  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 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 presence of both types of dissipation, the
momentum dissipation shifts the critical coupling strength of the dissipative
phase transition induced by the position dissipation.
