1. Introduction

While improvements in single photon detection technologies have contributed to remarkable advancements in many fields, further development will have immediate impact in an even wider variety of applications. For example, loophole-free tests of Bell’s Inequality [1], which are interesting for basic scientific as well as cryptographic applications [2], quantum simulators of physical processes [3], single-molecule imaging and spectroscopy [4], and photon-counting deep-space laser communications [5] rely on the use and development of fast, high-efficiency single photon detectors. Superconducting transition-edge sensors have demonstrated a record 98% detection efficiency [6], but they operate at relatively low speeds and their sub-Kelvin operating temperature complicates the development of large arrays. Large arrays of photon-counting avalanche photo-diodes have been demonstrated, but material and other constraints limit their detection efficiency, speed, and dark count rates [7, 8].

Superconducting nanowire single photon detectors (SNSPDs) [9] have the potential for achieving simultaneously all of the desired characteristics for single photon detection. SNSPDs are thin (<10 nm) and narrow (~100 nm) superconducting wires that are cooled below the superconducting critical temperature and current-biased close to the superconducting critical current density. Absorption of a single photon results in a local current redistribution that can cause the critical current density to be exceeded and a voltage pulse to be generated. The associated dynamics can be extremely fast, resulting in a timing resolution of tens of picoseconds for the best NbN-based SNSPDs. The detector recovery time, generally determined by the kinetic inductance [10] of the nanowire, is typically several nanoseconds, indicating that SNSPDs may be able to count at hundreds of Mcps rates. The internal detection efficiency of SNSPDs, defined as the probability that an absorbed photon results in an output voltage pulse [11], can be close to unity, implying that high system efficiencies should be achievable by enhancing the absorption of the photons and ensuring optical coupling losses are low.

Although the physics underlying device operation implies that all of the desirable detector characteristics described above should be achievable, in practice there are technical challenges involved in achieving them simultaneously. For example, the ability to count continuously at high rates, frequently cited as one of the most unique capabilities of SNSPDs, is generally not achievable at high efficiency using the standard readout scheme, due to a nonlinear interaction between the detector and the AC-coupled amplifier used to read out the signal [12]. Additionally, achieving fast reset times to enable high count rates generally requires small active areas for lower kinetic inductance [10] but this makes high-efficiency optical coupling challenging. Similarly, attempts to decrease the reset time by increasing the load impedance seen by the detector [13] or using parallel nanowires to reduce the inductance [14] can result in a lower efficiency due to latching [13, 15–17]. These and other tradeoffs in detector performance make it important to consider only the system performance parameters which can be achieved simultaneously when evaluating the potential benefits of SNSPDs in any given application. In this paper, we describe an SNSPD system that simultaneously achieves 68% system detection efficiency at a photon flux of 100 million photons per second, few kcps dark count rates, and <80 ps timing resolution.

The detectors were fabricated from a 5 nm thick NbN film sputtered on a silicon wafer with a 260 nm-thick thermally grown silicon oxide coating. The use of oxidized silicon substrates rather than the sapphire substrates previously used by our group enables higher absorption in the NbN nanowire for the simple cavity structure described here. The NbN film was patterned into detectors with 80 nm-wide wires on a pitch of 140 nm. A 250 nm thick SiO₂ spacer and a gold mirror were deposited on top of the patterned NbN detector. The oxide layer thicknesses were chosen to optimize the absorption of 1550 nm photons in the NbN film. Light was coupled to the detectors through the back of the silicon wafer using an anti-reflection-coated SMF28 optical fiber that was actively positioned at cryogenic temperatures above an aspheric lens fixed to the detector mount, which provided a demagnification of 2. The device consisted of an array of four interleaved SNSPDs, patterned into a circle approximately 14 μm in diameter. Use of a detector array enabled a higher count rate for the given area, and the interleaved design ensured that all wires sampled the same optical mode, providing approximate photon number resolution up to n = 4 [18]. The detectors were cooled in a continuously-operating Gifford-McMahon cryocooler to a base temperature of 2.5 K. The electrical signals from each of the four detector channels were read out using DC-coupled active cryogenic preamplifiers which enabled counting at rates for each wire approaching the inverse of the recovery time of a few nanoseconds [12] (determined by the wires’ kinetic inductance and the 160 Ω input impedance of the amplifiers, the maximum value for these particular wires which did not induce detector latching below the critical current [15]).

