Abstract

Detecting light is fundamental to all optical experiments and applications. At the single photon level, the quantized nature of light requires specialised detectors, which typically saturate when more than one photon is incident. Here, we report on a massively-multiplexed single-photon detector, which exploits the saturation regime of a single click detector to exhibit a dynamic range of 123 dB, enabling measurement from optical energies as low as 107 photons per pulse to ∼ 2.5 × 105photons per pulse. This allows us to calibrate a single photon detector directly to a power meter, as well as characterize the nonclassical features of a variety of quantum states.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical detectors are based on a broad range of physical principles, which dictate the range of powers to which they are sensitive. The dynamic range of an optical detector is defined as the difference between its noise floor and saturation intensity. Above the saturation intensity, the detector response is constant, such that different light levels cannot be distinguished. We differentiate saturation from the breakdown intensity of the detector, namely pulse energies above which the detector response is permanently changed (i.e. latched or damaged). For different optical detectors, the saturation intensity and breakdown intensity is determined by its principle of operation. For example, ideal single photon binary (“click, no-click”) detectors are saturated when at least one photon is incident. As such, single-photon level detectors cannot be used to measure pulse energies beyond one photon. To overcome this limitation, multiplexing schemes are used to divide an incoming pulse such that the average intensity per multiplexing bin is below the saturation level. Existing multiplexed single-photon detection schemes [1–15] still suffer from saturation effects in that they are not sensitive to photon numbers greater than the number of bins in the multiplexed device [16]. Photon-number-resolving detectors also suffer from saturation, however this may be overcome by careful analysis of the detector response function [17].

Here, we show that we can overcome this saturation limitation, and extend the sensitivity of single-photon binary detectors to 250000 photons per pulse. To do this, we use a detector coupled to a loop of fibre, as first introduced by Banaszek and Walmsley [3]. Below the saturation limit, this detector architecture generates a logarithmic response to the incoming pulse energy [10, 18]. However, we show that this device can be pushed beyond its saturation level, and information on the incident pulse energy can still be extracted, limited only by the breakdown level of the click detector. This produces a massively-multiplexed detector with a dynamic range of 123 dB. We perform measurements at low photon-numbers, where this detector is capable of differentiating different quantum states based on their photon statistics, and at high pulse energy, whereby the same device can be directly compared with a power meter. This provides a traceable comparison at the single-photon level to optical standards without requiring calibrated attenuation [19] or synchrotron radiation [20, 21].

2. Time-multiplexed detector design

Our multiplexed detector comprises a variable beam splitter with one output connected to one input, and the other output connected to a single-photon detector, as shown in Fig. 1. The variable beam splitter can be active, where the entire pulse is switched into the loop, before decaying, or passive, whereby the reflectivity of the beam splitter is constant and part of the initial pulse energy is reflected directly to the detector, comprising the first bin. For an input pulse of given intensity, an output pulse train with a characteristic decay of optical energy is produced. We ensure the pulse duration and dead time of the detector are much shorter than the round trip time of the loop, discretizing the ring-down in a series of time bins j.

 figure: Fig. 1

Fig. 1 Binary detector coupled to a resonator with coupling R(t). For active switching, R(t = 0) = 0, i.e. all the light is switched into the loop. Subsequently, R(t) = R is constant. In the passive case, R(t) = R is constant for all times.

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The amount of light coupled to the first bin depends on whether active or passive switching of the light pulse into and out of the loop is used. In each subsequent bin some fraction of light remaining in the loop is coupled to the detector. If this energy is below the saturation level of the detector, the probability of a click in a given bin j follows an exponential decay, as previously studied [3, 5, 10, 18]. However, if the pulse energy remains above the saturation level, then the click probability of the initial bins will be close to unity. In general, we can calculate the click probability of a particular bin j, which must account for the coupling to previous detection bins and the number of photons in the incoming pulse. The detection probability of bin j is

pj=(1νj)n=0P(j|n)ρin(n)+νj,
where P (j|n ) is the probability that bin j is occupied with at least one photon, given an incident number of photons n, ρin (n ) is the photon number probability distribution of the input state and νj ≪ 1 is the dark count probability. A general expression for P (j|n ) for j ≥ 2 is, in each case
P(j|n)={1[1(Rη)j1η(1R)]nactive,1[1(Rη)j1R1(1R)2]npassive,
where η is the loop roudtrip efficiency. The probability for the first bin, P(1|n), also depends on whether the loop is actively or passively switched. This may be written:
P(1|n)={1[1η(1R)]nactive,1Rnpassive.

From these expressions, pj can be analytically expressed in closed form for several classes of optical states, namely photon number (Fock) states, coherent states and thermal states, in terms of their mean photon number n¯. Analytic forms for each state, in the case of active and passive loop architecture, are given in the Appendix. In the low mean photon number regime, all classes produce probabilities pj ≥2 which are modelled by an exponential decay, an example of which is shown in Fig. 2(a). However, as the mean photon number of the incident light increases, saturation of the early bins occurs, leading to photon detection probability histograms such as in Fig. 2(b).

 figure: Fig. 2

Fig. 2 (a) Click probability pj for a passive loop detector as a function of bin j, for a Fock state (blue), coherent state (green) and thermal state (orange), each with a mean photon number of n¯=3, outcoupling parameter R = 0.5, loop efficiency η = 0.9 and noise contribution ν = 10−3. (b) As above, but with the mean photon number n¯=300 in each case (all other parameters remain the same). In general, each of these classes produces slightly different distribution of clicks per bin pj, for fixed mean photon number. This occurs due to the nonlinear response of the click detectors, and is most clearly identified close to the saturation regime (e.g. around bin 5) in (b).

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Note, however, that despite this saturation, the power incident on the detector can still be inferred directly from the data. This allows single-photon-level detectors to increase their effective sensitivity towards very bright states.

3. Bright-light sensitivity

To demonstrate sensitivity to bright light, we conducted an experiment in which a pulsed laser with a repetition rate of 50 kHz was connected to a passive loop structure (for more details see Appendix). After the loop, 1.61±0.08 nW average power was measured with a power meter, corresponding to 251000±12500 photons per pulse. An example of the resulting histogram of the bin click probabilities pj is shown in Fig. 3. From this histogram, and Eq. (2), we can determine the mean number of photons per pulse measured by the click detector to be n¯out=208011±460 with a relative error of σn¯/n¯ of 0.22%. The ratio between n¯out and the input mean photon number, as measured by the power meter, gives the detection efficiency of 82.8%. This procedure does not require cascaded calibrated attenuators [19]; further details on the calibration procedure and error analysis are provided in the Appendix. Moreover, as an alternative to a bright light standard, one could use this device to bridge to the bright light regime using a known single-photon detector calibrated to a quantum luminescence standard, i.e. a correlated single photon source arising from parametric down-conversion [22, 23].

 figure: Fig. 3

Fig. 3 Histogram of click probabilities on linear and log scales, for a coherent state input with an average of ∼250 000 photons per pulse to the passive loop detector with a repetition rate of 50 kHz. Error bars are based on estimating the success probability of a Binomial distribution (shown in black).

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The dynamic range of the detector is defined by DR=10log10(n¯/ν)=10log10(nmax/νηR), where nmax is determined by the damage threshold of the detector used, i.e. the pulse energy that causes the detector to become unresponsive to subsequent pulses. Using the bright measurement above, with an input photon number per pulse of n¯=2.5×105 and a the lower limit (minimum sensitivity) given by the noise floor (ν = 1.2 × 10−7 photons per pulse), we therefore demonstrate a dynamic range of 123 dB.

4. Measuring nonclassical signatures

In addition to measuring bright states of light, the detector is also sensitive to nonclassical features of the input photon distribution; correlations between different click events in different bins can yield further insight. There exists extensive analysis of statistics arising from multiplexed detectors which can determine whether or not the underlying photon statistics are consistent with a classical distribution [18, 24–35]. One important example is the sub-binomial parameter [26], which translates sub-Poissonian statistics of light into sub-Binomial click statistics. However these analyses typically rely on equal splitting between bins. To overcome this limitation, the generalisation by Lee and co-workers [33] leads to the definition of the Poisson-binomial parameter

QPB=N(Δc)2c(Nc)N2σ21,
where ck describes the probability of k bins firing, which has a mean, and variance, given by
c=k=0Nkck;(Δc)2=k=0N(kc)2ck
and
m=1Nj=0Npj;σ2=1Nj=0N(pjm)2.

