Non-perturbative Dynamical Casimir Effect in Optomechanical Systems: Vacuum Casimir-Rabi Splittings

By rapidly changing a boundary condition for the electromagnetic field, e.g., by moving a mirror very quickly, fluctuations in the quantum vacuum can be converted into real photons. This is known as the dynamical Casimir effect (DCE), the first experimental demonstration of which was realized only a few years ago, using superconducting circuits. In most theoretical studies treating the DCE, the trajectory of the mirror is classical. We use a fully quantum-mechanical description of both the cavity field and the oscillating mirror in optomechanical setup. We do not linearize the dynamics, nor do we adopt any parametric or perturbative approximation. We show that the resonant generation of photons from the vacuum is determined by a ladder of mirror-field Rabi splittings, and that vacuum Casimir-Rabi oscillations can occur. We also study the case where the mirror is coherently driven. We find that, for strong optomechanical coupling, a resonant production of photons out from the vacuum can be observed even for mechanical frequencies below the cavity frequency. Since high mechanical frequencies, which are hard to achieve experimentally, were thought to be imperative for realizing the DCE, this result removes a major obstacle for its experimental observation in optomechanical setup.