Phase-space approach to cavity field dynamics in a squeezed thermal reservoir

Quantum systems, such as a single-mode cavity field coupled to a thermal bath, typically experience destructive effects due to interactions with their noisy environment. When the bath combines both thermal fluctuations and a nonclassical feature like quadrature squeezing, forming a squeezed thermal reservoir, the system's behaviour can change substantially. In this work, we study the evolution of the cavity field in this generalized environment using an alternative phase-space approach based on the Glauber-Sudarshan $P$-function. We derive a compact analytical expression for the time-dependent $P$-function for arbitrary initial cavity field states and demonstrate its utility through specific examples. Additionally, we obtain analytical expressions, as a function of time, for some statistical properties of the cavity field, as well as for the nonclassical depth, $\tau_m$, a nonclassicality measure calculated directly from the $P$-function.