Entrainment in a periodically driven three-mode bosonic model

Abstract

We investigate the response of the dissipative photonic mode of a generic three-mode bosonic model subject to periodic driving. We numerically obtain the exemplary dynamics of the photon mode using the equations of motions obtained from the Heisenberg-Langevin equation and applying mean-field approximation. Subsequently, we study the entrainment of limit cycles due to a periodically driven coupling strength. Exploring a range of driving frequencies and strengths, we identify eight distinct types of responses and construct the corresponding phase diagram of the driven system. These include harmonic, and subharmonic entrainment, limit cycle (LC), and normal phase (NP), as well as the emergence of dark states and a superharmonic entrainment. Our results showcase a rich non-equilibrium physics in a periodically driven and dissipative bosonic system.