New Approach for Solving Master Equations of Density Operators for the Raman-Coupled Model with Cavity Damping

Abstract

By virtue of the thermo entangled state representation, in which one mode is fictitious accompanying the system mode, we exhibit a novel approach to deriving density operator for a Raman-coupled model with damping of the cavity mode. The normal ordering forms of density matrix elements can be obtained, and the corresponding Wigner functions are also derived.

Quantum Master Equation with Damping Operator Including Interaction Effect for the Raman-Coupled Model with Cavity Damping

“…The model is equivalent to the dispersive Jaynes-Cummings mode [33,34]. When the interaction effect on the damping operator of the quantum master equation is ignored, the model can be analytically solved by the phase-space method [36] and the thermo field dynamics together with the Lie algebra method [37]. We will show that the model can be still solved, even if the interaction effect on the damping operator is taken into account.…”

“…Therefore we can conclude that the interaction effect on the damping operator of the quantum master equation cannot be ignored whenever we consider the relaxation process of an interacting quantum system under the influence of a Markovian or non-Markovian environmental system. For this purpose, we will investigate the Raman-coupled model [35] in this paper, where the cavity photon interacts with a Markovian thermal reservoir of finite temperature [36,37]. The model is equivalent to the dispersive Jaynes-Cummings mode [33,34].…”

“…The Raman-coupled model [35][36][37] considered in this paper consists of a two-level atom, a cavity photon and an environmental system. The two-level atom has equal energy level and the environmental system which causes the cavity damping is assumed to be a set of harmonic oscillators.…”

“…Although the Wigner function is usually applied for investigating the dynamics [36,37], the Husimi Q-function [5] is more convenient for our purpose. The Q-function of the operator ρ jk (t) is obtained from (29), (33) and (38),…”

New approach to solving master equations of density operator for the Jaynes Cummings model with cavity damping

“…In this present paper, instead of using phase space representation of density operator [8,9] we adopted thermo-entangled state (TES) representation to treat time evolution of density operator in the J-C model with cavity damping where Xu and Yuan derived density operator for a Raman-coupled model in cavity damping [10]. This paper is organized as follows In sect.2, we review the (TES) representation and in sect.3, the equation of motion of the density operator is decoupled.…”