This describes the mean probability and variance, respectively, of a bin providing a click event, given individual bin click probabilities pj, for a total of N bins. For uniform splitting among the bins, m = pj and σ2 = 0, such that Eq. (4) reduces to the binomial parameter QB [26]. A sufficient condition for nonclassical light is negativity of the QPB parameter.

To demonstrate its ability to distinguish nonclassical light, we performed an experiment (Fig. 4) with three different types of states over a broad range of power levels power levels input to both active and passive implementations of the loop detector. We present the QPB and QB parameters as a function of mean photon number for heralded single photons, thermal states and coherent states in an actively-switched Fig. 5(a) and passively-switched Fig. 5(b) loop in. The multi-thermal states present statistics somewhere between thermal and Poissonian statistics, due to more than a single spectral mode emerging from the crystal. We estimate from our pump bandwidth and crystal parameters a spectral purity of 57%, or a Schmidt number of K = 1.8 contributing thermal modes. The classicality of the multi-thermal photon statistics, in combination with the exponentially decaying pj probabilities, is not captured by a naive application of the QB parameter to our data, as it shows negativity (nonclassicality). The QPB parameter, on the other hand, handles this effect as expected. Both parameters correctly identify the nonclassicality of the heralded signal photons.

 figure: Fig. 4

Fig. 4 Detection of sub-binomial light with a dynamic loop detector. Heralded single photons and thermal states (from Periodically-poled Potassium Titanyl Phosphate - PPKTP waveguide), and coherent states are coupled into the loop with a fast Pockels cell polarization switch. Then on each pass through the loop a small fraction of the light, determined by the angle of the half-wave plate (HWP), is coupled out to the superconducting nanowire single photon detector (SNSPD).

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 figure: Fig. 5

Fig. 5 Classicality parameters QPB and QB as measured by the loop detector for heralded PDC states, for (a) actively switched loop (with coupling parameter R = 0.1); and (b) passively switched loop (with R = 0.5). Error bars are based on 10000 Monte-Carlo-Simulations where the mean and variance are given by the measured ck distributions.

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5. Conclusion

In summary, we have demonstrated how multiplexing a single binary detector can be used to measure light levels across a large dynamic range (123 dB). We have used this device to perform precise calibration, as well as identify nonclassical phenomena in the click statistics. This high dynamic range can be used in a broad range of applications, for example precision absorption spectroscopy and characterisation of high-extinction components across a broad range of energies.

Appendix

A. Methods

Light sources

For coherent states, we use a picosecond-pulsed semiconductor laser at 1550 nm with a variable repetition rate, varying the mean photon number by attenuation. For multi-thermal states and heralded single photons, we pump a periodically-poled potassium titanyl phosphate waveguide designed for type II parametric down-conversion. The signal and idler modes (around 1540 nm) are split on a polarization beam splitter (PBS), and the idler is detected to herald the signal single photons, or undetected for (nearly) thermal states in the signal mode.

Loop architecture

For quantum characterisation, these states are sent to the active loop detector, which is made up of a free-space and fibre loop, with optional deterministic incoupling accomplished with an electro-optic Pockels cell [36]. The input light pulses are vertically polarized, then switched to horizontal with the Pockels cell to remain in the loop, passing through a fibre delay line (loop length 480 m, corresponding to a delay of 2.4 µs). The outcoupling half-wave plate (HWP) sets the fraction of the light outcoupled on each round trip, by rotating some of the light to vertical polarization. Note that the outcoupling optics is not the same as the incoupling optic, resulting in slightly different loss for the first bin, compared to subsequent bins. The outcoupled light is sent to a commercial superconducting nanowire single photon detector (SNSPD) from Quantum Opus. The Klyshko efficiency of the photon (when using down-conversion) coupled directly through the loop (half round-trip) is (20 ± 2)%, and the round trip loop transmission is (82 ± 2)% Depending on whether the Pockels cell was activated, we implement either the active or passive loop detector structure.

For the high dynamic range measurements, we implemented a passive loop architecture constructed exclusively from optical fibres (loop length 30 m, corresponding to a delay of 156 ns between bins) and a low-loss fibre beam splitter. All components were polarization-maintaining, such that the (polarization dependent) detector efficiency is constant for each bin, and the beam-splitter ratio (which is also typically polarization-dependent) is constant for each round trip. The round trip loop transmission in this case was 86%, which includes additional (artificially-induced) loss to produce a faster decay rate and therefore allows for a higher repetition rate. In these experiments, we used a commercial superconducting nanowire single photon detector (SNSPD) from Photon Spot.

Detector and data acquisition

In both the active and passive experiments, the detector output was recorded on a time-tagger, allowing for all events to be recorded. Gating windows of 4 ns were applied in post processing to reduce the effect of dark counts. The gating windows are separated by the corresponding loop delay, corresponding to the time for the pulse to propagate the length of the fibre loop, and well above the dead time of the detector.

B. Analytic expressions for bin click probabilities

Based on Eq. (1) and expressions for the photon number distributions ρin for Fock states ρFock=δn¯,n, coherent states ρcoh=exp[n¯2]n¯nn! and thermal states ρtherm=n¯n(1+n¯)n+1, and whether the loop is actively or passively switched, the following analytic expressions for the bin click probability pj can be derived:

Active:

pjFock=1(1ν)[1(1R)R1(Rη)j]n¯
pjcoh=1(1ν)exp[(1R)R1(ηR)jn¯]
pjtherm=1(1ν)RR+(1R)(Rη)jn¯

Passive:

pjFock={1(1ν)Rn¯j=11(1ν)[1(1R)2R1(Rη)j1]n¯j2
pjcoh={1(1ν)exp[(1R)n¯]j=11(1ν)exp[(1R)2R1(ηR)j1n¯]j2
pjtherm={1(1ν)11+(1R)n¯j=11(1ν)R2ηR2η+(1R)2(Rη)jn¯j2

In all cases we assume a mean photon number n¯ and a constant dark-count probability per bin (noise floor) νj = ν for all time bins.

C. Calibration procedure

The high dynamic range of the detector can be used to bridge the gap between bright light and quantum-based optical power standards. To calibrate the detector efficiency to a known bright light standard, we suggest the following procedure, using the setup shown in Fig. 6. Given a coherent state with a mean photon number determined with a power meter n¯PM=power/(photonenergy×repetitionrate), one can define a system detection efficiency ηSDE as

ηSDE=n¯measuredndarkcountsn¯PM
where n¯measured is calculated from on-off detector response at the output of the loop detector.

 figure: Fig. 6

Fig. 6 Schematic of calibration setup. n¯in indicates the mean photon number per pulse incident on the loop. n¯out is the mean photon number after the loop, summed over all bins. n¯out can be switched between an on-off detector or a power meter. Reliable switching is important for the calibration procedure as systematic errors can be produced during this process.

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To calculate n¯measured, we begin with the mean photon number per bin n¯j. For the active case this is given by

n¯j=n¯in(1R)Rj1ηj,
and for the passive case
n¯j={n¯inRj=1n¯in(1R)2Rj2ηj1j2
where, in both cases n¯ is the number of photons per pulse present prior to entering the loop.

With these equations we can also calculate the total outgoing mean photon number

n¯out=j=1n¯j.

Which means for the active case

n¯out=n¯in(1+R)η1+Rη
and for the passive case
n¯out=n¯in(Rη+2Rη)1+Rη.

Experimentally we can now measure the click probability per bin pj with the click detector under test (cf. Fig. 7(a)). Using Eqs. (8) and (11) (and substituting n¯=n¯in) for coherent states as well as Eqs. (17) and (18) each bin probability pj gives an estimate for the mean photon number per pulse n¯out|j (see Fig. 8). For the active case we can write

n¯out|j=Rη(Rη)jln[1ν1pj]1+Rη
and for the passive case
n¯out|j={(R+η2ηR)ln[1ν1pj]R(1Rη)j=1(R+η2ηR)(Rη)1jR1ln[1ν1pj](1Rη)(R1)2j2.

 figure: Fig. 7

Fig. 7 Histogram showing the bin probability in linear (top) and logarithmic (bottom) scale for a calibration measurement (a) and a highly attenuated input (b), using a passive loop. Red curves: Fit based on Eq. (11). The fit for the attenuated coherent state gives an estimate for R = 0.91370 ± 5 · 10−5 and η = 0.8615 ± 3 · 10−4.

