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

Markovian dynamics of an open quantum system needs a fast decay of the bath correlation to make the evolution of the system memoryless, which usually requires a rapid restoration of the bath state. In this work, we quantitatively study how fast the the bath state needs to be restored in order to realize Markovian dynamics of an open system. We consider a simple model of a qubit system coupled to a qubit bath with the qubit bath continuously refreshed by quantum cooling. A surprising result is that there exists a threshold of the cooling rate above which the non-Markovianity of the system dynamics suddenly vanishes and the system transitions to Markovian dynamics while the decay rate of bath correlation is at the same order of the system evolution speed. This is in marked contrast to the usual understanding that Markovian quantum dynamics is generally a limiting behavior under the Born-Markov approximation, and suggests broader existence of Markovian dynamics in the quantum regime.