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 II: Thermal activation in the quantum regime (continuation)

Abstract

In this short contribution we present a commentary on the interpretation of our thermal activation data obtained in the quantum regime of a SQUID, as discussed in part I [Bol et al., Physica B 133 (1985) 196]. Under certain circumstances a superconducting ring containing a weak superconducting junction, a SQUID, has two metastable magnetic flux states separated by a potential energy barrier Δ V. In this metabistable system stochastic magnetic flux transitions were observed due to intrinsic thermal activation. It was found that the transition rate was strongly reduced compared with the predictions of the classical thermal activation theory of Kramers or with the modern thermal activation theory of Grabert and Weiss which is an extension to the quantum regime where kT ⪅ h ̷ ω 0 (ω 0 being the free oscillation frequency corresponding to the metastable potential well). In these theories the transition rate is proportional to exp(-ΔV/ kT), in which V is treated as a temperature independence potential just as in the case in microscopic activated processes. In fact, however, from the thermodynamic point of view the relevant quantity in the exponent is the magnetic availability of the system with respect to the surroundings fixed by the temperature of the heat bath and the external magnetic field. Only when the system is completely isothermal can the potential V be identified with the Gibbs function. But in general when a flux transition takes place between the metastable potential wells, some energy will be dissipated possibly causing a temporary temperature rise due to self-heating. In principle, therefore, the system behaves neither perfectly isothermal nor adiabatic.