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 figure: Fig. 8

Fig. 8 Inferred mean photon number per pulse n¯j after the loop from measured click probabilities pj. Red line: mean value of n¯measured=208011. The first bins j ≤ 25 are excluded because dead times from back reflections reduced the count rate (see next section for further details).

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To arrive at a final estimate of the mean photon number n¯measured, we use the arithmetic mean weighted by the experimental error in the individual estimates of n¯out|j, as determined above. This provides our unbiased estimator of n¯out, with the weights given by the inverse of the variances σn¯out|j2 (see next section for details on how these errors are calculated) of each measurement of n¯out|j, i.e.

n¯measured=jwjn¯out|jjwj,
where
wj=1σn¯out|j2.

Fig. 8 shows the measured values for n¯out|j and n¯measured. The limits on the summation over j are chosen such that the errors in the individual measurements of n¯out|j are not underestimated (i.e. that their uncertainties are reliable). From Fig. 9, this is from bin| 25 onwards. The use of the weighted arithmetic mean penalises values with high error bars; therefore including high bin numbers, where the uncertainty is high, does not limit our precision.

 figure: Fig. 9

Fig. 9 Relative uncertainty contributions σi2n¯2(dn¯di)2 from each error source, arising from uncertainty in the measured bin probabilities pj (red line), the loop loss η (green line), the loop reflectivity R (blue line) and the noise ν (gold line). Note that these quantities are evaluated using the a posteriori weighted mean n¯ i.e. the mean photon number averaged over all j. The blue dots are the total relative error contributions, and red crosses the relative error in pj, evaluated at the individually determined photon number n¯out|j (in contrast to the solid lines). The deviation of these measures at low bin number j ≲ 25 arises from undercounting caused by back-reflection-induced inefficiency, resulting in an underestimate of the error associated with pj. This is discussed further in the following section.

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With this summation (j ≥ 25), the mean photon number per pulse is n¯measured=208011±460. The value of n¯measured can now be compared to the value from the power meter nPM = 251000 ± 12500 to calculate the System Detection Efficiency (SDE), i.e. Eq. (13). The results in an ηSDE = 82.8 ± 4%. The dominant error comes from the power meter reading, not n¯measured, and we neglect errors in laser drift and fibre coupling efficiency. The value of ηSDE includes the fibre into the cryostat and the detector efficiency. It can be seen from Eq. (19) that the value of n¯out for the active case only depends of the product ηR. This product is well known as the slope of the histogram in the decay region (logarithmic plot) is 1 − ηR. The passive case, however, is different. Here the individual values of η and R must be known to infer nout. Therefore we need an additional measurement step for the passive case in order to determine at least one of R and η. We suggest to add an unknown attenuator before or after the loop such that the first bin is non-saturated. An example measurement can be seen in Fig. 7(b). By fitting this histogram with Eq. (11) values for R and η can be determined. The full information about these two values is contained in the jump from the first bin to the second as well as in following linear decay region. Therefore the attenuator must be strong enough that the first bin in non-saturated (otherwise the uncertainties in the click probability are too high, c.f. next section) and low enough to see the linear decay region before the dark count level. The advantage of this method is that the beam splitter reflectivity R and the loop efficiency η can be determined without changing the loop.

It should be noted that losses before the loop and after the loop (up to the point where either a power meter or a click detector is placed) do not matter for the calibration procedure as this is a rescaling of the power that is already considered by the power meter reading.

This method can be easily altered to measure the power of bright pulses if the SDE is known, for example to bridge a quantum standard to bright light.

D. Estimation of uncertainty

The relative uncertainty in n¯measured arises from the uncertainty in the component quantities from which n¯out is calculated. For each bin j, we obtain an independent estimate of n¯out, i.e. n¯out|j. This is given by Eq. (20) The relative uncertainty in each of these estimates of n¯out|j is given by Gaussian error propagation:

σn¯out|jn¯out|j=[σpj2n¯out2|j(dn¯outdpj)2+σR2n¯out2|j(dn¯outdR)2+ση2n¯out2|j(dn¯outdη)2+σν2n¯out2|j(dn¯outdν)2]1/2|j={σpj21(1pj)2ln(1ν1pj)2+σR2[1jR+1R(1Rη)+1R(12R)+η(12R)22R13R+2R2]2+ση2[1jη+(1R)2(R+η2Rη)(1Rη)]2+σν21(1ν)2ln(1ν1pj)2}1/2|j.

The absolute errors are all experimentally determined: σR, ση are determined by the fitting procedure, explained in the previous section. σν is determined from Poissonian error from the dark-count probability measurements. Only σpj, determined by Poisson error in the click statistics, depends on the bin number; the other absolute errors are constant for each bin. For the data shown above, the absolute and relative uncertainties are given in table 1: The contribution of each source of error to the relative error in the photon count rate to be determined is shown graphically in Fig. 9. The blue dots correspond to evaluating Eq. (23) as a function of the bin number j, to show the overall uncertainty in determining n¯out|j at each bin. The solid lines correspond to evaluating the individual contributions σi2n¯out2(dn¯outdi)2 for i ∈{pj, R, η, ν}. Note that we use the weighted arithmetic mean as our estimate of the mean photon number n¯out, rather than the individually determined estimates for n¯out|j, since these estimates under-count at low bin numbers, for reasons described in the section on limits and assumptions, below. As a comparison, we show with red crosses σpj2n¯out2|j(dn¯outdi)2|j, i.e. the relative uncertainty contribution due to pj, evaluated at the individual bin number j, and not the weighted average. The result of the undercounting shows a clear underestimate of the relative uncertainty at j ≲ 25.

Tables Icon

Table 1. Absolute and relative errors of the measured values

The resulting uncertainty of the weighted arithmetic mean is thus given by the inverse root of the sum of the weights, i.e.

σn¯=1(jwj)1/2.

Given the weights calculated above, and summing from bin 25, we obtain a relative error of σn¯2/n¯2=0.22% in our determination of the mean photon number after the loop.

The uncertainty in determining an unknown System Detection Efficiency (SDE) stems from uncertainties in its constituent quantities. We compare our method to that used in [19], in which the expression for the SDE is SDE = PCR /[PC a2, a3RSW/(1 − ρ)/Eλ] given by the photon count rate PCR, the power on the power meter Pc, the attenuations a2, a3, the switch ratio RSW, the reflectivity of the fibre connected to the switch ρ, and the photon energy Eλ. The principle uncertainties arise in the quantities PCR, PC, a2,3 and RSW. The relative uncertainties in PC and RSW remains present in both experiments. To evaluate each approach, we compare the relative error contributions arising from calibrated attenuation and determination of the photon count rate. In [19] (using the values in Table SI 2 and Eq. (1)), this contribution is the root quadrature sum of σPCR/PCR = 0.14% and σα/n¯=0.20%. Since two attenuators were used, this value contributes twice to the overall relative uncertainty. Thus the relative uncertainty arising from these two sources is (σPCR/PCR)2+2(σα/α)2=0.32%. Our method does not use calibrated attenuators, thereby removing this source of measurement error, to comparable error therefore arises in σn¯/n¯=0.22%, as indicated above. Our method therefore provides a significant reduction in the error when compared with using calibrated attenuators.

The precision with which the inference of input mean photon number detected via the loop can be achieved depends on both the fitting error for determining R and η, as well as the statistical error from the number of data points used. Both of these depend on the number of occupied bins above the noise floor of the device. For noise ν ≪ 1, we can approximate the number of occupied bins above the noise floor as

jmaxlog10[νnmax]log10[η(1R)].

