Dual Readout : jitter optimization

To overcome the jitter limitation, I investigated the use of a dual readout scheme. Such readout has originally been proposed with the aim of reducing the geometrical jitter of SNSPDs [71] (i.e the jitter due to the hotspot location in the SNSPD meander). The propagation time of the signal through the nanowire, which acts as a transmission line, induces a delay proportional to the propagation length. Reading the output signal on both ends of the wire allows us to monitor both timings. The absorption time of the photon can then be deduced using the average of the two recorder timings. This method can be effectively used to reduce the jitter [71] or to characterize the geometrical component of the jitter of an SNSPD [84]. In our case, the propagation time alone cannot explain the different timings recorded, but as the two terminations of the secondary coils of the transformers are symmetrical, using the signal generated at both outputs can provide more information about the timing and help correct the issue. Figure 4.5 shows the schematic of this new solution, which is essentially the same as the one proposed on fig. 4.1, but with a second coaxial line to read the signal on both terminations of the series transformer secondary coils.

Results reported in the literature describe the correction of geometrical jitter using the averaged timing of the two outputs [71, 84]. In our case, this scheme could allow to correct multiple jitter distribution observed with the series transformer scheme. The different signals can be seen on the second output as well, as shown on figure 4.6. By testing the setup pixel by pixel it can be verified that, as expected, the timings are symmetrical (i.e. the pixel with the shortest timing on output 1 corresponds to the latest timing on output 2). Multi-photon absorption and thermal crosstalk effects can also be observed, as this specific data shown on figure 4.6 was recorded with a more compact detector design, with no additional distance between the pixels. Detection efficiency and detection rate measurement have been performed on the second output to ensure both readout were giving similar results.

Figure 4.5: Electronic schematics of the series transformer solution with a dual readout scheme. The principle is the same as the series transformer schematics shown on fig. 4.1, with both ends of the secondary coils line connected to a coaxial line each. Both outputs are then amplified and readout at room temperature. Inset : illustration of a recorded detection event using a dual-readout scheme. The detector produces two output voltage pulses with opposite polarity. In our setup, the difference of timing between the two outputs is generated by the different paths created by the transformers scheme.

Timing jitter measurements were done with a pulsed laser, using the laser trigger as the timing reference for both output signals. Recording of the output voltage traces shows that both outputs exhibit different delays, with respect to the laser trig signal, and that the timing order of the pixels is indeed reversed on the second output. To characterize the timings of the different pixels and output, we recorded the timestamps of the different events : the laser trigger and the detection events on both outputs. The timestamps acquisition was performed for each pixel individually, by turning the desired bias currents on or off. Figure 4.7 shows the histogram of the timestamps obtained, with respect to the laser trigger event at time t= 0 (t1 andt2 grayed areas on fig. 4.7). As described in reference [84] we also calculated, for each individual detection event, the average timing of the two outputs as well as the difference (tavg = t1+t2

2 and t_{dif f} = t2−t1). The histogram of the values tavg and t_{dif f} obtained are also shown on fig. 4.7. Unlike what was expected, the average timingst_avg do not show a single narrow distribution. This

4.1. Series transformers

Figure 4.6: Persistence traces of the two outputs voltage of the dual readout with the transformer-series circuit. The four pixel signal can bee seen around 5 ns. Two-photon absorption can be seen with higher amplitude signals (and the pixels in which they occur identified). In addition, effect of the thermal crosstalk (due to the compact design of the detector used to acquire this data) is noticeable as a second pulse which happen at different timings after the photon-absorption event.

might be partly due to the fact that the signal amplitude of both outputs is slightly different and therefore the threshold value used for discrimination is not equivalent on both outputs. It was not possible to fully correct the problem by adapting the threshold values individually. Another explanation can be that the discrete transformers used do not have a consistent behavior between one another.

As the distribution of each pixel is individually well defined, it is however possible to correct for the different delays observed. This requires to identify which pixel triggers the event and apply a time offset corresponding to its specific delay. In order to use this scheme in a free-running experiment, this needs to be done without using the laser trigger time as a reference. We can identify the pixel by looking at the difference of timing t_{dif f} between the two outputs. Figure 4.8a shows a zoom on the corresponding distribution, it can be seen that each pixel timings have well defined ranges, which allow to discriminate perfectly between them.

The mean value of the tavg distributions obtained are also measured individually and stored (tavgi on fig. 4.8b). This will allow for correcting the timings of pixel event in the

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Figure 4.7: Timing distributions obtained on each pixel separately (the bias current was turned off on the non-used pixels). The pixel measurements are identified by the color code.

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(a) Difference of the timings of the two out-puts. The distributions are fully distinguish-able which will allow discriminating between the different pixels even when all are biased simultaneously.

9200 9250 9300 9350 9400 9450 9500 9550 9600 Detection timestamp [ps]

pixel 1 pixel 2 pixel 3 pixel 4

(b) Average of the timings of the two outputs.

The mean of each pixel timing distribution can be measured and stored for implementing the timing correction of the event recorded.

Figure 4.8: Zoom on the distributions of t_{dif f} andt_avg presented on fig. 4.7 (first and third grayed areas from the left).

4.1. Series transformers

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Figure 4.9: Timing distribution obtained on both outputs (red and blue) with all the pixels biased simultaneously with Ib close to Ic. The corrected timing values tcorrected

distribution is plotted in green. The inset presents a zoom on this final distribution.

The distribution obtained exhibits the Gaussian profile with an exponential tail typically obtained with SNSPDs. The timing resolution of the ID900 TDC is limited to 20 ps which could be deconvoluted from the distribution obtained. The high-resolution mode of the device provides the 13 ps time bins used to display the histogram.

The same measurement was then performed while biasing all of the pixels simultaneously, which is the actual purpose of the design. In this case, it is not possible to directly know which pixel absorbed a photon, but the comparison of both outputs permits it, using the different timing range measured and shown on fig. 4.8a. For each detection, the difference of the timingst_{dif f} was calculated and the pixel number iidentified. Then the corrected timing can be calculated as :

t_corrected =t_avg−t_avgi = (t₂−t₁)/2−t_avgi (4.1)

Figure 4.9 shows the raw distribution obtained for both outputs (t1 andt2), as well as the final distribution obtained by correcting the timings using the method presented above.

A final timing jitter of 48.33 ps FWHM is obtained, which is well within the performances of classical SNSPDs and enable the use of the scheme for application in quantum experiments.

Of course, the data presented in this work has been post-processed to find the desired values tdif f, tavg, and tcorrected. In a final design, the calculation should be done in real-time. This can be achieved on an FPGA board, which is already in use in our

the calculation of the finalt_corrected value is done without the need of the laser trigger reference which enables the use of the solution for experiments requiring free-running detection.

The electronic readout solution I proposed here allowed to connect a multi-nanowire SNSPD to a single coaxial line. This new readout could reproduce the results obtained with the multipixel scheme (presented in section 3.2) in terms of detection efficiency, maximum detection rate, and timing jitter. A great advantage of this solution is that no additional nanofabrication was required. The circuit can be used to read an SNSPDs build from multiple nanowires (as described here), but could also permit reading multiple SNSPDs simultaneously.