Quantum synchronization due to information backflow

Abstract: The phase synchronization of a single qubit in a dissipative bath in the absence of driving field is demonstrated. Using the Husimi $Q$-function we show that the phase preference is present in the long time limit only during non-Markovian evolution with a finite detuning. This happens due to the information backflow signifying that non-Markovianity is a resource for quantum synchronization. To quantify synchronization we use the shifted phase distribution as well as its maximal value. From the maximal value of the shifted phase distribution we observe the signatures of quantum synchronization {\it viz} the Arnold tongue. In our case the region ofsynchronization is outside the tongue region and the region inside the tongue is the desynchronized region. This is in contrast to the results in the literature, where the synchronization is within the tongue region.