Geometrical jitter and bolometric regime in photon detection by straight superconducting nanowire

We present a direct observation of the geometrical jitter in single photon detection by a straight superconducting nanowire. Differential measurement technique was applied to the 180-{\mu}m long nanowire similar to those commonly used in the technology of superconducting nanowire single photon detectors (SNSPD). A non-gaussian geometrical jitter appears as a wide almost uniform probability distribution (histogram) of the delay time (latency) of the nanowire response to detected photon. White electrical noise of the readout electronics causes broadened, Gaussian shaped edges of the histogram. Subtracting noise contribution, we found for the geometrical jitter a standard deviation of 8.5 ps and the full width at half maximum (FWHM) of the distribution of 29 ps. FWHM corresponds to the propagation speed of the electrical signal along the nanowire of $6.2\times10^{6}$ m/s or 0.02 of the speed of light. Alternatively the propagation speed was estimated from the central frequency of the measured first order self-resonance of the nanowire. Both values agree well with each other and with previously reported values. As the intensity of the incident photon flux increases, the wide probability distribution collapses into a much narrower Gaussian distribution with a standard deviation dominated by the noise of electronics. We associate the collapse of the histogram with the transition from the discrete, single photon detection to the uniform bolometric regim

Photon-number dependent afterpulsing in superconducting nanostrip single-photon detectors

Superconducting nanostrip single-photon detectors (SNSPD) are wide-spread tools in photonic quantum technologies. Here, we study afterpulsing in commercial SNSPD made of amorphous superconducting material. We find that the probability of an afterpulse is not a constant but depends on the mean number of photons per light pulse including mean numbers much less than one. Our observations exclude the electrical circuit as the primary cause of afterpulsing. We propose a phenomenological model which qualitatively explains our findings via the introduction of slowly relaxing "afterpulsing centers". We argue that two-level systems in amorphous materials are the most plausible physical candidates for the role of such afterpulsing centers

Size Effects and Excess Noise in Superconducting Nanowire Single-Photon Detectors

Superconducting Nanowire Single-Photon Detectors (SNSPDs) offer unique performance such as extended spectral sensitivity (from visible to near-infrared range), low dark count rate (1 dark count per hour), and high timing resolution (a few picoseconds) making them highly desirable for applications in quantum computing, quantum communication, and quantum/classical light detection. However, new sophisticated applications such as deep-space communication or direct detection of dark matter particles require even more stringent performance criteria from the SNSPD technology. Among others, they require extremely low, if any, dark count levels and broad spectral sensitivity up to the middle infrared range. We identify new strategies for improving the overall performance of these devices from a material science perspective by investigating size effects and excess noise in superconducting nanowires. The photon detection mechanism in a current-carrying superconducting nanowire is relatively simple. An absorbed photon with energy largely exceeding the superconducting gap locally breaks superconductivity that eventually drives the nanowire into the resistive state which is experimentally registered as a photon count. The dynamics of this process is governed by phonons and electron systems and thermal coupling to the substrate. The miniaturization of device sizes in superconducting nanoelectronics, and particularly in SNSPDs, which are conventionally made of 5 nm-thick and 100 nm-wide superconducting nanowires, leads to modification of their thermal properties at low temperatures. The reciprocal film thickness limits the phonon wave vectors perpendicular to the film plane, significantly altering the phonon spectrum and the heat capacitance of phonons. Our extensive studies of superconducting NbTiN films [1, 2] with polycrystalline granular morphology revealed the impact of mean grain size on the phonon heat capacitance. Such size effect can be used to tune the cut-off in the spectral sensitivity of SNSPDs via engineering the phonon properties. In SNSPDs, besides stochastic dark counts caused by thermal fluctuations [3], there are conditional dark counts, or afterpulsing [4], as a kind of excess noise that presents a significant challenge in improving device performance. We observed that the probability of an afterpulse in an SNSPD made of amorphous MoSi depends on the mean number of photons per light pulse, including values much less than one. Our proposed phenomenological model explains our findings by introducing slowly relaxing afterpulsing centers, which we believe may be two-level systems in amorphous materials. While two-level systems are well-known sources of decoherence and losses in superconducting qubits and resonators, their impact on SNSPD performance is yet to be explored. Therefore, understanding the microscopic details and material science aspects may play a dominant role in further improving the performance of superconducting devices

