Effects of a dissipative coupling to the momentum of a particle in a double well potential

Double well potentials offer the possibility of coherent state preparation and therefore constitute important building blocks in the analysis of quantum information and quantum engineering devices. Here we present a study of the coherent tunneling in a parabolic double well potential in the presence of different dissipative interactions. Specifically, we investigate the effects of an environmental coupling to the momentum and/or to the position of a particle in the potential. Using the semiclassical approximation to calculate instanton paths in Euclidean time, we find that momentum dissipation enhances the coherent tunnel splitting. In the presence of both types of dissipation, momentum dissipation shifts the critical coupling strength of the dissipative phase transition induced by the position dissipation.