Evolution of the quantized field coupled to a thermal bath: a phase space approach

TL;DR

This paper introduces a phase space method using the Glauber-Sudarshan P-function to analytically describe the evolution of a quantized electromagnetic field mode in a thermal bath, avoiding complex master equation solutions.

Contribution

It presents a novel phase space approach that provides analytical solutions for the field's evolution in thermal environments, simplifying previous methods.

Findings

Analytical expressions for the time-evolved P-function are derived.

The method circumvents solving the master equation directly.

Applicable to finite temperature thermal baths.

Abstract

We present an alternative method for describing the evolution of a mode of the quantized electromagnetic field in contact with a finite temperature thermal bath. We use the expansion of the field density operator in terms of coherent states and the related Glauber-Sudarshan $P$-function in phase space. The method allows us to obtain analytical expressions of the system's time-evolved $P$-function without needing to solve the corresponding master equation.