Solving non-Markovian open quantum systems with multi-channel reservoir coupling

TL;DR

This paper extends the non-Markovian quantum state diffusion approach to systems with multi-channel reservoir coupling, deriving exact master equations and solutions for complex three-level systems with correlated reservoirs.

Contribution

It introduces a generalized non-Markovian QSD framework for multi-channel reservoir coupling and derives exact master equations for such systems, including a three-level vee-type configuration.

Findings

Exact master equation derived for multi-channel reservoir coupling

Analytical solution obtained for three-level vee-type system

Numerical analysis of system evolution with correlated reservoirs

Abstract

We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically.