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We study the dynamical Casimir effect using a fully quantum-mechanicaldescription of both the cavity field and the oscillating mirror. We do notlinearize the dynamics, nor do we adopt any parametric or perturbativeapproximation. By numerically diagonalizing the full optomechanicalHamiltonian, we show that the resonant generation of photons from the vacuum isdetermined by a ladder of mirror-field {\em vacuum Rabi splittings}. We findthat vacuum emission can originate from the free evolution of an initial puremechanical excited state, in analogy with the spontaneous emission from excitedatoms. By considering a coherent drive of the mirror, using a master-equationapproach to take losses into account, we are able to study the dynamicalCasimir effect for optomechanical coupling strengths ranging from weak toultrastrong. We find that a resonant production of photons out of the vacuumcan be observed even for mechanical frequencies lower than the cavity-modefrequency. Since high mechanical frequencies, which are hard to achieveexperimentally, were thought to be imperative for realizing the dynamicalCasimir effect, this result removes one of the major obstacles for theobservation of this long-sought effect. We also find that the dynamical Casimireffect can create entanglement between the oscillating mirror and the radiationproduced by its motion in the vacuum field, and that vacuum Casimir-Rabioscillations can occur.

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