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By use of the two measures presented recently, the indivisibility and thebackflow of information, we study the non-Markovianity of the dynamics for atwo-level system interacting with a zero-temperature structured environmentwithout using rotating wave approximation (RWA). In the limit of weak couplingbetween the system and the reservoir, and by expanding the time-convolutionless(TCL) generator to the forth order with respect to the coupling strength, thetime-local non-Markovian master equation for the reduced state of the system isderived. Under the secular approximation, the exact analytic solution isobtained and the sufficient and necessary conditions for the indivisibility andthe backflow of information for the system dynamics are presented. In the moregeneral case, we investigate numerically the properties of the two measures forthe case of Lorentzian reservoir. Our results show the importance of thecounter-rotating terms to the short-time-scale non-Markovian behavior of thesystem dynamics, further expose the relations between the two measures andtheir rationality as non-Markovian measures. Finally, the complete positivityof the dynamics of the considered system is discussed.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

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