Entropic analysis of optomechanical entanglement for a nanomechanical resonator coupled to an optical cavity field

We investigate entanglement dynamics for a nanomechanical resonator coupled to an optical cavity field through the analysis of the associated entanglement entropies. The effects of time variation of several parameters, such as the optical frequency and the coupling strength, on the evolution of entanglement entropies are analyzed. We consider three kinds of entanglement entropies as the measures of the entanglement of subsystems, which are the linear entropy, the von Neumann entropy, and the Rényi entropy. The analytic formulae of these entropies are derived in a rigorous way using wave functions of the system. In particular, we focus on time behaviors of entanglement entropies in the case where the optical frequency is modulated by a small oscillating factor. We show that the entanglement entropies emerge and increase as the coupling strength grows from zero. The entanglement entropies fluctuate depending on the adiabatic variation of the parameters and such fluctuations are significant especially in the strong coupling regime. Our research may deepen the understanding of the optomechanical entanglement, which is crucial in realizing hybrid quantum-information protocols in quantum computation, quantum networks, and other domains in quantum science.