Exact non-Markovian dynamics of qubits coupled to two interacting environments

As the memory effect may be helpful in quantum information processing, non-Markovian dynamics plays an important role in the description of many-body open systems. Among these topics, the system consisting of independent qubits interacting with several coupled environments is of particular interest. In this paper, we study the exact non-Markovian dynamics of two independent qubits. Each of the qubits interacts individually with its environment, and these two environments coupled with each other. We investigate the non-Markovianity measure of the system for the whole parameter regime without the rotating-wave approximation (RWA) and compare the results with that under the RWA. We find that the non-Markovianity measure for two qubits manifests a transition from a non-Markovian to Markovian regime regardless of the coupling strength between the environments. The physical origin of this transition is revealed, and a possible observation of the prediction in superconducting quantum interference devices is discussed.