Non-Markovian dynamics for an open two-level system without rotating wave approximation: Indivisibility versus backflow of information

TL;DR

This paper investigates the non-Markovian behavior of a two-level quantum system interacting with a structured environment, analyzing measures of indivisibility and information backflow without the rotating wave approximation, revealing the significance of counter-rotating terms.

Contribution

It derives an exact analytic solution for the non-Markovian dynamics without RWA and explores the relations between two measures of non-Markovianity, emphasizing the role of counter-rotating terms.

Findings

Counter-rotating terms significantly affect short-time non-Markovian behavior.

The paper establishes conditions for indivisibility and information backflow.

Numerical analysis confirms the importance of these measures in structured reservoirs.

Abstract

By use of the two measures presented recently, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and the reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relations between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed.