Quantum dynamics in a tiered non-Markovian environment

TL;DR

This paper presents a new analytical method for studying open quantum systems interacting with a tiered environment, capturing non-Markovian dynamics and environmental effects with high accuracy and broad applicability.

Contribution

The authors develop a phase space analytical approach for non-Markovian quantum dynamics in tiered environments, enabling combined treatment of continuous baths and discrete modes.

Findings

Accurate analytical expressions for thermalization temperature.

Corrections to environmental response functions due to tiered environment.

Validation against exact numerical simulations confirms high accuracy.

Abstract

We introduce a new analytical method for studying the open quantum systems problem of a discrete system weakly coupled to an environment of harmonic oscillators. Our approach is based on a phase space representation of the density matrix for a system coupled to a two-tiered environment. The dynamics of the system and its immediate environment are resolved in a non-Markovian way, and the environmental modes of the inner environment can themselves be damped by a wider `universe'. Applying our approach to the canonical cases of the Rabi and spin-boson models we obtain new analytical expressions for an effective thermalisation temperature and corrections to the environmental response functions as direct consequences of considering such a tiered environment. A comparison with exact numerical simulations confirms that our approximate expressions are remarkably accurate, while their analytic nature offers the prospect of deeper understanding of the physics which they describe. A unique advantage of our method is that it permits the simultaneous inclusion of a continuous bath as well as discrete environmental modes, leading to wide and versatile applicability.