Abstract: The topic of superconductivity in strongly disordered materials has attracted significant attention. These materials appear to be rather promising for fabrication of various nanoscale devices such as bolometers and transition edge sensors of electromagnetic radiation. The vividly debated subject of intrinsic spatial inhomogeneity responsible for the non-Bardeen-Cooper-Schrieffer relation between the superconducting gap and the pairing potential is crucial both for understanding the fundamental issues of superconductivity in highly disordered superconductors, and for the operation of corresponding nanoelectronic devices. Here we report an experimental study of the electron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. The temperature dependence of the critical current follows the textbook Ginzburg-Landau prediction for the quasi-one-dimensional superconducting channel I c approximately (1-T/T c)(3/2). We find that conventional models based on the the phase slip mechanism provide reasonable fits for the shape of R(T) transitions. Better agreement with R(T) data can be achieved assuming the existence of short 'weak links' with slightly reduced local critical temperature T c. Hence, one may conclude that an 'exotic' intrinsic electronic inhomogeneity either does not exist in our structures, or, if it does exist, it does not affect their resistive state properties, or does not provide any specific impact distinguishable from conventional weak links.

Abstract: We have found experimentally that the rise time of voltage pulse in NbN superconducting single photon detectors increases nonlinearly with increasing the length of the detector L. The effect is connected with dependence of resistance of the detector Rn, which appears after photon absorption, on its kinetic inductance Lk and, hence, on the length of the detector. This conclusion is confirmed by our calculations in the framework of two temperature model.
D.Yu.V. acknowledges the support from the Russian Foundation for Basic Research (Project No. 15-42-02365). K.V.S. acknowledges the financial support from the Ministry of Education and Science of the Russian Federation (Contract No. 3.2655.2014/K).

Abstract: Traditionally, photon detectors are operated in a direct detection mode counting incident photonswith a known quantum efficiency. This procedure allows one to detect weak sources of radiation but allthe information about its frequency is limited by the optical filtering/resonating structures used which arenot as precise as would be required for some practical applications. In this work we propose heterodynereceiver based on a photon counting mixer which would combine excellent sensitivity of a photon countingdetector and excellent spectral resolution given by the heterodyne technique. At present, Superconducting-Nanowire-Single-Photon-Detectors (SNSPDs) [1] are widely used in a variety of applications providing thebest possible combination of the sensitivity and speed. SNSPDs demonstrate lack of drawbacks like highdark count rate or autopulsing, which are common for traditional semiconductor-based photon detectors,such as avalanche photon diodes.In our study we have investigated SNSPD operated as a photon counting mixer. To fully understandits behavior in such a regime, we have utilized experimental setup based on a couple of distributedfeedback lasers irradiating at 1.5 micrometers, one of which is being the Local Oscillator (LO) and theother mimics the test signal [2]. The SNSPD was operated in the current mode and the bias currentwas slightly below of the critical current. Advantageously, we have found that LO power needed for anoptimal mixing is of the order of hundreds of femtowatts to a few picowatts, which is promising for manypractical applications, such as receiver matrices [3]. With use of the two lasers, one can observe thevoltage pulses produced by the detected photons, and the time distribution of the pulses reproduces thefrequency difference between the lasers, forming power response at the intermediate frequency which canbe captured by either an oscilloscope (an analysis of the pulse statistics is needed) or by an RF spectrumanalyzer. Photon-counting nature of the detector ensures quantum-limited sensitivity with respect to theoptical coupling achieved. In addition to the chip SNSPD with normal incidence coupling, we use thedetectors with a travelling wave geometry design [4]. In this case a NbN nanowire is placed on the topof a Si3N4 nanophotonic waveguide, thus increasing the efficient interaction length. For this reason it ispossible to achieve almost complete absorption of photons and reduce the detector footprint. This reducesthe noise of the device together with the expansion of the bandwidth. Integrated device scheme allowsus to measure the optical losses with high accuracy. Our approach is fully scalable and, along with alarge number of devices integrated on a single chip can be adapted to the mid and far IR ranges wherephoton-counting measurement may be beneficial as well [5].Acknowledgements: This work was supported in part by the Ministry of Education and Science of theRussian Federation, contract No. 14.B25.31.0007 and by RFBR grant No. 16-32-00465.