The upper limit to the dynamic range n max is determined by the damage threshold of the detector used, i.e. the pulse energy that causes the detector to become unresponsive to subsequent pulses. For SNSPDs the first failure mode is latching at high count rates, where the device creates a self-sustaining hotspot and cannot reset without manual reduction of the bias current. We have found a large region of pulse energy (1 to 107 photons per pulse) where the latching point depends only on the repetition rate and not on the pulse energy (see Fig. 11). Thus SNSPDs are ideal candidates for the loop detector, as they can handle many photons in the first bins and still be single-photon sensitive with low noise in the later bins. We have tested up to n¯=4.8×107 photons per 100 ps pulse at 100 kHz repetition rate with a WSi SNSPD, and found no latching or degradation of performance.

 figure: Fig. 10

Fig. 10 (a) Raw time-tags for a bright pulse, zoomed in on the first 24 bins, showing clear excess counts outside of the expected loop bins (orange). This arises from spurious back-reflections present in the setup. (b) Click probability as a function of bin number. In early bins 2 ≤ j ≲ 20, back reflections cause a reduction in the expected counts since they induce dead time, which can be seen by a deviation from the expected click probabilities.

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 figure: Fig. 11

Fig. 11 Single bin click probability as a function of incident number of photons per pulse and pulse repetition rate. Once latching occurs, no counts can be measured (upper right corner).

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E. Limitations and assumptions

The procedure we present relies on a few important assumptions to be applied correctly. Most generally, the detector efficiency to be calibrated must remain constant for all bins. Effects which change this assumption should be avoided, or where possible, appropriately accounted for. We neglect random drift of the efficiency or laser power, since the timescale over which we take data is relatively short (ca. 150 s). More critical is bin-to-bin variations in efficiency. This could be caused by a different polarization for each bin, and an associated polarization-dependent efficiency. We obviate this error source by using polarization-maintaining fibre components to build our loop. A further source of error arises from missed counts due to back-reflection-induced dead time losses. In early bins, there are a great many photons circulating in the setup. While most photons are in the loop, a small fraction may be reflected back towards the detector, out of synch with the actual photons to be measured. Whilst these will be detected outside the acceptance window, their detection will cause some dead time, during which time the detector is “blind” to further photons. This effect is visible in the raw time-tag data, shown in Fig. 10(a). This plot is effectively an optical-time-domain-reflectometery (OTDR) spectrum, evaluated over many orders of magnitude. It shows counts appearing outside the expected bins (shown in orange).

Thus, true events may be missed. This is effect is clearly seen in Fig. 10(b), where the second bin in particular is significantly lower than expected. Reducing back reflections is therefore crucial to the reliable operation of this system.

F. Trade-off between operating speed and dynamic range

In the case of SNSPDs, the upper limit on the dynamic range is determined by the number of occupied bins per unit time that the detector can handle before it latches. Crucially, over a certain range of repetition rates, it does not depend on the power delivered the detector. We demonstrate this by varying the repetition rate and mean photon number per pulse incident on the detector. The resulting count rate is shown in Fig. 11.

One might expect that the product of photons per pulse n¯ and repetition rate r (i.e. n¯×r=P, the power delivered to the detector) would be constant, with a corresponding constant latching threshold. This is true up to a mean photon number of one photon per pulse, where the latching threshold is ∼ 106 photons per second or 0.1 pW at a wavelength of 1550 nm. However, above this, the mean photon number per pulse plays almost no part in determining the latching threshold. This allows us to put much more incident power on the detector before it latches, provide the repetition rate is slightly lower. The highest we achieved is 5 × 107 photons per pulse at a repetition rate of 100 kHz, yielding an optical power of 0.6 µW. This measurement was limited by available laser pulse energy; higher power may well be achievable. The consequences of this effect may also be interesting in terms of the detector dynamics and heat dissipation models, which clearly behave nonlinearly with incident optical power.

Funding

European Union Horizon 2020 665148 (QCUMbER); DFG (Deutsche Forschungsgemeinschaft) SFB/TRR 142; Natural Sciences and Engineering Research Council of Canada; European Commission ERC project QuPoPCoRN (725366).

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2. J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74(7), 902–904 (1999). [CrossRef]  

3. K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52–54 (2003). [CrossRef]   [PubMed]  

4. D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387 (2003). [CrossRef]   [PubMed]  

5. J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003). [CrossRef]  

6. M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003). [CrossRef]  

7. D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004). [CrossRef]  

8. S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 542–3337–352 (2007). [CrossRef]  

9. V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007). [CrossRef]  

10. G. A. P. Thé and R. V. Ramos, “Multiple-photon number resolving detector using fibre ring and single-photon detector,” J. Mod. Opt. 54(8), 1187–1202 (2007). [CrossRef]  

11. A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008). [CrossRef]  

12. M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78(2), 025804 (2008). [CrossRef]  

13. G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009). [CrossRef]  

14. E. Pomarico, B. Sanguinetti, R. Thew, and H. Zbinden, “Room temperature photon number resolving detector for infared wavelengths,” Opt. Express 18(10), 10750–10759 (2010). [CrossRef]   [PubMed]  

15. M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015). [CrossRef]  

16. R. Kruse, J. Tiedau, T. J. Bartley, S. Barkhofen, and C. Silberhorn, “Limits of the time-multiplexed photon-counting method,” Phys. Rev. A 95(2), 023815 (2017). [CrossRef]  

17. T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, R. Mirin, and S. W. Nam, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” Opt. Express 20(21), 23798–23810 (2012). [CrossRef]   [PubMed]  

18. J. G. Webb and E. H. Huntington, “Photostatistics reconstruction via loop detector signatures,” Opt. Express 17(14), 11799–11812 (2009). [CrossRef]   [PubMed]  

19. F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013). [CrossRef]  

20. I. Müller, R. M. Klein, and L. Werner, “Traceable calibration of a fibre-coupled superconducting nano-wire single photon detector using characterized synchrotron radiation,” Metrologia 51(6), S329 (2014). [CrossRef]  

21. I. Müller, R. D. Horansky, J. H. Lehman, S. W. Nam, I. Vayshenker, L. Werner, G. Wuebbeler, and M. White, “Verification of calibration methods for determining photon-counting detection efficiency using superconducting nano-wire single photon detectors,” Opt. Express 25(18), 21483–21495 (2017). [CrossRef]  

22. D. N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detectors,” Sov. J. Quantum Electron. 10(9), 1112 (1980). [CrossRef]  

23. A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Absolute detector quantum-efficiency measurements using correlated photons,” Metrologia 32(6), 479 (1995). [CrossRef]  

24. O. Haderka, J. PeȈrina, M. Hamar, and J. PeȈrina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71(3), 033815 (2005). [CrossRef]  

25. T. Kiesel and W. Vogel, “Complete nonclassicality test with a photon-number-resolving detector,” Phys. Rev. A 86(3), 032119 (2012). [CrossRef]  

26. J. Sperling, W. Vogel, and G. S. Agarwal, “Sub-binomial light,” Phys. Rev. Lett. 109(9), 093601 (2012). [CrossRef]   [PubMed]  

27. J. Sperling, W. Vogel, and G. S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85(2), 023820 (2012). [CrossRef]  

28. T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110(17), 173602 (2013). [CrossRef]   [PubMed]  

29. G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014). [CrossRef]  

30. D. Liu, L. You, Y. He, C. Lv, S. Chen, L. Zhang, Z. Wang, and X. Xie, “Photon-number resolving and distribution verification using a multichannel superconducting nanowire single-photon detection system,” J. Opt. Soc. Am. B, JOSAB 31(4), 816–820 (2014). [CrossRef]  

31. R. Chrapkiewicz, “Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on-off detectors,” J. Opt. Soc. Am. B, JOSAB 31(10), B8–B13 (2014). [CrossRef]  

32. J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015). [CrossRef]   [PubMed]  

33. C. Lee, S. Ferrari, W. H. P. Pernice, and C. Rockstuhl, “Sub-poisson-binomial light,” Phys. Rev. A 94(5), 053844 (2016). [CrossRef]  

34. J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017). [CrossRef]  

35. M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018). [CrossRef]   [PubMed]  

36. T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys . 18(6), 063017 (2016). [CrossRef]  

References

  • View by:

