Macroscopic quantum tunneling with decoherence

The tunneling probability for a system modelling macroscopic quantum tunneling is computed. We consider an open quantum system with one degree of freedom consisting of a particle trapped in a cubic potential interacting with an environment characterized by a dissipative and a diffusion parameter. A representation based on the energy eigenfunctions of the isolated system, i. e. the system uncoupled to the environment, is used to write the dynamical master equation for the reduced Wigner function of the open quantum system. This equation becomes very simple in that representation. The use of the WKB approximation for the eigenfunctions suggests an approximation which allows an analytic computation of the tunneling rate, in this real time formalism, when the system is initially trapped in the false ground state. We find that the decoherence produced by the environment suppresses tunneling in agreement with results in other macroscopic quantum systems with different potentials. We confront our analytical predictions with an experiment where the escape rate from the zero voltage state was measured for a current-biased Josephson junction shunted with a resistor.