Eur. Phys. J. D (2012) 66: 255
https://doi.org/10.1140/epjd/e2012-30354-3

Regular Article

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

Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Department of Physics, Hunan Normal University, Changsha 410081, P.R. China

^a e-mail: hszeng@hunnu.edu.cn

Received: 6 June 2012
Received in final form: 6 August 2012
Published online: 9 October 2012

Abstract

By use of the recently presented two measures, 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 its 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 relation between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed.