Opto-electronic bias of a superconducting nanowire single photon detector using a cryogenic photodiode

The principle of operation of an SNSPD is based on the photon-induced breakdown of superconductivity in a thin and narrow wire. The wire is electrically biased close to its critical current, such that the absorption of at least one photon is sufficient to make the wire normally conductive and a voltage pulse can be read out. Depending on their material and geometry, SNSPDs typically require a bias current in the range of 1–50 µA.²² In our implementation, this is provided by the photocurrent of an off-the-shelf photodiode from Marktech (MTPD1346D-010). To that end, we first characterize the performance of the photodiode under cryogenic conditions. For a photodiode in shunted operation, the conversion ratio from an optical input power P to a photocurrent I is described by the responsivity $R(λ)=I/P(λ)$⁠. The conversion depends on the active material and operation wavelength λ. We characterize the responsivity of an off-the-shelf InGaAs–InP photodiode depending on the wavelength and temperature. To do so, the photodiode is mounted in a cryostat and a single mode fibre illuminates it from above. A tunable continuous-wave laser provides a power of 1 mW into the fiber, and an ampere meter reads out the photocurrent generated by the photodiode through a coaxial cable, as it can be seen in Fig. 2. While cooling down the photodiode from ambient temperatures to 0.8 K, the illumination wavelength is swept in a range from 1440 to 1640 nm in 2 nm steps, and the generated photocurrent is measured. The acquired responsivity is displayed in Fig. 2(b).

The photodiode achieves a responsivity of about 0.65 A/W at ambient temperatures at 1540 nm, as it can be seen in Fig. 2(b). Over the entire temperature range, the responsivity is maintained over a wavelength range of 1440–1540 nm. A responsivity of 0.55 A/W is measured at 1540 nm at a stable operation temperature of 0.8 K. In contrast, the responsivity of the photodiode is reduced over a wavelength range of 1540–1640 nm below a temperature of 150 K. This is explained by the temperature-dependent bandgap of InGaAs–InP with the Varshni model²³ and has been reported previously.¹⁸ The temperature dependence of the bandgap cannot be directly extracted from this dataset because the temperature sensors for the cold stage of the cryostat are not precisely calibrated in the range from 270 to 20 K.

The bias current for an SNSPD needs to be adjusted to generate photocurrents below the critical current. Therefore, we need to determine the photocurrent depending on the input power over a sufficient range to accurately set the desired bias current. To do this, we insert a variable attenuator to limit the optical power on the photodiode while the laser is operated at stable power output at 2 mW with a wavelength of 1540 nm. The illumination power of the photodiode is varied in 0.25 dB steps, the current is read out with a picoammeter, and the results are shown in Fig. 2(c). The photodiode shows a linear dependence in the responsivity in the range from 1 mW to 100 nW at room temperature and 1 mW to 10 pW at cryogenic temperatures. The photodiode is not responsive for lower input powers because the dark current is larger than the generated photocurrent. The photodiode has a significantly larger dynamic range at cryogenic temperatures since the dark current is reduced with the decrease in temperature. The upper limit of the characterization is 1 mW so as not to exceed the heat load limit of the cryostat, given by the manufacturer.

In summary, the responsivity of the photodiode decreases slightly 0.55 A/W at cryogenic temperatures; however, the linear dependence between the input power and photocurrent is maintained. The photodiode can provide the bias current for an SNSPD of about 5 µA with 8 µW of input power, which does not surpass the heat load limit of the cryostat of about 1 mW at 0.8 K. The photodiode is characterized in shunted operation, since the superconducting meander of the SNSPD shunts the circuit. We additionally characterized the load capabilities of the photodiode at 0.8 K in Sec. IV, in which we show that the generated photocurrent is not suppressed by the typical circuit loads with these optical input intensities at 0.8 K.

We realize the current bias of the SNSPD with a photocurrent generated by a photodiode located at the cold stage of the cryostat to show the proof of principle of the concept. We compare the performance with a conventional bias via a current source at ambient temperatures. Both biasing methods are realized with the same SNSPD, during separate cooldowns of the cryostat. The fabrication parameters of the SNSPD follow those from Marsili et al.²⁴ We specifically compare the voltage response of the click signal, the count rate dependent on the bias, the derived System Detection Efficiency (SDE), and the timing jitter.

The photocurrent bias is realized by connecting the photodiode, SNSPD, and a 50 Ω resistor in parallel at the cold stage of the cryostat, as schematically shown in Fig. 1. The photodiode is illuminated through an optical fiber with a laser emitting at 1530 nm. An optical power of 6.7 µW is transmitted onto photodiode, resulting in a bias current of 5 µA. The cold stage of the cryostat reached a stable temperature at 0.8 K. The SNSPD generates click signals that are transmitted through coaxial cables and amplified further with two room temperature amplifiers (Mini-Circuit ZKL-2R5+). The resulting signal is displayed in Fig. 3 (blue), with an amplitude of 50 mV, a rise time of 2.5 ns, and a fall time of 100 ns. The detected click events show the proof-of-principle for optically biasing an SNSPD.

The conventional bias is realized with the same SNSPD using a single commercial biasing and readout circuit at room temperature (Photonspot) consisting of a constant current source, integrated amplifier, and a 50 Ω shunt resistor. The resulting click signal of the current bias is depicted in Fig. 3 (orange), with a bias current of 5 µA, an amplitude of 120 mV, and a fall time of 100 ns. Both click signals have a similar shape and only deviate in their amplitude due to the use of different amplifiers. For further performance analysis, the click signals are acquired with a timetagger with a threshold height at 50% of the maximum peak height.

The bias-dependent count rate of the SNSPD is investigated to compare the detection efficiency of both biasing methods. To do so, the timetagger detects the click signals of the SNSPD and acquires a count rate for both biasing methods. A pulsed laser with a repetition rate (RR) of 400 kHz, wavelength of 1550 nm, and attenuated to a mean photon number of ∼2 photons per pulse is used to illuminate the SNSPD. The resulting bias dependent count rate is given in Fig. 4(a) and Fig. 4(b) for the photocurrent bias and the conventional bias. Both biasing methods show a similar dependence between the count rate and the applied bias, following a sigmoidal function. To compare the response of each device, the click rate of the SNSPD is compared at the point of inflection in the System Detection Efficiency (SDE) that is common in both bias dependent count rate distributions and highlighted in Fig. 4. At this point of inflection, the photocurrent bias reached a Photon Count Rate (PCR) of 256 kcps and a Dark Count Rate (DCR) of 12.2 kcps. In comparison, the conventional bias reached a PCR of 251 kcps and a DCR of below 1 kcps. Both biasing methods reach a similar signal count rate, but the DCR increases under the photocurrent bias.

The increase in the DCR can be attributed to additional photons from the photodiode illumination being scattered onto the SNSPD. To investigate the scattering, we illuminate the photodiode with a power equal to the 90% of the critical bias at 6.8 µW, but we bias the SNSPD with the conventional bias. The dark count rate is investigated here at the 90% of the maximum bias because this is closer to the point of typical operation. The resulting DCR with this conventional current bias reaches a count rate of 31 kcps. This is higher than the DCR at the point of inflection of the SDE due to the increased bias.

The bias dependent count rate shows different behavior for each biasing method beyond the count rate plateau, as it can be seen in Fig. 4. Under the conventional bias of the SNSPD, no counts beyond a bias current of 5.6 µA are measured, which is indicative of latching. At bias currents beyond this point, absorbed photons generate a hotspot from which the SNSPD cannot reset; therefore, no additional click signals are registered.

However, under photocurrent bias, the count rate increases significantly for an optical bias power of 7.6 µW [see Fig. 4(a)]. Individual traces are generated in the range from 7.6 to 11.6 µW, which are acquired by the timetagger. We attribute this to latching and self-resetting dynamics:^25,26 The provided photocurrent in the SNSPD could surpass the critical current in the meander in this regime and therefore induce a hotspot. The 50 Ω shunt resistor placed directly at the SNSPD redirects the current such that hotspot resets. This process then repeats. In contrast, in the conventional bias method, the added coaxial connection to the shunt resistor at room temperature delays the current redirection, meaning the hotspot cannot reset and the meander remains resistive. In other words, the propagation delay of the coaxial cable alters the resetting behavior and the SNSPD latches.

The count rate of the SNSPD reaches a plateau for the optical and electrical biasing method above a bias with 90% of the maximal bias. We derive the system detection efficiency (SDE) by comparing the count rate of the SNSPD with a calibrated detector with the same input of the mean photon number. The mean photon number $n̄$ is calculated by the Photon Count Rate (PCR) for a given repetition rate RR of the attenuated excitement laser with a detection efficiency η of the click detector²⁷ 

A calibrated detector with a detection efficiency of 83% ± 5% is used to set a mean photon number of 2.2 ± 0.13 for the photocurrent bias and 2.4 ± 0.14 for the conventional bias. The resulting SDE dependent on the bias is shown in Fig. 5. The SDE should be independent of the current source since only a constant current is supplied to the SNSPD. To compare biasing methods in respect to their SDE, we normalize the bias to the point of inflection of a sigmoidal function. The point of inflection for the conventional bias is at 4.2 µA, and at 5.8 µW for the photocurrent bias while having a maximum SDE of 79.3% ± 5% and 82.5% ± 5%, respectively.