2. Detection efficiency, dark count rate, and timing jitter

Figure 1 displays the fiber-coupled system detection efficiency at 1550 nm and the dark count rate for all four devices as a function of bias current. Accurate measurement of the system detection efficiency, defined as the probability that a photon in the optical fiber will result in a detectable electrical pulse, required careful calibration of the optical power levels. A NIST-calibrated power meter was used to measure the power level from the laser and to calibrate two optical attenuators, which were used in series to attenuate the laser light to sufficiently low levels. The power calibration was performed using an optical fiber that was not AR coated, which would result in an overestimation of the detection efficiency by approximately 4% due to Fresnel reflection. We corrected for this effect by dividing the measured power on the power meter by 0.96 to obtain the power within the optical fiber. At each bias current, an automated attenuator blocked the laser light and dark count data was collected for 10 seconds using a commercial timestamping board. The light was then unblocked and efficiency data was collected for 10 seconds. All count rates were sufficiently low that corrections due to dead time effects from the detectors or the timestamp board were <1%. Similarly, errors due to counting statistics and calibration of the laser power and attenuators are expected to contribute less than 1%. The dominant source of error for the detection efficiency measurement is due to laser power fluctuation, which contributes on order 1% uncertainty.

 

Fig. 1 (a) Total system detection efficiency summed over all four detector channels. Variations of efficiency between devices were minimal, so only the sum is shown for clarity. The system detection efficiency exhibits a weak saturation near the critical current, implying high internal detection efficiency (note that this saturation is visible with the detection efficiency plotted on a linear scale). (b) Dark count rate. The color lines indicate the dark count rate per device, and the heavy black line is the total dark count rate summed over the four channels. The dark count rate decreases quickly away from the critical current, and then displays a weaker bias-current dependence at lower currents. This behavior was also observed in [19], where the weaker dependence at lower currents arises from the fact that in this regime the “dark” count rate is dominated by background photons rather than true dark counts. (c) Timing resolution as a function of bias current, for each of the four channels. The line colors correspond to the same detector channels as for part (b) of the figure. The timing jitter degrades as the bias current is lowered, which may be due to either a change in the timescales governing destruction of the superconducting state or the lower signal-to-noise ratio, or both. Variations in one or both of these is likely responsible for the difference in jitter between different channels. The inset shows a histogram of the electrical pulse arrival time relative to the optical pulse, for one of the devices, where the absolute value on the horizontal axis has been (arbitrarily) centered on the measured distribution.

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Both the detection efficiency and dark count rate increased with increasing bias current, and the detection efficiency reached a maximum value of approximately 76% at low count rates where recovery-time effects can be ignored. The timing jitter measured in the single photon regime was between 60 and 80 ps for each device at this detection efficiency. Timing jitter data was obtained using a pulsed modelocked laser and either the timestamping board or a fast real-time oscilloscope. In neither case did the instrumental jitter contribute significantly to the measurement.

3. Detector recovery time

A common limitation of single-photon detectors is their finite recovery time after a detection event, during which the detection efficiency for subsequent photons is reduced (or zero). As a consequence of the recovery time, the observed count rate saturates as it approaches the inverse of the recovery time. This effect manifests as an effective reduction in the average detection efficiency and can also skew the statistics of the detection events. Recovery times can vary widely for different single photon detector technologies. For example, superconducting nanowire single photon detectors can have recovery times as short as several nanoseconds, while InGaAs APDs typically have tens of microsecond recovery times. In addition, some detectors have a dead time τ_dead during which they are completely unable to detect photons, and after which the detection efficiency quickly returns to a baseline value, while others exhibit a more continuous recovery of the efficiency after a detection event. In general, given an observed count rate R_obs one would like to be able to infer the input count rate R_in, but this requires knowledge of both the source’s photon statistics and how the detection efficiency recovers in time after a photon is detected. Even when the source and detector behavior are known, it is often not possible to analytically determine R_in. Here, we derive a general method for determining R_in as a function of R_obs for a detector with an arbitrary detection efficiency recovery profile ε(t-t_d), where t_d is the time at which the photon was detected, when it is used with a Poisson-distributed photon source.

In the simple case of a dead time τ_dead, the relation between the dead-time-free and the dead-time-corrected count rates for a low-intensity source of Poisson-distributed photons is easy to deduce; the fraction of time during which the detector is unable to count photons is equal to R_obsτ_dead so the detector is only active for a fractional time (1-R_obsτ_dead). Therefore, as long as the arrival of photons is random, R_obs is related to R_in, the rate of photons being sent to a detector with efficiency ε, by

 

Fig. 2 Detection efficiency recovery following a detection event at t = 0. At time t = nδt, the efficiency is defined as ε_n. At long times, the detector efficiency recovers to its baseline value ε₀.