Superconducting fluctuations and characteristic time scales in amorphous WSi

We study magnitudes and temperature dependences of the electron-electron and electron-phonon interaction times which play the dominant role in the formation and relaxation of photon induced hotspot in two dimensional amorphous WSi films. The time constants are obtained through magnetoconductance measurements in perpendicular magnetic field in the superconducting fluctuation regime and through time-resolved photoresponse to optical pulses. The excess magnetoconductivity is interpreted in terms of the weak-localization effect and superconducting fluctuations. Aslamazov-Larkin, and Maki-Thompson superconducting fluctuation alone fail to reproduce the magnetic field dependence in the relatively high magnetic field range when the temperature is rather close to Tc because the suppression of the electronic density of states due to the formation of short lifetime Cooper pairs needs to be considered. The time scale {\tau}_i of inelastic scattering is ascribed to a combination of electron-electron ({\tau}_(e-e)) and electron-phonon ({\tau}_(e-ph)) interaction times, and a characteristic electron-fluctuation time ({\tau}_(e-fl)), which makes it possible to extract their magnitudes and temperature dependences from the measured {\tau}_i. The ratio of phonon-electron ({\tau}_(ph-e)) and electron-phonon interaction times is obtained via measurements of the optical photoresponse of WSi microbridges. Relatively large {\tau}_(e-ph)/{\tau}_(ph-e) and {\tau}_(e-ph)/{\tau}_(e-e) ratios ensure that in WSi the photon energy is more efficiently confined in the electron subsystem than in other materials commonly used in the technology of superconducting nanowire single-photon detectors (SNSPDs). We discuss the impact of interaction times on the hotspot dynamics and compare relevant metrics of SNSPDs from different materials

Timing jitter in photon detection by straight superconducting nanowires: Effect of magnetic field and photon flux

We studied the effect of the external magnetic field and photon flux on timing jitter in photon detection by straight superconducting NbN nanowires. At two wavelengths 800 and 1560 nm, statistical distribution in the appearance time of the photon count exhibits Gaussian shape at small times and exponential tail at large times. The characteristic exponential time is larger for photons with smaller energy and increases with external magnetic field while variations in the Gaussian part of the distribution are less pronounced. Increasing photon flux drives the nanowire from quantum detection mode to the bolometric mode that averages out fluctuations of the total number of nonequilibrium electrons created by the photon and drastically reduces jitter. The difference between Gaussian parts of distributions for these two modes provides the measure for the electron-number fluctuations. Corresponding standard deviation increases with the photon energy. We show that the two-dimensional hot-spot detection model explains qualitatively the effect of magnetic field

Phonon heat capacity and self-heating normal domains in NbTiN nanostrips

Self-heating normal domains in thin superconducting NbTiN nanostrips with the granular structure were characterized via steady-state hysteretic current–voltage characteristics measured at different substrate temperatures. The temperature dependence and the magnitude of the current, which sustains a domain in equilibrium at different voltages, can only be explained with a phonon heat capacity noticeably less than expected for 3D Debye phonons. This reduced heat capacity coincides with the value obtained earlier from magnetoconductance and photoresponse studies of the same films. The rate of heat flow from electrons at a temperature Te to phonons in the substrate at a temperature TB is proportional to (Tep−TBp) with the exponent p ≈ 3, which differs from the exponents for heat flows mediated by the electron–phonon interaction or by escaping of 3D Debye phonons via the film/substrate interface. We attribute both findings to the effect of grains on the phonon spectrum of thin NbTiN films. Our findings are significant for understanding the thermal transport in superconducting devices exploiting thin granular films.Peer Reviewe

