New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation

Abstract

By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation ⟨η|, which can arrange master equations of density operators ρ(t) in quantum statistics as state-vector evolution equations due to the elegant properties of ⟨η|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant κ we find that the matrix element of ρ(t) at time t in ⟨η| representation is proportional to that of the initial ρ0 in the decayed entangled state ⟨ηe−κt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = ∫(d2η/π)⟨η|ρ⟩D(η), which is different from all the previous known representations.