Universal Features of Counting Statistics of Thermal and Quantum Phase Slips in Nanosize Superconducting Circuits

Abstract

We perform measurements of phase-slip-induced switching current events on different types of superconducting weak links and systematically study statistical properties of the switching current distributions. We employ two types of devices in which a weak link is formed either by a superconducting nanowire or by a graphene flake subject to proximity effect. We demonstrate that, independently on the nature of the weak link, higher moments of the distribution take universal values. In particular, the third moment (skewness) of the distribution is close to −1 both in thermal and quantum regimes. The fourth moment (kurtosis) also takes a universal value close to 5. The discovered universality of skewness and kurtosis is confirmed by an analytical model. Our numerical analysis shows that introduction of extraneous noise into the system leads to significant deviations from the universal values. We suggest to use the discovered universality of higher moments as a robust tool for checking against undesirable effects on noise in various types of measurements.PACS numbers: 74.78. Na,74.50.+r,74.25.Sv, Introduction.-The field of quantum noise has recently seen rapid development caused both by its growing significance in many areas of condensed matter physics as well as by a constant improvement in the capabilities of high precision measurements [1]. Perhaps the most intensively studied question to date is related to the statistics of charge transport in mesoscopic conductors. In such systems probability distribution of current fluctuations, the so-called full counting statistics, was rigorously derived for various normal and superconducting circuits [2] and tested in the state-of-the-art measurements of the third moment (skewness) of current fluctuations [3]. Given that charge is a quantum mechanical conjugate variable to the phase, it is of fundamental interest to study corresponding statistics of phase fluctuations. Superconducting nanowires and related proximity devices offer a natural platform for this purpose, which we explore in the present work.The macroscopic quantum tunneling of the phase across a current-biased Josephson junction [4] or a superconducting nanowire [5][6][7] is arguably the most profound and well-known manifestation of quantum fluctuations at the macroscopic level. This phenomenon is observed by registering phase slip events [8], which proliferate at currents close to the critical and drive transitions between supercurrent-carrying and dissipative branches of current-voltage characteristics [6, 7, 9, 10]. Macroscopic quantum tunneling is usually described in the framework that treats quantum or thermally activated transitions of the phase between neighboring minima of a tilted washboard potential in the presence of a dissipative environment [4, 5,11]. Complimentary approaches employ an effective action for BCS superconductors [9, 10,16].

Breakdown of the escape dynamics in Josephson junctions

“…3), SCDs of JCT C are asymmetric over the entire temperature range. In JCT C, the γ factor is temperature independent, consistent with what is observed in pure phase slip systems [42] (see Fig. 3; the black dashed line indicates the mean value γ −0.8 for JCT C).…”

“…2(a), respectively]. The temperature dependence of the skewness γ gives additional distinctive criteria to confirm the intermediate dissipation regime [36,42]. This is signaled by a transition for JCT B for instance from γ −0.…”

Statistics of localized phase slips in tunable width planar point contacts

“…It has been theoretically shown1426 that the distribution of switching currents depends on the frequency f and amplitude A through the sweep rate fA . To illustrate this fact, the rightmost curve of Fig.…”

“…The degree of asymmetry (skewness) and tailness (kurtosis) of the Gumbel distribution are given by the third and fourth moments of the function, respectively, and acquire constant (universal26) values. Strictly speaking, Eq.…”

Quadratic Characteristics of Environment Induced Voltage Shot Noise in Josephson Junctions

“…A linear trend of the voltage noise with the mean voltage is found in the phase diffusion regime and a decreasing trend in the running state regime. A recent experimental study on phase-slip from a metastable state to a resistive state in nano-scaled weak links showed universality of higher moments in the tunneling counting statistics 10 . Using full counting statistics derived from the Langevin equation, more recent theoretical investigations 7–9 explored the region where the phase particle tunneling (phase slip) picture emerges.…”