  1. H. Paul, P. Törmä, T. Kiss, and I. Jex, “Photon chopping: new way to measure the quantum state of light,” Phys. Rev. Lett. 76(14), 2464–2467 (1996).
    [Crossref] [PubMed]
  2. J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74(7), 902–904 (1999).
    [Crossref]
  3. K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52–54 (2003).
    [Crossref] [PubMed]
  4. D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387 (2003).
    [Crossref] [PubMed]
  5. J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
    [Crossref]
  6. M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003).
    [Crossref]
  7. D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
    [Crossref]
  8. S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 542–3337–352 (2007).
    [Crossref]
  9. V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007).
    [Crossref]
  10. G. A. P. Thé and R. V. Ramos, “Multiple-photon number resolving detector using fibre ring and single-photon detector,” J. Mod. Opt. 54(8), 1187–1202 (2007).
    [Crossref]
  11. A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
    [Crossref]
  12. M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78(2), 025804 (2008).
    [Crossref]
  13. G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009).
    [Crossref]
  14. E. Pomarico, B. Sanguinetti, R. Thew, and H. Zbinden, “Room temperature photon number resolving detector for infared wavelengths,” Opt. Express 18(10), 10750–10759 (2010).
    [Crossref] [PubMed]
  15. M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
    [Crossref]
  16. R. Kruse, J. Tiedau, T. J. Bartley, S. Barkhofen, and C. Silberhorn, “Limits of the time-multiplexed photon-counting method,” Phys. Rev. A 95(2), 023815 (2017).
    [Crossref]
  17. T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, R. Mirin, and S. W. Nam, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” Opt. Express 20(21), 23798–23810 (2012).
    [Crossref] [PubMed]
  18. J. G. Webb and E. H. Huntington, “Photostatistics reconstruction via loop detector signatures,” Opt. Express 17(14), 11799–11812 (2009).
    [Crossref] [PubMed]
  19. F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
    [Crossref]
  20. I. Müller, R. M. Klein, and L. Werner, “Traceable calibration of a fibre-coupled superconducting nano-wire single photon detector using characterized synchrotron radiation,” Metrologia 51(6), S329 (2014).
    [Crossref]
  21. I. Müller, R. D. Horansky, J. H. Lehman, S. W. Nam, I. Vayshenker, L. Werner, G. Wuebbeler, and M. White, “Verification of calibration methods for determining photon-counting detection efficiency using superconducting nano-wire single photon detectors,” Opt. Express 25(18), 21483–21495 (2017).
    [Crossref]
  22. D. N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detectors,” Sov. J. Quantum Electron. 10(9), 1112 (1980).
    [Crossref]
  23. A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Absolute detector quantum-efficiency measurements using correlated photons,” Metrologia 32(6), 479 (1995).
    [Crossref]
  24. O. Haderka, J. PeȈrina, M. Hamar, and J. PeȈrina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71(3), 033815 (2005).
    [Crossref]
  25. T. Kiesel and W. Vogel, “Complete nonclassicality test with a photon-number-resolving detector,” Phys. Rev. A 86(3), 032119 (2012).
    [Crossref]
  26. J. Sperling, W. Vogel, and G. S. Agarwal, “Sub-binomial light,” Phys. Rev. Lett. 109(9), 093601 (2012).
    [Crossref] [PubMed]
  27. J. Sperling, W. Vogel, and G. S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85(2), 023820 (2012).
    [Crossref]
  28. T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110(17), 173602 (2013).
    [Crossref] [PubMed]
  29. G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
    [Crossref]
  30. D. Liu, L. You, Y. He, C. Lv, S. Chen, L. Zhang, Z. Wang, and X. Xie, “Photon-number resolving and distribution verification using a multichannel superconducting nanowire single-photon detection system,” J. Opt. Soc. Am. B, JOSAB 31(4), 816–820 (2014).
    [Crossref]
  31. R. Chrapkiewicz, “Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on-off detectors,” J. Opt. Soc. Am. B, JOSAB 31(10), B8–B13 (2014).
    [Crossref]
  32. J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
    [Crossref] [PubMed]
  33. C. Lee, S. Ferrari, W. H. P. Pernice, and C. Rockstuhl, “Sub-poisson-binomial light,” Phys. Rev. A 94(5), 053844 (2016).
    [Crossref]
  34. J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
    [Crossref]
  35. M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018).
    [Crossref] [PubMed]
  36. T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
    [Crossref]

2018 (1)

M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018).
[Crossref] [PubMed]

2017 (3)

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

I. Müller, R. D. Horansky, J. H. Lehman, S. W. Nam, I. Vayshenker, L. Werner, G. Wuebbeler, and M. White, “Verification of calibration methods for determining photon-counting detection efficiency using superconducting nano-wire single photon detectors,” Opt. Express 25(18), 21483–21495 (2017).
[Crossref]

R. Kruse, J. Tiedau, T. J. Bartley, S. Barkhofen, and C. Silberhorn, “Limits of the time-multiplexed photon-counting method,” Phys. Rev. A 95(2), 023815 (2017).
[Crossref]

2016 (2)

C. Lee, S. Ferrari, W. H. P. Pernice, and C. Rockstuhl, “Sub-poisson-binomial light,” Phys. Rev. A 94(5), 053844 (2016).
[Crossref]

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
[Crossref]

2015 (2)

J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
[Crossref] [PubMed]

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

2014 (4)

G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
[Crossref]

D. Liu, L. You, Y. He, C. Lv, S. Chen, L. Zhang, Z. Wang, and X. Xie, “Photon-number resolving and distribution verification using a multichannel superconducting nanowire single-photon detection system,” J. Opt. Soc. Am. B, JOSAB 31(4), 816–820 (2014).
[Crossref]

R. Chrapkiewicz, “Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on-off detectors,” J. Opt. Soc. Am. B, JOSAB 31(10), B8–B13 (2014).
[Crossref]

I. Müller, R. M. Klein, and L. Werner, “Traceable calibration of a fibre-coupled superconducting nano-wire single photon detector using characterized synchrotron radiation,” Metrologia 51(6), S329 (2014).
[Crossref]

2013 (2)

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110(17), 173602 (2013).
[Crossref] [PubMed]

2012 (4)

T. Kiesel and W. Vogel, “Complete nonclassicality test with a photon-number-resolving detector,” Phys. Rev. A 86(3), 032119 (2012).
[Crossref]

J. Sperling, W. Vogel, and G. S. Agarwal, “Sub-binomial light,” Phys. Rev. Lett. 109(9), 093601 (2012).
[Crossref] [PubMed]

J. Sperling, W. Vogel, and G. S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85(2), 023820 (2012).
[Crossref]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, R. Mirin, and S. W. Nam, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” Opt. Express 20(21), 23798–23810 (2012).
[Crossref] [PubMed]

2010 (1)

2009 (2)

J. G. Webb and E. H. Huntington, “Photostatistics reconstruction via loop detector signatures,” Opt. Express 17(14), 11799–11812 (2009).
[Crossref] [PubMed]

G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009).
[Crossref]

2008 (2)

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78(2), 025804 (2008).
[Crossref]

2007 (3)

S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 542–3337–352 (2007).
[Crossref]

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007).
[Crossref]

G. A. P. Thé and R. V. Ramos, “Multiple-photon number resolving detector using fibre ring and single-photon detector,” J. Mod. Opt. 54(8), 1187–1202 (2007).
[Crossref]

2005 (1)

O. Haderka, J. PeȈrina, M. Hamar, and J. PeȈrina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71(3), 033815 (2005).
[Crossref]

2004 (1)

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

2003 (4)

K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52–54 (2003).
[Crossref] [PubMed]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387 (2003).
[Crossref] [PubMed]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003).
[Crossref]

1999 (1)

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74(7), 902–904 (1999).
[Crossref]

1996 (1)

H. Paul, P. Törmä, T. Kiss, and I. Jex, “Photon chopping: new way to measure the quantum state of light,” Phys. Rev. Lett. 76(14), 2464–2467 (1996).
[Crossref] [PubMed]

1995 (1)

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Absolute detector quantum-efficiency measurements using correlated photons,” Metrologia 32(6), 479 (1995).
[Crossref]

1980 (1)

D. N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detectors,” Sov. J. Quantum Electron. 10(9), 1112 (1980).
[Crossref]

Achilles, D.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387 (2003).
[Crossref] [PubMed]

Agarwal, G. S.

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

J. Sperling, W. Vogel, and G. S. Agarwal, “Sub-binomial light,” Phys. Rev. Lett. 109(9), 093601 (2012).
[Crossref] [PubMed]

J. Sperling, W. Vogel, and G. S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85(2), 023820 (2012).
[Crossref]

Allman, M. S.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

Ansari, V.

