Thermal activation in the quantum regime and macroscopic quantum tunnelling in the thermal regime in a metabistable system consisting of a superconducting ring interrupted by a weak junction: Part I: Thermal activation in the quantum regime

Abstract

Under certain circumstances a superconducting ring containing a weak superconducting junction, a SQUID, has two metastable magnetic flux states separated by a potential barrier Δ U. If the junction has a small capacitance stochastic magnetic flux transitions are observed even at very low temperatures. This article mainly concerns the intrinsic thermal activation in the quantum regime, where the mean energy of the oscillator, corresponding to the metastable potential wells, is different from the equipartition value kT due to the high frequencies and low temperature involved in our experiments. We have found strong deviations from the classical thermodynamic activation theory of Kramers where the transition rate is proportional to exp( -ΔU kT ). We are able to explain our experimental findings by replacing the classical equipartition value kT for the mean energy in the exponent with the value for the mean excitation energy of the Brownian motion of a quantum oscillator, accounting for the appropriate damping.