Nonideal quantum measurement effects on the switching-current distribution of Josephson junctions

Abstract

The quantum character of Josephson junctions is ordinarily revealed through the analysis of the switching currents, i.e. the current at which a finite voltage appears: A sharp rise of the voltage signals the passage (tunnel) from a trapped state (the zero voltage solution) to a running state (the finite voltage solution). In this context, we investigate the probability distribution of the Josephson junctions switching current taking into account the effect of the bias sweeping rate and introducing a simple nonideal quantum measurements scheme. The measurements are modelled as repeated voltage samplings at discrete time intervals, that is with repeated projections of the time dependent quantum solutions on the static or the running states, to retrieve the probability distribution of the switching currents. The distribution appears to be immune of the quantum Zeno effect, and it is close to, but distinguishable from, the Wentzel-Kramers-Brillouin approximation. For energy barriers comparable to the quantum fundamental energy state and in the fast bias current ramp rate the difference is neat, and remains sizeable in the asymptotic slow rate limit. This behaviour is a consequence of the quantum character of the system that confirms the presence of a backreaction of quantum measurements on the outcome of mesoscopic Josephson junctions.

Anomalous transport effects on switching currents of graphene-based Josephson junctions

“…It is convenient to introduce the mechanical analogous, in which a graphene-based JJ is assimilated to a representative point on a potential derived from the peculiar current-phase relation (3) [21,27]…”

“…In figure 2 the SC distributions, computed in the presence of both Gaussian and Lévy noise contributes, are shown for several values of the Lévy noise amplitude and Lévy parameter α, while the thermal noise amplitude is set to g = -10 G 3 . We observe that: (i) if α is fixed, as g L grows the Lévy noise effects are enhanced, so that the low-current tail of the SC distributions raises, while the peak decreases, see figure 2(a); (ii) if the g L value is fixed, as α increases the lowcurrent tail of the SC distributions is depleted and the peak grows (see figure 2(b)).…”

“…In particular it is possible to retrieve the current at which the passage from the superconducting state to the finite voltage occurs in JJ, usually called switching current (SC). Repeating the measurements in the presence of a random disturbance, or because of quantum effects [3], the junction can switch to the finite voltage at slightly different current levels, thus producing a distribution of SCs. Conversely, the analysis of the distribution of the switching currents can be used to reveal the presence of noise or quantum effects.…”

Stochastic first passage time accelerated with CUDA

“…where k B is the Boltzmann constant, T is the absolute temperature, δ(•) the Dirac function, • is the expectation operator. The normalized units [6] are the following. The current is normalized to the critical current I 0 :…”

“…Kramers' rate theory [2,3]). From the experimental point of view, in Josephson Junctions (JJ) superconducting devices [4] the measurement of the threshold for the escapes is the only possibility (or the simplest way) to gain information on the internal dynamics of systems as quantum devices [5,6], threshold detectors [7][8][9] and arrays of JJ [10,11] of great interest for high frequency, up to the THz region, local oscillators [12]. The threshold for escapes is an essential physical information also in diverse systems .…”