other detectors where the pulses have

varying heights and slew rates [8] thereby causing a timing

measurement using a ﬁxed threshold to ’walk’ along the ris-

ing edge of the pulse (the labeled delay in Fig. 1a). At low

count rates SNSPDs exhibit very uniform pulse heights. How-

ever, at high counts rates where the inter-arrival time is on the

order of the reset time of the detector, current-reset and am-

pliﬁer effects lead to smaller and distorted pulses. If photon

inter-arrival times are not known a priori in the intended ap-

plication, the uncorrected time walk manifests as a perceived

increase in jitter (Fig. 1b).

The time-walk effect in SNSPDs is typically not reported,

as jitter is usually measured at low count rates where the de-

tector has ample time to reset following each detection. But

as communication and quantum information applications push

into higher count rates, the high count rate induced jitter be-

comes more relevant. LIDAR, quantum and classical opti-

cal communication, and imaging applications may all beneﬁt

from the development of new detection systems and methods

that keep jitter as low as possible in this regime.

We ﬁrst consider the features of SNSPD operation and read-

out that cause an increase in jitter with count rate. Then we

present multiple ways of mitigating or avoiding these effects,

before reviewing our preferred method that relies on a calibra-

tion and correction process.

The jitter increase observed at high rate originates from two

groups of system characteristics: (i) the intrinsic reset proper-

ties of the nanowire, and (ii) properties of the ampliﬁcation

chain. These inﬂuence the system’s jitter differently, thus it

is helpful to consider them separately. Added jitter from ei-

ther or both sources can emerge when an SNSPD system is

operated at high count rates.

The nanowire reset process determines how the detector be-

comes single-photon sensitive again after a detection. When

an SNSPD ﬁres, the current ﬂow in the nanowire momentar-

ily drops to near zero, then recovers in an inverted exponen-

tial fashion (Fig. 1a). An incident photon may trigger another

detection before the bias current fully returns to its saturated

value, producing a pulse with a lower amplitude and slew rate.

A ﬁxed threshold comparator will trigger on this lower pulse

later in time than a full amplitude pulse. If uncorrected for,

this time walk manifests as an increase in jitter at high count

rates.

The choice of readout ampliﬁers may also contribute to

added high count rate jitter. Pulses may be shifted in volt-

age and distorted if they arrive when the RF signal has not

yet reached a steady zero state following the previous detec-

tion. For example, pulses may arrive within an ampliﬁer-

induced undershoot region following previous pulses. This

phenomenon is illustrated in Fig. 1a as the area below 0 mV.

The duration of ringing or undershoot effects varies widely

depending on the design of the readout circuit. If they last

arXiv:2210.01271v1 [quant-ph] 3 Oct 2022

longer than the reset time of the nanowire bias current, the

calibration technique may correct for the potentially complex

interactions between pulse waveforms that overlap in time.

FIG. 1. a) Diagram illustrating two major sources of correlated high

count rate jitter. First, detections may occur during the reset time of a

previous detection. At this time the bias current in the nanowire is be-

low its saturated value so that a photodetection triggers an RF pulse

with correspondingly lower amplitude. Second, an RF pulse may

arrive in the undershoot region of a previous pulse, where the under-

shoot is a period of negative voltage induced by the low-frequency

cutoff properties of the readout ampliﬁer chain. b) Measured his-

tograms of detections from short 3 ps mode-locked laser pulses. With

lower attenuation and higher count rate, the observed timing uncer-

tainty is greater. Inset shows where respective count rates fall on

a maximum count rate (MCR) curve [9]. The MCR of an SNSPD

is often quoted at the 3 dB point, where the normalized efﬁciency

drops to −3 dB of its maximum value. The jitter increase due to time

walk manifests as a tail in the instrument response functions (inside

dashed black box) even at count rates signiﬁcantly below the 3-dB

point where detector efﬁciency has not started to drop signiﬁcantly

(e.g. the 1.7 Mcps data).

There are various methods for correcting for increased jit-

ter at high count rates. These include (i) the use of extra hard-

ware that cancels out some distortions, or (ii) simple software-

based data ﬁltering that ignores distorted time tags. We review

these techniques before covering the calibration and correc-

tion approach.

Variations in pulse height are a primary component of the

distortions that appear at high rates. Such variations in other

systems are commonly corrected with a constant fraction dis-

criminator (CFD) that allows for triggering at a ﬁxed percent-

age of pulse height rather than at a ﬁxed voltage. Adding a

CFD to an existing setup is straightforward, and there is prece-

dent for their use with SNSPDs [5]. But CFDs do not opti-

mally correct for variations in pulse shape that go beyond var-

ied vertical scaling. Also, multi-channel time-to-digital con-

verters (TDCs) used to read out large SNSPD arrays typically

only include ﬁxed-threshold comparators [4]. Implementing

CFDs on many channels may not be straightforward or cost-

effective.

In a simple software-based jitter mitigation method, each

time-tagged event may be accepted or rejected based on how

soon it arrives after the previous pulse. Those that arrive

within some pre-determined deadtime are assumed to be cor-

rupted by pulse distortions. These are rejected, and the rest are

accepted. This method can lower system jitter and maintain

high data rates, especially in the cases where only a few per-

cent of pulses are ﬁltered out. However, it can severely limit

count rate near the 3 dB point where the majority of counts

are rejected (see the supplementary material).

The calibration and correction approach we use requires no

new hardware and preserves the original count rate of the de-

tector. We calculate the time between a given current SNSPD

detection event and a preceding event. This inter-arrival time

is used to determine a timing correction for the current event

using a look-up table. A calibration routine described next is

needed build this look-up table. Applying these corrections

during real-time processing removes deterministic delays cor-

related with the time between time tags, leaving only stochas-

tic jitter.

FIG. 2. a) A qualitative diagram illustrating how inter-pulse timing

measurements t0and dare extracted. A small fraction of laser pulses

contain a photon due to the low mean photon number per pulse of the

attenuated laser. Pairs of subsequent photon arrivals are separated

by a time denoted by t0=ntl. b) Possible distributions of delay d

measurements for two different t0. The median of these deﬁnes the

extracted delay parameters ˜

dwhich form the y-axis in the calibration

curve illustrated in (c). The ˜

dvs t0curve in (c) approaches zero for

t0approaching inﬁnity. Blue and green arrows with matching color

and style denote the same measure in (a), (b), and (c).

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Time-walkandjittercorrectioninSNSPDsathighcountratesAndrewMuellerAppliedPhysics,CaliforniaInstituteofTechnology,1200ECaliforniaBlvd,Pasadena,CA,USAandJetPropulsionLaboratory,CaliforniaInstituteofTechnology,4800OakGroveDr.,Pasadena,CA,USAEmmaE.Wollman,BorisKorzh,AndrewD.Beyer,RyanRogalin,andMatthewD...

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Time-walk and jitter correction in SNSPDs at high count rates Andrew Mueller Applied Physics California Institute of Technology 1200 E California Blvd Pasadena CA USA and

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