Local thermal fluctuations in current-carrying superconducting nanowires

We analyze the effect of different types of fluctuations in internal electron energy on the rates of dark and photon counts in straight current-carrying superconducting nanowires. Dark counts appear due to thermal fluctuations in statistically independent cells with the effective size of the order of the coherence length; each count corresponds to an escape from the equilibrium state through an appropriate saddle point. For photon counts, spectral broadening of the deterministic cut off in the spectra of the detection efficiency can be phenomenologically explained by local thermal fluctuations in the electron energy within cells with the same effective volume as for dark counts

Physical mechanisms of timing jitter in photon detection by current carrying superconducting nanowires

We studied timing jitter in the appearance of photon counts in meandering nanowires with different fractional amount of bends. Timing jitter, which is the probability density of the random time delay between photon absorption in current-carrying superconducting nanowire and appearance of the normal domain, reveals two different underlying physical scenarios. In the deterministic regime, which is realized at large currents and photon energies, jitter is controlled by position dependent detection threshold in straight parts of meanders and decreases with the current. At small photon energies, jitter increases and its current dependence disappears. In this probabilistic regime jitter is controlled by Poisson process in that magnetic vortices jump randomly across the wire in areas adjacent to the bends.Comment: 10 pages, 2 tables, 6 figure

Assessment of landscape and environmental conditions of Susuman district of Magadan region

In Susuman district of Magadan region, against the background of natural processes, the manifestation of human economic activity is very noticeable, causing a change in the relief. This is due to the industrial development of placer gold deposits, which led to serious violations of the natural complexes of river valleys. The peculiarity of the territory of Susuman district is the imposition of severe climatic conditions and the specifics of human anthropogenic activity, which creates such particularly crisis situations in the environment as thermokarst, soil erosion, waterlogging, flooding of all low landforms, pollution with heavy metals. To assess the violations of the landscape, an analysis of the severity of environmental situations was carried out, which showed that the environmental situation in the area is tense, and in some areas it turns into a critical one. It should be noted that the actual area of disturbed land in  Susuman district is much larger than the statistical one. The largest areas of the district are in the gradation of significant and minor anthropogenic loads. The weighted average coefficient shows the average degree of anthropogenic load on this territory, which is still preserved due to a large area of forests. However, this does not mean that there is no risk of deterioration of the landscape and environmental situation in  Susuman district.  With intensive use of land for mineral exploitation and extraction without compliance with environmental measures, the area of disturbed land will increase by 3-4 thousand hectares every ten years. In addition, some landscapes have irreversible violations.  Therefore, it is recommended not to rely on natural restoration of landscapes but to carry out technical and biological land reclamation. &nbsp

Electron energy relaxation in disordered superconducting NbN films

We report on the inelastic-scattering rate of electrons on phonons and relaxation of electron energy studied by means of magnetoconductance, and photoresponse, respectively, in a series of strongly disordered superconducting NbN films. The studied films with thicknesses in the range from 3 to 33 nm are characterized by different Ioffe-Regel parameters but an almost constant product q_Tl(q_T is the wave vector of thermal phonons and l is the elastic mean free path of electrons). In the temperature range 14-30 K, the electron-phonon scattering rates obey temperature dependencies close to the power law 1/\tau_{e-ph} \sim T^n with the exponents n = 3.2-3.8. We found that in this temperature range \tau_{e-ph} and n of studied films vary weakly with the thickness and square resistance. At 10 K electron-phonon scattering times are in the range 11.9-17.5 ps. The data extracted from magnetoconductance measurements were used to describe the experimental photoresponse with the two-temperature model. For thick films, the photoresponse is reasonably well described without fitting parameters, however, for thinner films, the fit requires a smaller heat capacity of phonons. We attribute this finding to the reduced density of phonon states in thin films at low temperatures. We also show that the estimated Debye temperature in the studied NbN films is noticeably smaller than in bulk material.Comment: 23 pages, 6 figure