J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
[Crossref] [PubMed]

Baek, B.

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

Banaszek, K.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52–54 (2003).
[Crossref] [PubMed]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387 (2003).
[Crossref] [PubMed]

Barbieri, M.

T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110(17), 173602 (2013).
[Crossref] [PubMed]

Barkhofen, S.

R. Kruse, J. Tiedau, T. J. Bartley, S. Barkhofen, and C. Silberhorn, “Limits of the time-multiplexed photon-counting method,” Phys. Rev. A 95(2), 023815 (2017).
[Crossref]

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
[Crossref]

Bartley, T.

M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018).
[Crossref] [PubMed]

Bartley, T. J.

R. Kruse, J. Tiedau, T. J. Bartley, S. Barkhofen, and C. Silberhorn, “Limits of the time-multiplexed photon-counting method,” Phys. Rev. A 95(2), 023815 (2017).
[Crossref]

T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110(17), 173602 (2013).
[Crossref] [PubMed]

Benkhaoul, M.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Beyer, A.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

Bitauld, D.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Bohmann, M.

M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018).
[Crossref] [PubMed]

J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
[Crossref] [PubMed]

Brecht, B.

J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
[Crossref] [PubMed]

Brida, G.

G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009).
[Crossref]

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007).
[Crossref]

Calkins, B.

Castelletto, S.

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007).
[Crossref]

Castelletto, S. A.

S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 542–3337–352 (2007).
[Crossref]

Chen, S.

D. Liu, L. You, Y. He, C. Lv, S. Chen, L. Zhang, Z. Wang, and X. Xie, “Photon-number resolving and distribution verification using a multichannel superconducting nanowire single-photon detection system,” J. Opt. Soc. Am. B, JOSAB 31(4), 816–820 (2014).
[Crossref]

Chrapkiewicz, R.

R. Chrapkiewicz, “Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on-off detectors,” J. Opt. Soc. Am. B, JOSAB 31(10), B8–B13 (2014).
[Crossref]

Clements, W. R.

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

Datla, R. U.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Absolute detector quantum-efficiency measurements using correlated photons,” Metrologia 32(6), 479 (1995).
[Crossref]

Datta, A.

T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110(17), 173602 (2013).
[Crossref] [PubMed]

Degiovanni, I. P.

G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009).
[Crossref]

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007).
[Crossref]

S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 542–3337–352 (2007).
[Crossref]

Divochiy, A.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Donati, G.

T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110(17), 173602 (2013).
[Crossref] [PubMed]

Eckstein, A.

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

Elster, F.

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
[Crossref]

Ferrari, S.

C. Lee, S. Ferrari, W. H. P. Pernice, and C. Rockstuhl, “Sub-poisson-binomial light,” Phys. Rev. A 94(5), 053844 (2016).
[Crossref]

Fiore, A.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Fitch, M. J.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003).
[Crossref]

Franson, J. D.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003).
[Crossref]

Gábris, A.

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
[Crossref]

Gaggero, A.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Gerrits, T.

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, R. Mirin, and S. W. Nam, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” Opt. Express 20(21), 23798–23810 (2012).
[Crossref] [PubMed]

Gol’tsman, G.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Haderka, O.

M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78(2), 025804 (2008).
[Crossref]

O. Haderka, J. PeȈrina, M. Hamar, and J. PeȈrina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71(3), 033815 (2005).
[Crossref]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Hamar, M.

O. Haderka, J. PeȈrina, M. Hamar, and J. PeȈrina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71(3), 033815 (2005).
[Crossref]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Harder, G.

J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
[Crossref] [PubMed]

G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
[Crossref]

Harrington, S.

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

He, Y.

D. Liu, L. You, Y. He, C. Lv, S. Chen, L. Zhang, Z. Wang, and X. Xie, “Photon-number resolving and distribution verification using a multichannel superconducting nanowire single-photon detection system,” J. Opt. Soc. Am. B, JOSAB 31(4), 816–820 (2014).
[Crossref]

Hogue, H. H.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74(7), 902–904 (1999).
[Crossref]

Horansky, R. D.

I. Müller, R. D. Horansky, J. H. Lehman, S. W. Nam, I. Vayshenker, L. Werner, G. Wuebbeler, and M. White, “Verification of calibration methods for determining photon-counting detection efficiency using superconducting nano-wire single photon detectors,” Opt. Express 25(18), 21483–21495 (2017).
[Crossref]

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

Hradil, Z.

G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
[Crossref]

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Huntington, E. H.

Jacobs, B. C.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003).
[Crossref]

Jex, I.

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
[Crossref]

H. Paul, P. Törmä, T. Kiss, and I. Jex, “Photon chopping: new way to measure the quantum state of light,” Phys. Rev. Lett. 76(14), 2464–2467 (1996).
[Crossref] [PubMed]

Ježek, M.

M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78(2), 025804 (2008).
[Crossref]

Jin, X.-M.

T. J. Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct observation of sub-binomial light,” Phys. Rev. Lett. 110(17), 173602 (2013).
[Crossref] [PubMed]

Kaurova, N.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Kiesel, T.

T. Kiesel and W. Vogel, “Complete nonclassicality test with a photon-number-resolving detector,” Phys. Rev. A 86(3), 032119 (2012).
[Crossref]

Kim, J.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74(7), 902–904 (1999).
[Crossref]

Kiss, T.

H. Paul, P. Törmä, T. Kiss, and I. Jex, “Photon chopping: new way to measure the quantum state of light,” Phys. Rev. Lett. 76(14), 2464–2467 (1996).
[Crossref] [PubMed]

Klein, R. M.

I. Müller, R. M. Klein, and L. Werner, “Traceable calibration of a fibre-coupled superconducting nano-wire single photon detector using characterized synchrotron radiation,” Metrologia 51(6), S329 (2014).
[Crossref]

Klyshko, D. N.

D. N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detectors,” Sov. J. Quantum Electron. 10(9), 1112 (1980).
[Crossref]

Kolthammer, W. S.

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

Korneev, A.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Kruse, R.

R. Kruse, J. Tiedau, T. J. Bartley, S. Barkhofen, and C. Silberhorn, “Limits of the time-multiplexed photon-counting method,” Phys. Rev. A 95(2), 023815 (2017).
[Crossref]

Kumor, D.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

Lagoudakis, K. G.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Lee, C.

C. Lee, S. Ferrari, W. H. P. Pernice, and C. Rockstuhl, “Sub-poisson-binomial light,” Phys. Rev. A 94(5), 053844 (2016).
[Crossref]

Lehman, J. H.

Leoni, R.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Lévy, F.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Lita, A.

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

Lita, A. E.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, R. Mirin, and S. W. Nam, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” Opt. Express 20(21), 23798–23810 (2012).
[Crossref] [PubMed]

Liu, D.

D. Liu, L. You, Y. He, C. Lv, S. Chen, L. Zhang, Z. Wang, and X. Xie, “Photon-number resolving and distribution verification using a multichannel superconducting nanowire single-photon detection system,” J. Opt. Soc. Am. B, JOSAB 31(4), 816–820 (2014).
[Crossref]

Lv, C.

D. Liu, L. You, Y. He, C. Lv, S. Chen, L. Zhang, Z. Wang, and X. Xie, “Photon-number resolving and distribution verification using a multichannel superconducting nanowire single-photon detection system,” J. Opt. Soc. Am. B, JOSAB 31(4), 816–820 (2014).
[Crossref]

Marsili, F.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Mattioli, F.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
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Micuda, M.

M. Mičuda, O. Haderka, and M. Ježek, “High-efficiency photon-number-resolving multichannel detector,” Phys. Rev. A 78(2), 025804 (2008).
[Crossref]

Migdall, A.

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, R. Mirin, and S. W. Nam, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” Opt. Express 20(21), 23798–23810 (2012).
[Crossref] [PubMed]

G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009).
[Crossref]

Migdall, A. L.

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007).
[Crossref]

S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 542–3337–352 (2007).
[Crossref]

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Absolute detector quantum-efficiency measurements using correlated photons,” Metrologia 32(6), 479 (1995).
[Crossref]

Minaeva, O.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Mirin, R.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, R. Mirin, and S. W. Nam, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” Opt. Express 20(21), 23798–23810 (2012).
[Crossref] [PubMed]

Mirin, R. P.

