Damping in a Squeezed Bath and Its Time Evolution through the Complete Class of Gaussian Quasi-Distributions

By virtue of the thermo-entangled states representation of the density operator and using the dissipative interaction picture, we solve the master equation of a driven damped harmonic oscillator in a squeezed bath. We show that the essential part of the dynamics can be expressed by the convolution of the initial Wigner function with a special kind of normalized Gaussian in the phase space and relate the dynamics with the change of Gaussian ordering of the density operator.