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For the special case of n = 1, the probability of sampling ε₁ should just be equal to the observed count rate times δt, or p(ε₁) = R_obsδt. Finding the observed rate requires calculating the weighted average of the input count rate times the detection efficiency. To do this, we multiply the input rate by each ε_n and its associated probability, and sum over all n. We find:

The above analysis assumes that the dark count rate is always negligible compared to the photon-induced count rate. If this is not the case, we need to modify the expressions given above. For a dark count rate with a dependence on bias current R_dark(Ι), and a corresponding relationship to detection efficiency R_dark(ε), the probability of sampling each ε_n then becomes:

We again have a set of N equations and N unknowns that can be solved numerically, as long as R_dark(ε_n) is known. The latter quantity can be directly measured experimentally, up to currents where R_dark becomes sufficiently large that the dark-count rate itself becomes affected by the finite recovery time. For higher currents, it should be possible to map out the true dark count rate as a function of time by starting at a low current, using the equations above to find the uncorrected dark count rate, and then increasing the current a small amount and repeating until the entire dark count versus current curve is mapped out.

To quantify the effect of recovery time and to test the model, we obtained data at different continuous-wave power levels. For data at high count rates, the commercial timestamping board could not be used due to its ~70 ns dead time. Instead, a high-speed, real-time oscilloscope was used to measure the detection rate. The two methods were found to be in good agreement at low count rates. For the model, we assumed that immediately after detection of a photon the current in the detector dropped to zero and then recovered exponentially with a 1/e recovery time equal to the inductance divided by the load resistance. We ignored the small delay between the drop in the current and the recovery, as well as the dependence of the kinetic inductance on the current through the device [10].

Figure 3 shows the measured count rate, summed over the four detectors, as a function of the input rate, and the corresponding fit, which resulted in an extracted L/R reset time of 5 ns per device. This value is consistent with our expectations based on the measured inductance of similar devices and uncertainties in the resistor values at low temperatures. The right-hand axis displays the effective detection efficiency penalty due to the reset time, assuming a source with Poisson statistics. While the detectors can count photons at extremely high rates, the reset time lowers the average efficiency to 68% for incident photon rates of 100 million photons per second and to 35% for rates of 1 billion photons per second. Clearly, the use of detectors with short recovery times is essential in order to maintain the detection efficiency and counting statistics when the count rate is high.

 

Fig. 3 Effects of reset time on detector performance at high count rate. The left-hand axis displays the sum of the count rates across the four detector channels, and the right-hand axis shows the (average) effective extra loss due to the reset time for a Poissonian source.

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4. Conclusions and future work

Several factors limit the observed detection efficiency, including a 7% reflection off the back surface of the oxidized silicon wafer, a slightly non-ideal cavity structure for enhancing the absorption at 1550 nm, and an internal detection efficiency that is less than unity (indicated by the incomplete saturation of the measured detection efficiency near the critical current [20]). The first two factors can be improved using more advanced optical designs with tighter tolerances for the dielectric layers. Higher internal efficiencies can be achieved by making the wires narrower [20,21] or using alternate materials with lower T_c and/or lower carrier densities [22], but these approaches may require sacrificing device speed. Significantly lower timing jitter, below 30 ps, has been observed in lower-efficiency NbN nanowire detectors on sapphire substrates [18], and the larger jitter we observe here may be associated with the use of NbN grown on oxidized silicon substrates or the lower signal to noise ratio associated with the smaller bias currents accessible for these thin and narrow wires. In fact, we also observe increased latching in these devices relative to detectors grown on sapphire, indicating slower heat transfer from electrons in the wire to phonons in the substrate [15], which may also be responsible for the increased timing jitter. Improved materials engineering may allow the present high efficiency to be combined with the 30ps timing jitter observed using sapphire substrates. Finally, the dark count rate can be reduced by operating at lower temperatures, as long as sufficient cooling power is available at those temperatures. This may be particularly difficult, however, for large numbers of detectors with a wide field of view and integrated readouts.

While superconducting detectors can provide unparalleled performance for single- or few-pixel systems, an ultimate goal for many applications is the development of large arrays for imaging, higher count rates, or photon number resolution. Compared to other high-efficiency superconducting detectors [6,22], the relatively high operating temperature of 2.5 K for our NbN-based SNSPDs presents several advantages relevant to the creation of large-scale SNSPD arrays. Our operating temperature can be reached using commercially-available, cryogen-free cooling systems that are easily operated, provide continuous cooling, and can tolerate hundreds of milliWatts of heat load with little increase in base temperature. This simplifies the readout of many pixels and makes possible the use of active cryogenic elements such as amplifiers and digital preprocessing circuits that inevitably generate heat. It can also significantly reduce the requirements for filtering of blackbody radiation for free-space coupling, desirable for many applications. Therefore, our results not only demonstrate that competing detector metrics can be achieved simultaneously in SNSPDs at the few-pixel level, but they also point to the feasibility of developing large-scale arrays of high-performance single-photon detectors.