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Optics Express

Photon statistics of one- and two-photon subtracted states at telecom wavelength reconstructed via direct detection

Pasquale Ercolano, A. Porzio, Mikkel Ejrnaes, Daniela Salvoni, Ciro Bruscino, Martina Peluso, Jia Huang, Chengjun Zhang, H. Li, Lixing You, L. Parlato, Giovanni Piero Pepe

Published Jun 30, 2025• 1 citation
Publisher

Abstract

Photon-number-resolving superconducting photon detectors promise to simplify detection schemes where only photon statistics matters in the few-photon regimes. Employed in one- and two-photon subtraction protocols, they allowed reconstruction of the photon number distribution for coherent and thermal states obtained from a pulsed laser at telecom wavelengths. The experimental setup is based on photon detection events recorded using a photon-number-resolving detector based on an array of eight superconducting NbN nanostrips working at 2.2 K. Photon subtraction was implemented using a low-reflectivity beam splitter and two superconducting nanostrip single photon detectors with an efficiency higher than 90% and a dark count rate of 1 cps. Our results confirm that our scheme accurately reproduces the theoretically expected effects of the annihilation operator on the states, achieving a fidelity higher than 99%.

DOI
10.1364/oe.568296

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Photon-number-resolving superconducting photon detectors promise to simplify detection schemes where only photon statistics matters in the few-photon regimes. Employed in one- and two-photon subtraction protocols, they allowed reconstruction of the photon number distribution for coherent and thermal states obtained from a pulsed laser at telecom wavelengths. The experimental setup is based on photon detection events recorded using a photon-number-resolving detector based on an array of eight superconducting NbN nanostrips working at 2.2 K. Photon subtraction was implemented using a low-reflectivity beam splitter and two superconducting nanostrip single photon detectors with an efficiency higher than 90% and a dark count rate of 1 cps. Our results confirm that our scheme accurately reproduces the theoretically expected effects of the annihilation operator on the states, achieving a fidelity higher than 99%.
Single photon detectors based on superconducting nanostrips demonstrated high performance at 1550 nm, combining high efficiency and low noise. Arranged in arrays, these devices can implement photon-number resolution, expanding the range of applicability of superconducting detectors. A detector of this kind was used in our recent work to implement the annihilation operator and the characterization of quantum states in terms of their photon number distribution. The reconstructed distributions were consistent with the theoretical predictions, exhibiting fidelities higher than 99.9%. In this work, this procedure was repeated with each pixel singularly to define a detector fidelity matrix, evaluating the fidelity among all the possible pixel combinations. In this way, we introduce an additional tool that quantifies not only the quality of the reconstructed photon number distribution when compared to the theoretical expectation, but also the mutual fidelity when different pixels are chosen as independent, and then the fabrication uniformity.
Detectors capable of resolving the number of photons are essential in many applications, ranging from classic photonics to quantum optics and quantum communication. In particular, photon-number-resolving detectors based on arrays of superconducting nanostrips can offer a high detection efficiency, a low dark count rate and a recovery time of a few nanoseconds. In this work, we use a detector of this kind for the unbiased generation of random numbers by following two different methods based on the detection of photons. In the former, we exploit the property that the light is equally distributed on each strip of the entire detector, whereas in the latter we exploit the fact that, for a high average number of photons, the parity of the Poissonian distribution of the number of photons emitted by the laser tends to be zero. In addition, since these two methods are independent, it is possible to use them at the same time.
The use of improved fabrication technology, highly disordered NbN thin films, and intertwined section topology makes it possible to create high-performance photon-number-resolving superconducting single-photon detectors (PNR SSPDs) that are comparable to conventional single-element SSPDs at the telecom range. The developed four-section PNR SSPD has simultaneously an 86±3% system detection efficiency, 35 cps dark count rate, ∼2 ns dead time, and maximum 90 ps jitter. An investigation of the PNR SSPD’s detection efficiency for multiphoton events shows good uniformity across sections. As a result, such a PNR SSPD is a good candidate for retrieving the photon statistics for light sources and quantum key distribution systems.
Photon number resolving detectors find space in many fields, such as quantum optics, boson sampling and fluorescence spectroscopy. In particular, the reconstruction of the input photon distribution is essential in quantum communications to detect photon-number-splitting attacks. In this work, we discuss the operation configurations of a photon number resolving detector based on superconducting nanostrips at a wavelength of 1550 nm from a temporal point of view. We set a time binning and acquired the number of recorded pulses per bin by means of a time-to-digital converter. We studied the predictions of two theoretical models and compared them to the experimental data in order to analyse their operation regimes depending on the binwidth and to employ them for the reconstruction of the input photon distribution. We applied this method to a continuous-wave laser source, showing that the former can be used for the characterization of non-pulsed light sources, even with a photon emission rate so low that the dark count rate of a superconducting nanostrip is not negligible.
Abstract We experimentally demonstrate high-fidelity detection of 0, 1- and 2-photon states in a commercial superconducting nanowire single photon detector (SNSPD) under 20 MHz pulsed coherent illumination. The arrival of a different number of photons induces distinct temporal dynamics in the disruption of the superconducting state of the detector. Therefore, specific features emerge in the arrival-time histograms, that we show are directly correlated with the photon-number state. We show that, across a broad range of time-averaged light intensities, the probabilities of detecting 1- and 2 + -photon events collapse onto the Poisson distribution of coherent light. We identify the voltage detection threshold as a critical factor for photon number resolving (PNR) capabilities. Even under demanding conditions of high repetition rate illumination, we found that a high trigger level significantly enhances total detection fidelity, achieving 0.920 and 0.845 for 1-photon and for 2-photon events. These results correspond to remarkably low conditional misidentification probabilities, 0.000 02 and 0.0013, describing the classification error among detected 1- and 2-photon events. We identify an inherent 39 ps latency difference between single- and multi-photon detection events. We show that the measured 2-photon conditional misidentification probability corresponds to the one of a multiplexed PNR detector with 730 pixels. We believe that our findings provide a framework for developing high/fidelity spatially multiplexed SNSPD by exploiting the intrinsic PNR capabilities of individual constituting elements.