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

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.

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Cited by in corpus (9)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Crossover Between Non-Markovian and Markovian Dynamics Induced by a Hierarchical Environment
• Effects of the rotating wave and secular approximations on non-Markovianity
• Generalized formalism for information backflow in assessing Markovianity and its equivalence to divisibility
• Non-perturbative interpretation of the Bloch vector's path beyond rotating wave approximation
• Measurement-induced cooling of a qubit in structured environments
• Bounds for the divisibility-based and distinguishability-based non-Markovianity measures
• Quantifying quantum non-Markovianity based on quantum coherence via skew information
• Hierarchical-environment-assisted non-Markovian and its effect on thermodynamic properties