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Register a new userPhysical mechanisms of timing jitter in photon detection by current carrying superconducting nanowires
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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.
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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.
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.
Using two-temperature model coupled with modified time-dependent Ginzburg-Landau equation we calculate the delay time $tau_d$ in appearance of growing normal domain in the current-biased superconducting strip after absorption of the single photon. We demonstrate that $tau_d$ depends on the place in the strip where photon is absorbed and monotonically decreases with increasing of the current. We argue, that the variation of $tau_d$ (timing jitter), connected either with position-dependent response or Fano fluctuations could be as small as the lowest relaxation time of the superconducting order parameter $sim hbar/k_BT_c$ ($T_c$ is the critical temperature of the superconductor) when the current approaches the depairing current.
Using kinetic equation approach we study dynamics of electrons and phonons in current-carrying superconducting nanostrips after absorption of single photon of near-infrared or optical range. We find that the larger the ratio $C_e/C_{ph}|_{T_c}$ ($T_c$ is a critical temperature of superconductor, $C_e$ and $C_{ph}$ are specific heat capacities of electrons and phonons, respectively) the larger part of photons energy goes to electrons, they become stronger heated and, hence, could thermalize faster during initial stage of hot spot formation. Thermalization time $tau_{th}$ could be less than one picoseconds for superconductors with $C_e/C_{ph}|_{T_c}gg 1$ and small diffusion coefficient $Dsimeq 0.5 cm^2/s$ when thermalization occurs mainly due to electron-phonon and phonon-electron scattering in relatively small volume $sim xi^2d$ ($xi$ is a superconducting coherence length, $d<xi$ is a thickness of the strip). At larger times due to diffusion of hot electrons effective temperature inside the hot spot decreases, the size of hot spot increases, superconducting state becomes unstable and normal domain spreads in the strip at current larger than so-called detection current. We find dependence of detection current on the photons energy, place of its absorption in the strip, width of the strip, magnetic field and compare it with existing experiments. Our results demonstrate that materials with $C_e/C_{ph}|_{T_c} ll 1$ are bad candidates for single photon detectors due to small transfer of photons energy to electronic system and large $tau_{th}$. We also predict that even several microns wide dirty superconducting bridge is able to detect single near-infrared or optical photon if its critical current exceeds 70 $%$ of depairing current and $C_e/C_{ph}|_{T_c} gtrsim 1$.
Counting rate is a key parameter of superconducting nanowire single photon detectors (SNSPD) and is determined by the current recovery time of an SNSPD after a detection event. We propose a new method to study the transient detection efficiency (DE) and pulse amplitude during the current recovery process by statistically analyzing the single photon response of an SNSPD under photon illumination with a high repetition rate. The transient DE results match well with the DEs deduced from the static current dependence of DE combined with the waveform of a single-photon detection event. This proves that the static measurement results can be used to analyze the transient current recovery process after a detection event. The results are relevant for understanding the current recovery process of SNSPDs after a detection event and for determining the counting rate of SNSPDs.
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