Crossover Between Non-Markovian and Markovian Dynamics Induced by a Hierarchical Environment

TL;DR

This paper investigates how a hierarchical environment influences the transition between Markovian and non-Markovian dynamics in a qubit, revealing an unexpected pattern in the system's memory effects.

Contribution

It demonstrates the complex interplay between coupling strength, reservoir correlation time, and non-Markovian behavior in a hierarchical quantum environment.

Findings

Identifies a new phenomenon of anomalous Markovian-non-Markovian transition patterns.

Shows non-monotonic influence of reservoir memory effects on system dynamics.

Highlights the role of hierarchical environment structure in quantum memory effects.

Abstract

Non-Markovian evolution of an open quantum system can be induced by the memory effects of a reservoir. Although a reservoir with stronger memory effects may seem like it should cause stronger non-Markovian effects on the system of interest, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a qubit (a two-level atom) that is coupled to a hierarchical environment, which contains a single-mode cavity and a reservoir consisting of infinite numbers of modes. We show how the non-Markovian character of the system is influenced by the coupling strength between the qubit and cavity and the correlation time of the reservoir. In particular, we found a new phenomenon whereby the qubit Markovian and non-Markovian transition exhibits a anomalous pattern in a parameter space depicted by the coupling strength and the correlation time of the reservoir.