Abrupt transitions between Markovian and non-Markovian dynamics in open quantum systems

A rapid restoration of the bath state is usually required to induce Markovian dynamics for an open quantum system, which typically can be realized only in limits such as weak system-bath coupling and infinitely large bath. In this work, we investigate the Markovianity of a qubit system coupled to a single-qubit bath with the qubit bath being continuously refreshed by quantum cooling. A surprising result is that there exists a finite threshold for the cooling rate at which the system transitions from non-Markovian dynamics to Markovian dynamics, which is in sharp contrast to the usual understanding that Markovian dynamics is an asymptotic behavior under the Born-Markov approximation. We also study the time correlation of the bath, and find that the decay rate of bath time correlation is of the same order as the system evolution speed. This suggests that quantum Markovian dynamics can exist beyond the usual short bath correlation limit.