Comparison between non-Markovian dynamics with and without rotating wave approximation

In the limit of weak coupling between the system and its reservoir, we derive the time-convolutionless (TCL) non-Markovian master equation for a two-level system interacting with a zero-temperature structured environment with no rotating wave approximation (NRWA). By comparing with the dynamics with RWA, we demonstrate the impact of the RWA on the system dynamics, as well as the effects of non-Markovianity on the preservation of atomic coherence, squeezing, and entanglement.