Abstract
We study the dynamical Casimir effect using a fully quantum-mechanical description of both the cavity field and the oscillating mirror. We do not linearize the dynamics, nor do we adopt any parametric or perturbative approximation. By numerically diagonalizing the full optomechanical Hamiltonian, we show that the resonant generation of photons from the vacuum is determined by a ladder of mirror-field {\em vacuum Rabi splittings}. We find that vacuum emission can originate from the free evolution of an initial pure mechanical excited state, in analogy with the spontaneous emission from excited atoms. By considering a coherent drive of the mirror, using a master-equation approach to take losses into account, we are able to study the dynamical Casimir effect for optomechanical coupling strengths ranging from weak to ultrastrong. We find that a resonant production of photons out of the vacuum can be observed even for mechanical frequencies lower than the cavity-mode frequency. Since high mechanical frequencies, which are hard to achieve experimentally, were thought to be imperative for realizing the dynamical Casimir effect, this result removes one of the major obstacles for the observation of this long-sought effect. We also find that the dynamical Casimir effect can create entanglement between the oscillating mirror and the radiation produced by its motion in the vacuum field, and that vacuum Casimir-Rabi oscillations can occur.
Highlights
Quantum field theory predicts that vacuum fluctuations can be converted into real particles by the energy provided through certain external perturbations [1,2,3,4,5,6,7,8]
We find that the resonant generation of photons from the vacuum is determined by a ladder of mirror-field vacuum Rabi-like energy splittings
A detailed derivation of the optomechanical Hamiltonian can be found in Ref. [67]
Summary
Quantum field theory predicts that vacuum fluctuations can be converted into real particles by the energy provided through certain external perturbations [1,2,3,4,5,6,7,8]. Exceptions consider fluctuations of the position of the mirror driven by vacuum radiation pressure using linear dispersion theory [46,47] or focus on the mirror motion as the main dynamical degree of freedom (d.o.f.) In the latter case, studies have shown how the DCE induces friction forces on the mirror [48,49] or leads to decoherence of mechanical quantum superposition states [50]. In circuit optomechanics, it has been shown that the radiation pressure effect can be strongly enhanced by introducing a qubit-mediated [57,58] or modulated [61] interaction between the mechanical and the electromagnetic resonator This ultrastrong-coupling (USC) regime, where the optomechanical coupling rate is comparable to the mechanical frequency, can give rise to strong nonlinearities even in systems described by the standard optomechanics interaction Hamiltonian, which depends linearly on the mirror displacement [62,63]. In our approach, the vibrating mirror is treated as a harmonic (anharmonicity originates only from the interaction) quantum d.o.f. on the same footing as the cavity field and we do not find unstable regions
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