An additional potential difference between the cold stage of the cryostat and the ambient temperature is measured without any applied bias. The offset current is in the order of 700 ± 100 nA, which must be accounted for when calculating the bias current. This potential difference could be induced by thermo-electric voltage induced by different temperatures and connections as well as noise pickup of the cold stage.²⁸ In contrast, the photodiode bias is immune to the potential difference since the load resistor and SNSPD are on the same potential. Nonetheless, the normalized system detection efficiency overlap for both biasing schemes with the offset current compensated as shown in Fig. 5.

The plateau in the detection efficiency for the photocurrent bias is extended in comparison to the conventional bias. The increased plateau length could originate from an improved current stability with the photocurrent bias. The photodiode generates the bias current in close proximity to the SNSPD and could be more immune to noise pickup of the cables in the cryostat.

One of the many benefits of SNSPDs is their low timing jitter of the detection signal. The jitter should not be influenced by the biasing method as long as a constant current is supplied to the SNSPD. To verify this, we compare the system timing jitter in both biasing regimes. To do so, we use an attenuated pulsed laser with a repetition rate of 625 kHz and a pulse width below 1 ps at a center wavelength 1545 nm to excite the SNSPD. In the characterization, a bias point at 90% of the maximum bias (6.8 µW and 5 µA) is chosen. The resulting histogram of the photocurrent bias (blue) and conventional current bias (orange) shows in Fig. 6 the jitter in the timing delay between a trigger signal of the optical input pulse and a generated click signal of the SNSPD. The distribution of the timing delay for the photocurrent bias has a Full Width Half Maximum (FWHM) of 513 ± 3 ps. In comparison, the conventional current bias has a FWHM of 495 ± 3 ps. The FWHM of the timing jitter of both methods agree within a few percent relative error. A small difference can arise from a difference in the bias set point. The SNSPD was biased at 90% of the maximum bias that deviates from comparison of the point of inflection because of the difference in the plateau length. Hence, the jitter was acquired at different relative bias points. This mismatch in the relative bias leads to a change in the bias dependent width in the jitter distribution that has been previously reported.^7,29–31 Additionally, the conventional bias and the photocurrent bias schemes use different amplifiers to detect the click signals. A single commercial amplifier is used in the conventional bias scheme, and two chained amplifiers are used in the photocurrent bias scheme. The chained amplifiers can introduce and amplify additional thermal noise such that additional jitter is added in the system. Nevertheless, both methods show no significant deviation in the overall system jitter.

We successfully biased an SNSPD with the photocurrent of a photodiode at cryogenic temperatures. This method enables us to optically bias an SNSPD and replace the electrical input connection with a light source, photodiode, and optical fiber. The used photodiode was characterized at cryogenic temperatures and showed a responsivity of at least 0.55 A/W. The optical bias with the photodiode reached a plateau at a bias power of 6.8 µW. In comparison to a constant current bias, no significant reduction in the detector performance was observed in terms of the system detection efficiency and timing jitter. The dark counts increased slightly, which is wholly attributable to photons leaking from the optical bias.

Connecting an SNSPD directly from room temperature to a cold stage, the thermal heat load is in the few milliwatt range.^11,28 Thermal anchors can reduce the effective heat load for the cold stage by absorbing the heat at intermediate stages. In comparison, a single mode fiber can be added from ambient temperatures to the cold stage directly since minimal heat is conducted through the fiber. This reduces the latent heat load by a factor of 100 compared with coaxial cable.^13,14

The optical bias of the SNSPD shows further possibilities of improvements and applications. The dark count rate of the SNSPD can be decreased by improved shielding of the bias light. The optical input of the SNSPD can also be combined with an electro-optical modulator^13–16 to achieve pure optical operation of an SNSPD. This removes the constraint of using any coaxial cable between room temperature and the cryogenic environment reducing the heat load further^11,14 and achieve galvanic isolation.¹¹ Extending this scheme, an optically pulsed photodiode would enable a simple method for bias current pulsing. Since the bandwidth would be limited by the photodiode, bandwidths exceeding 10 GHz¹⁹ under cryogenic conditions are feasible. This method can be investigated further to gate the detection of an SNSPD.

See the supplementary material for the load characterization of the photodiode at 0.8 K.

This work was supported by the Bundesministerium für Bildung und Forschung (Grant No. 13N14911). We thank Varun Verma (NIST) for providing the superconducting films for the Superconducting Nanowire Single Photon Detectors.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.