Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical 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 can not only able to describe the different types of damping in dissipative quantum optical systems but also 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).

Keywords:

• quantum optics
• open quantum systems
• non-Hermitian dynamics
• laser theory
• two-mode approximation
• master equation
• density operator

Acknowledgements

This article is based on the talks given at the conferences “12th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics” (02–06 July, 2013, Koç University, Istanbul, Turkey) and “Quantum Information Processing, Communication and Control 2” (25–29 November, 2013, KwaZulu-Natal, South Africa).

Notes

This work was supported by the National Research Foundation of South Africa.