Synchronization effects in a periodically driven two-level system

We study phase synchronization in a driven two-level system coupled to a non-Markovian bosonic reservoir. The dynamics is described by treating the system-bath coupling and the coherent drive without invoking the rotating-wave approximation, and simulated using the numerically exact hierarchical equations of motion. We observe that a robust phase locking develops and that the corresponding synchronization measure rapidly acquires a finite value when the system is tuned to what we identify as a resonant-ratio condition, namely, when the ratio between the drive amplitude and its frequency coincides with a zero of the Bessel function J0 . We provide an explanation for this phenomenon by means of a static approximation derived from a Fourier analysis of the periodically driven Hamiltonian