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

Moore, M.

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

Motka, L.

G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
[Crossref]

Müller, I.

Nam, S. W.

I. Müller, R. D. Horansky, J. H. Lehman, S. W. Nam, I. Vayshenker, L. Werner, G. Wuebbeler, and M. White, “Verification of calibration methods for determining photon-counting detection efficiency using superconducting nano-wire single photon detectors,” Opt. Express 25(18), 21483–21495 (2017).
[Crossref]

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

T. Gerrits, B. Calkins, N. Tomlin, A. E. Lita, A. Migdall, R. Mirin, and S. W. Nam, “Extending single-photon optimized superconducting transition edge sensors beyond the single-photon counting regime,” Opt. Express 20(21), 23798–23810 (2012).
[Crossref] [PubMed]

Nitsche, T.

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
[Crossref]

Novotný, J.

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
[Crossref]

Orszak, J. S.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Absolute detector quantum-efficiency measurements using correlated photons,” Metrologia 32(6), 479 (1995).
[Crossref]

Paul, H.

H. Paul, P. Törmä, T. Kiss, and I. Jex, “Photon chopping: new way to measure the quantum state of light,” Phys. Rev. Lett. 76(14), 2464–2467 (1996).
[Crossref] [PubMed]

Pe?rina, J.

O. Haderka, J. PeȈrina, M. Hamar, and J. PeȈrina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71(3), 033815 (2005).
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O. Haderka, J. PeȈrina, M. Hamar, and J. PeȈrina, “Direct measurement and reconstruction of nonclassical features of twin beams generated in spontaneous parametric down-conversion,” Phys. Rev. A 71(3), 033815 (2005).
[Crossref]

Perina, J.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Pernice, W. H. P.

C. Lee, S. Ferrari, W. H. P. Pernice, and C. Rockstuhl, “Sub-poisson-binomial light,” Phys. Rev. A 94(5), 053844 (2016).
[Crossref]

Piacentini, F.

G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009).
[Crossref]

Pittman, T. B.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003).
[Crossref]

Polyakov, S. V.

G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009).
[Crossref]

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007).
[Crossref]

Pomarico, E.

Ramos, R. V.

G. A. P. Thé and R. V. Ramos, “Multiple-photon number resolving detector using fibre ring and single-photon detector,” J. Mod. Opt. 54(8), 1187–1202 (2007).
[Crossref]

Rehacek, J.

G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
[Crossref]

Rehácek, J.

J. Řeháček, Z. Hradil, O. Haderka, J. Peřina, and M. Hamar, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67(6), 061801 (2003).
[Crossref]

Renema, J. J.

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

Rockstuhl, C.

C. Lee, S. Ferrari, W. H. P. Pernice, and C. Rockstuhl, “Sub-poisson-binomial light,” Phys. Rev. A 94(5), 053844 (2016).
[Crossref]

Sánchez-Soto, L. L.

G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
[Crossref]

Sanguinetti, B.

Schettini, V.

G. Brida, I. P. Degiovanni, F. Piacentini, V. Schettini, S. V. Polyakov, and A. Migdall, “Scalable multiplexed detector system for high-rate telecom-band single-photon detection,” Rev. Sci. Instruments 80(11), 116103 (2009).
[Crossref]

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13(4), 978–983 (2007).
[Crossref]

S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 542–3337–352 (2007).
[Crossref]

Seleznev, V.

A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lévy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nat. Photonics 2(5), 302–306 (2008).
[Crossref]

Sergienko, A.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Absolute detector quantum-efficiency measurements using correlated photons,” Metrologia 32(6), 479 (1995).
[Crossref]

Shaw, M. D.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

Shih, Y. H.

A. L. Migdall, R. U. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Absolute detector quantum-efficiency measurements using correlated photons,” Metrologia 32(6), 479 (1995).
[Crossref]

Silberhorn, C.

M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018).
[Crossref] [PubMed]

R. Kruse, J. Tiedau, T. J. Bartley, S. Barkhofen, and C. Silberhorn, “Limits of the time-multiplexed photon-counting method,” Phys. Rev. A 95(2), 023815 (2017).
[Crossref]

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, and C. Silberhorn, “Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer,” New J. Phys.  18(6), 063017 (2016).
[Crossref]

J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
[Crossref] [PubMed]

G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
[Crossref]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387 (2003).
[Crossref] [PubMed]

Sliwa, C.

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 519–101499–1515 (2004).
[Crossref]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387 (2003).
[Crossref] [PubMed]

Sperling, J.

M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018).
[Crossref] [PubMed]

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
[Crossref] [PubMed]

J. Sperling, W. Vogel, and G. S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85(2), 023820 (2012).
[Crossref]

J. Sperling, W. Vogel, and G. S. Agarwal, “Sub-binomial light,” Phys. Rev. Lett. 109(9), 093601 (2012).
[Crossref] [PubMed]

Stern, J. A.

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

Stevens, M.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

Stoklasa, B.

G. Harder, C. Silberhorn, J. Rehacek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, “Time-multiplexed measurements of nonclassical light at telecom wavelengths,” Phys. Rev. A 90(4), 042105 (2014).
[Crossref]

Takeuchi, S.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74(7), 902–904 (1999).
[Crossref]

Thé, G. A. P.

G. A. P. Thé and R. V. Ramos, “Multiple-photon number resolving detector using fibre ring and single-photon detector,” J. Mod. Opt. 54(8), 1187–1202 (2007).
[Crossref]

Thew, R.

Tiedau, J.

M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018).
[Crossref] [PubMed]

R. Kruse, J. Tiedau, T. J. Bartley, S. Barkhofen, and C. Silberhorn, “Limits of the time-multiplexed photon-counting method,” Phys. Rev. A 95(2), 023815 (2017).
[Crossref]

Tomlin, N.

Törmä, P.

H. Paul, P. Törmä, T. Kiss, and I. Jex, “Photon chopping: new way to measure the quantum state of light,” Phys. Rev. Lett. 76(14), 2464–2467 (1996).
[Crossref] [PubMed]

Vayshenker, I.

I. Müller, R. D. Horansky, J. H. Lehman, S. W. Nam, I. Vayshenker, L. Werner, G. Wuebbeler, and M. White, “Verification of calibration methods for determining photon-counting detection efficiency using superconducting nano-wire single photon detectors,” Opt. Express 25(18), 21483–21495 (2017).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

Verma, V. B.

M. S. Allman, V. B. Verma, M. Stevens, T. Gerrits, R. D. Horansky, A. E. Lita, F. Marsili, A. Beyer, M. D. Shaw, D. Kumor, R. Mirin, and S. W. Nam, “A near-infrared 64-pixel superconducting nanowire single photon detector array with integrated multiplexed readout,” Appl. Phys. Lett. 106(19), 192601 (2015).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon 7(3), 210–214 (2013).
[Crossref]

Vogel, W.

M. Bohmann, J. Tiedau, T. Bartley, J. Sperling, C. Silberhorn, and W. Vogel, “Incomplete detection of nonclassical phase-space distributions,” Phys. Rev. Lett. 120(6), 063607 (2018).
[Crossref] [PubMed]

J. Sperling, A. Eckstein, W. R. Clements, M. Moore, J. J. Renema, W. S. Kolthammer, S. W. Nam, A. Lita, T. Gerrits, I. A. Walmsley, G. S. Agarwal, and W. Vogel, “Identification of nonclassical properties of light with multiplexing layouts,” Phys. Rev. A 96(1), 013804 (2017).
[Crossref]

J. Sperling, M. Bohmann, W. Vogel, G. Harder, B. Brecht, V. Ansari, and C. Silberhorn, “Uncovering quantum correlations with time-multiplexed click detection,” Phys. Rev. Lett. 115(2), 023601 (2015).
[Crossref] [PubMed]

J. Sperling, W. Vogel, and G. S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85(2), 023820 (2012).
[Crossref]

J. Sperling, W. Vogel, and G. S. Agarwal, “Sub-binomial light,” Phys. Rev. Lett. 109(9), 093601 (2012).
[Crossref] [PubMed]

