Exact solution of the master equation for interacting quantized fields at finite temperature decay

TL;DR

This paper presents an exact analytical solution to the Lindblad master equation for two interacting quantized fields at finite temperature, enabling precise modeling of quantum dynamics in cavity systems.

Contribution

The authors develop a novel method using superoperator techniques and non-unitary transformations to diagonalize the effective Hamiltonian and solve the master equation exactly.

Findings

Derived an exact solution for the master equation in a quantum optical system.

Calculated photon coincidence rates for two indistinguishable photons in a cavity.

Provided a framework for analyzing the evolution of arbitrary initial states in quantum regimes.

Abstract

We analyze the Markovian dynamics of a quantum system involving the interaction of two quantized fields at finite temperature decay. Utilizing superoperator techniques and applying two non-unitary transformations, we reformulate the Lindblad master equation into a von Neumann-like equation with an effective non-Hermitian Hamiltonian. Furthermore, an additional non-unitary transformation is employed to diagonalize this Hamiltonian, enabling us to derive an exact solution to the Lindblad master equation. This method provides a framework to calculate the evolution of any initial state in a fully quantum regime. As a specific example, we present the photon coincidence rates for two indistinguishable photons initially interacting within a cavity.