Photon-number resolving detector based on a series array of superconducting
nanowires: Supplementary Material
S. Jahanmirinejad,1* G. Frucci,1 F. Mattioli,2 D. Sahin,1 A. Gaggero,2 R. Leoni,2 and A.
Fiore1
1
COBRA Research Institute, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The
Netherlands
2
Istituto di Fotonica e Nanotecnologie, CNR, Via Cineto Romano 42, 00156 Roma, Italy
*
corresponding author: s.jahanmiri.nejad@tue.nl
1
Table of Contents
Discussion on the effect of lowpass filter
3
Discussion on the observed excess noise
3
References
4
2
Discussion on the effect of lowpass filter
As it was mentioned in the text, a lowpass filter was useful in order to reduce the noise that we observed in our
response and to have a cleaner capture. However, removing the lowpass filter does not prevent the PNR capability
for the 4-photon detection. Figure SM1 shows a measurement of the same device, at a slightly higher photon flux
and at a higher temperature of ~5K (measured in a cryogenic probe station setup), with one more amplifier in the
chain and without using a lowpass filter. The peaks are still discernible, but more overlapped.
Figure SM 1. Histogram of the photoresponse pulse amplitude for the same 4-SND of Fig. 4, measured in the cryogenic probe station setup at a
higher temperature of T~5K, with an added amplifier in the chain, but without lowpass filtering the response. The estimated mean detected
photon number is μ~3.2.
Discussion on the observed excess noise
When distinct elements of the SND detect photons simultaneously, the output voltage amplitude changes
accordingly, with a linear dependence on the number of switching nanowires (i.e., number of detected photons).
However, the presence of the electrical noise causes some fluctuation in the output voltage pulse. Correspondingly,
the histogram of the peak output voltages consists of a series of Gaussian peaks, rather than a series of Dirac delta
functions. The width of each Gaussian peak corresponds to the electrical noise of the related photon detection event.
In the histogram of Fig. 4(b), we can observe an increase in the widths of the Gaussian peaks when the photon
number is increased. This is an evidence of an “excess noise” with increasing the photon number n, which may be
attributed to two major sources. The first is the accumulation of the intrinsic noise of each detection event, related to
3
the variation in the resistance of the normal region1 in each photon detection event. This noise, whose root mean
square (rms) value is expected to scale as n0.5, can be reduced by having more uniform nanowires. The second source
of excess noise is the variation of the amplifier noise due to the varying detector impedance, which is the source
impedance seen by the amplifier. In particular, the rms noise produced by the equivalent noise current generator of
the amplifier is expected to scale proportionally to the detector impedance, therefore to n, for small n (i.e., as long as
the detector impedance is smaller than the amplifier input impedance), and to saturate as n becomes larger. As the
amplifiers used in this measurement have large noise figures (3.3dB) and large noise current due to the bipolar
transistor technology, they have a large contribution to the total noise which increases with the device resistance.
Therefore, we believe that the noise performance is not the best we could achieve with this device. The other
possible noise sources, such as the thermal noise of the parallel resistors, are calculated to be negligible as compared
to the observed noise. Indeed, in the bandwidth of 20MHz-80MHz, the rms noise voltage of a resistance RP=29.5Ω
is estimated to be only a fraction of microvolt, while the generated signal across the resistance is in the order of tens
of microvolt. The inset in Fig. 4(b) plots the measured excess noise, defined as En = (σn2 – σ02)0.5, where σn and σ0 are
the standard deviations of the histogram peaks corresponding to n and 0 firing sections, respectively, as a function of
n. The data shows an approximately linear behavior (Enn), with some saturation for large n. As both sources of
excess noise would give rise to a sub-linear dependence it is not possible to reliably discriminate between the two
with the data in Fig. 4(b). We note that, with the presented readout circuit, the excess noise would limit the photon
number discrimination ability to N~4. However, using a cryogenic low-noise preamplifier and/or a preamplifier
circuit designed to optimize the signal-to-noise ratio should result in a much increased dynamic range.
References
1
J. Kitaygorsky, S. Dorenbos, E. Reiger, R. Schouten, V. Zwiller, and R. Sobolewski, IEEE Trans. Appl. Supercon. 19, 3, 346–349
(2009).
4