T. Kiesel and W. Vogel, “Complete nonclassicality test with a photon-number-resolving detector,” Phys. Rev. A 86(3), 032119 (2012).
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Figures (11)

Fig. 1
Fig. 1 Binary detector coupled to a resonator with coupling R(t). For active switching, R(t = 0) = 0, i.e. all the light is switched into the loop. Subsequently, R(t) = R is constant. In the passive case, R(t) = R is constant for all times.
Fig. 2
Fig. 2 (a) Click probability pj for a passive loop detector as a function of bin j, for a Fock state (blue), coherent state (green) and thermal state (orange), each with a mean photon number of n ¯ = 3 , outcoupling parameter R = 0.5, loop efficiency η = 0.9 and noise contribution ν = 10−3. (b) As above, but with the mean photon number n ¯ = 300 in each case (all other parameters remain the same). In general, each of these classes produces slightly different distribution of clicks per bin pj, for fixed mean photon number. This occurs due to the nonlinear response of the click detectors, and is most clearly identified close to the saturation regime (e.g. around bin 5) in (b).
Fig. 3
Fig. 3 Histogram of click probabilities on linear and log scales, for a coherent state input with an average of ∼250 000 photons per pulse to the passive loop detector with a repetition rate of 50 kHz. Error bars are based on estimating the success probability of a Binomial distribution (shown in black).
Fig. 4
Fig. 4 Detection of sub-binomial light with a dynamic loop detector. Heralded single photons and thermal states (from Periodically-poled Potassium Titanyl Phosphate - PPKTP waveguide), and coherent states are coupled into the loop with a fast Pockels cell polarization switch. Then on each pass through the loop a small fraction of the light, determined by the angle of the half-wave plate (HWP), is coupled out to the superconducting nanowire single photon detector (SNSPD).
Fig. 5
Fig. 5 Classicality parameters QPB and QB as measured by the loop detector for heralded PDC states, for (a) actively switched loop (with coupling parameter R = 0.1); and (b) passively switched loop (with R = 0.5). Error bars are based on 10000 Monte-Carlo-Simulations where the mean and variance are given by the measured ck distributions.
Fig. 6
Fig. 6 Schematic of calibration setup. n ¯ in indicates the mean photon number per pulse incident on the loop. n ¯ out is the mean photon number after the loop, summed over all bins. n ¯ out can be switched between an on-off detector or a power meter. Reliable switching is important for the calibration procedure as systematic errors can be produced during this process.
Fig. 7
Fig. 7 Histogram showing the bin probability in linear (top) and logarithmic (bottom) scale for a calibration measurement (a) and a highly attenuated input (b), using a passive loop. Red curves: Fit based on Eq. (11). The fit for the attenuated coherent state gives an estimate for R = 0.91370 ± 5 · 10−5 and η = 0.8615 ± 3 · 10−4.
Fig. 8
Fig. 8 Inferred mean photon number per pulse n ¯ j after the loop from measured click probabilities pj. Red line: mean value of n ¯ measured = 208011 . The first bins j ≤ 25 are excluded because dead times from back reflections reduced the count rate (see next section for further details).
Fig. 9
Fig. 9 Relative uncertainty contributions σ i 2 n ¯ 2 ( d n ¯ d i ) 2 from each error source, arising from uncertainty in the measured bin probabilities pj (red line), the loop loss η (green line), the loop reflectivity R (blue line) and the noise ν (gold line). Note that these quantities are evaluated using the a posteriori weighted mean n ¯ i.e. the mean photon number averaged over all j. The blue dots are the total relative error contributions, and red crosses the relative error in pj, evaluated at the individually determined photon number n ¯ out | j (in contrast to the solid lines). The deviation of these measures at low bin number j ≲ 25 arises from undercounting caused by back-reflection-induced inefficiency, resulting in an underestimate of the error associated with pj. This is discussed further in the following section.
Fig. 10
Fig. 10 (a) Raw time-tags for a bright pulse, zoomed in on the first 24 bins, showing clear excess counts outside of the expected loop bins (orange). This arises from spurious back-reflections present in the setup. (b) Click probability as a function of bin number. In early bins 2 ≤ j ≲ 20, back reflections cause a reduction in the expected counts since they induce dead time, which can be seen by a deviation from the expected click probabilities.
Fig. 11
Fig. 11 Single bin click probability as a function of incident number of photons per pulse and pulse repetition rate. Once latching occurs, no counts can be measured (upper right corner).

Tables (1)

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Table 1 Absolute and relative errors of the measured values

Equations (25)

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p j = ( 1 ν j ) n = 0 P ( j | n ) ρ in ( n ) + ν j ,
P ( j | n ) = { 1 [ 1 ( R η ) j 1 η ( 1 R ) ] n active , 1 [ 1 ( R η ) j 1 R 1 ( 1 R ) 2 ] n passive ,
P ( 1 | n ) = { 1 [ 1 η ( 1 R ) ] n active , 1 R n passive .
Q P B = N ( Δ c ) 2 c ( N c ) N 2 σ 2 1 ,
c = k = 0 N k c k ; ( Δ c ) 2 = k = 0 N ( k c ) 2 c k
m = 1 N j = 0 N p j ; σ 2 = 1 N j = 0 N ( p j m ) 2 .
p j Fock = 1 ( 1 ν ) [ 1 ( 1 R ) R 1 ( R η ) j ] n ¯
p j coh = 1 ( 1 ν ) exp [ ( 1 R ) R 1 ( η R ) j n ¯ ]
p j therm = 1 ( 1 ν ) R R + ( 1 R ) ( R η ) j n ¯
p j Fock = { 1 ( 1 ν ) R n ¯ j = 1 1 ( 1 ν ) [ 1 ( 1 R ) 2 R 1 ( R η ) j 1 ] n ¯ j 2
p j coh = { 1 ( 1 ν ) exp [ ( 1 R ) n ¯ ] j = 1 1 ( 1 ν ) exp [ ( 1 R ) 2 R 1 ( η R ) j 1 n ¯ ] j 2
p j therm = { 1 ( 1 ν ) 1 1 + ( 1 R ) n ¯ j = 1 1 ( 1 ν ) R 2 η R 2 η + ( 1 R ) 2 ( R η ) j n ¯ j 2
η SDE = n ¯ measured n dark counts n ¯ PM
n ¯ j = n ¯ in ( 1 R ) R j 1 η j ,
n ¯ j = { n ¯ in R j = 1 n ¯ in ( 1 R ) 2 R j 2 η j 1 j 2
n ¯ out = j = 1 n ¯ j .
n ¯ out = n ¯ in ( 1 + R ) η 1 + R η
n ¯ out = n ¯ in ( R η + 2 R η ) 1 + R η .
n ¯ out | j = R η ( R η ) j ln [ 1 ν 1 p j ] 1 + R η
n ¯ out | j = { ( R + η 2 η R ) ln [ 1 ν 1 p j ] R ( 1 R η ) j = 1 ( R + η 2 η R ) ( R η ) 1 j R 1 ln [ 1 ν 1 p j ] ( 1 R η ) ( R 1 ) 2 j 2 .
n ¯ measured = j w j n ¯ out | j j w j ,
w j = 1 σ n ¯ out | j 2 .
σ n ¯ out | j n ¯ out | j = [ σ p j 2 n ¯ out 2 | j ( d n ¯ out d p j ) 2 + σ R 2 n ¯ out 2 | j ( d n ¯ out d R ) 2 + σ η 2 n ¯ out 2 | j ( d n ¯ out d η ) 2 + σ ν 2 n ¯ out 2 | j ( d n ¯ out d ν ) 2 ] 1 / 2 | j = { σ p j 2 1 ( 1 p j ) 2 ln ( 1 ν 1 p j ) 2 + σ R 2 [ 1 j R + 1 R ( 1 R η ) + 1 R ( 1 2 R ) + η ( 1 2 R ) 2 2 R 1 3 R + 2 R 2 ] 2 + σ η 2 [ 1 j η + ( 1 R ) 2 ( R + η 2 R η ) ( 1 R η ) ] 2 + σ ν 2 1 ( 1 ν ) 2 ln ( 1 ν 1 p j ) 2 } 1 / 2 | j .
σ n ¯ = 1 ( j w j ) 1 / 2 .
j max log 10 [ ν n max ] log 10 [ η ( 1 R ) ] .

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