Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems

TL;DR

This paper compares non-Hermitian and Lindblad approaches to open quantum systems, proposes a unified master equation, and demonstrates its effectiveness through analytical solutions in a quantum optical system.

Contribution

It introduces a unified master equation combining non-Hermitian and Lindblad methods, enabling comprehensive analysis of dissipative quantum optical phenomena.

Findings

Unified master equation captures diverse damping behaviors.

Analytical solutions describe undamped anharmonic oscillations.

Method reproduces experimental features of open quantum systems.

Abstract

We compare two approaches to open quantum systems, namely, the non-Hermitian dynamics and the Lindblad master equation. In order to deal with more general dissipative phenomena, we propose the unified master equation that combines the characteristics of both of these approaches. This allows us to assess the differences between them as well as to clarify which observed features come from the Lindblad or the non-Hermitian part, when it comes to experiment. Using a generic two-mode single-atom laser system as a practical example, we analytically solve the dynamics of the normalized density matrix operator. We study the two-level model in a number of cases (depending on parameters and types of dynamics), compute different observables and study their physical properties. It turns out that one is able not only to describe the different types of damping in dissipative quantum optical systems but also to mimic the undamped anharmonic oscillatory phenomena which happen in quantum systems with more than two levels (while staying within the framework of the analytically simple two-mode approximation).