Crossover between non-Markovian and Markovian dynamics induced by a hierarchical environment

Non-Markovian evolution of an open quantum system can be induced by the memory effects of a reservoir. Although a reservoir with stronger memory effects may seem like it should cause stronger non-Markovian effects on the system of interest, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a qubit (a two-level atom) that is coupled to a hierarchical environment, which contains a single-mode cavity and a reservoir consisting of an infinite number of modes. We show how the non-Markovian character of the system is influenced by the coupling strength between the qubit and cavity and the correlation time of the reservoir. In particular, we found a phenomenon whereby the qubit Markovian and non-Markovian transition exhibits a anomalous pattern in a parameter space depicted by the coupling strength and the correlation time of the reservoir.