Measuring the distribution of current fluctuations through a Josephson junction with very short current pulses

We propose to probe the distribution of current fluctuations by means of the escape probability histogram of a Josephson junction (JJ), obtained using very short bias current pulses in the adiabatic regime, where the low-frequency component of the current fluctuations plays a crucial role. We analyze the effect of the third cumulant on the histogram in the small skewness limit, and address two concrete examples assuming realistic parameters for the JJ. In the first one we study the effects due to fluctuations produced by a tunnel junction, finding that the signature of higher cumulants can be detected by taking the derivative of the escape probability with respect to current. In such a realistic situation, though, the determination of the whole distribution of current fluctuations requires an amplification of the cumulants. As a second example we consider magnetic flux fluctuations acting on a SQUID produced by a random telegraph source of noise. Introduction. – The electronic transport properties of a mesoscopic conductor are completely characterized by its Full Counting Statistics (FCS), introduced in Ref. [1] and defined as the probability distribution for the transfer of charges over a certain time interval. At zero temperature and in the absence of interaction, for example, quantum transport is characterized by a binomial distribution. This contrasts with the Poissonian statistics, characteristic of classical uncorrelated particles, which is recovered in the tunneling limit [2]. The experimental determination of FCS, unfortunately, is a difficult task. Motivated by the expertise developed for current-noise measurements, one possibility is to adopt the strategy of building up the FCS through the measurement of the various cumulants of the distribution, noise being the second one. The third cumulant was indeed directly measured in Refs. [3, 4]. The alternative possibility is the direct determination of the entire FCS [5]. Recently, various proposals have been put forward in this direction making use of the high sensitivity to fluctuations of current-biased Josephson junctions (JJ) [8–17]. In this Letter we are interested in the second strategy and we analyze the case in which the measurement is performed applying very short current pulses, which allows to access a regime never explored before. According to the RCSJ model [18], the dynamics of the phase difference across a current-biased JJ is equivalent to that of a particle in a washboard potential, the phase playing the role of the spatial coordinate. In the harmonic approximation, the wells of such a tilted sine potential are characterized by the plasma frequency ωp. The wells are separated by barriers if the current applied to the JJ is smaller than the superconducting critical current Ic. In such a case, the phase-particle gets trapped in a well of the potential, causing the voltage across the JJ to vanish (supercurrent state). Escape from the well, which will cause the development of a finite voltage across the JJ (transition to the resistive state), can occur through two mechanisms. At low temperatures (T ≪ ~ωp/kB), the only possibility is macroscopic quantum tunneling (MQT) through the barrier which separates two successive wells. The effect of thermal fluctuations on the escape rate of the MQT was considered by Martinis and Grabert [19], who found an exponential enhancement of the rate proportional to T 2 for ohmic damping. The second mechanism, thermal activation (TA), is due to excitations of the particle that will allow the latter to overcome the barrier top. In the absence of perturbations, these are produced by thermal fluctuations at large temperatures (T > ~ωp/kB). In fact, the probability of escape from a potential well is sensitive to perturbations affecting the system, such