Laboratoire de Physique des Solides - UMR 8502

Phase dynamics of Josephson junctions Josephson

Nonlinear systems are responsible for a variety of interesting phenomena – turbulence, weather, or fractals.

(a) Sketch of switching from superconducting to normal state in the nonstationary regime. The phase can either relax and then jump out (blue circle) from the potential well or escape early (red circle). The escape corresponds to the transition into the dissipative state, and hence to the appearance of finite voltage across the junction. (b) The numerically calculated phase diagram. The attractor (blue) corresponds to the non-dissipative state, while the black curves correspond to the dissipative state. In the case of the early escape, the phase trajectory stays near the separatrix (red curve). (c) Probability of switching into the dissipative state, showing a bimodal distribution. Premature switching increases with bias frequency. (d) Probability of early switching N1 as function of ramp frequency for three different junctions (markers). The phase relaxation time is obtained from an exponential fit (solid curve).

Small changes in initial conditions can produce large changes in the response, so their behavior often seems unpredictable. The system we have studied is a Josephson junction – two small pieces of superconductor glued together across a thin layer of insulator or metal. In a superconductor, all electrons make up one wave with a unique phase. The superconducting current across the junction is a nonlinear function of the phase difference between the two superconductors. We have demonstrated a novel way to attain a regime characteristic of nonlinear oscillators : bifurcation. The current biased Josephson junction can be in one of two states, superconducting or dissipative, but in the stationary regime it can not approach both states from the same point – it will find itself in one or the other state depending on where it started. We show that if we excite the system with a fast pulse of current, it enables with a finite probability a jump to a previously unattainable state. By varying the excitation frequency, and measuring the jump probability, we determine directly the phase relaxation time as in a pump-probe experiment. This time is limited by dissipation, and fixes the timeframe for the phase to stay coherent, or well defined.

Contact : Marco Aprili

I. Petković and M. Aprili, Phys. Rev. Lett. 102, 157003 (2009)