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 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. Finally, we also show that all these findings apply not only to optomechanical systems, but also to parametric amplifiers operating in the fully quantum regime.
- Received 10 July 2017
- Revised 9 September 2017
DOI:https://doi.org/10.1103/PhysRevX.8.011031
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
According to quantum field theory, empty space is not empty but rather filled with virtual particles popping in and out of existence. These virtual particles can have real effects, such as the Casimir effect in which two plates placed nanometers apart are pulled toward each other. In the dynamical Casimir effect (DCE), a rapidly moving mirror can transform virtual photons into real ones. Recent experiments show evidence for the DCE, but these did not employ moving mechanical mirrors. Direct observations of a conversion from mechanical energy to pairs of photons would help clinch the case for DCE. However, previous theoretical descriptions indicated that such an observation would require mechanical oscillators with resonance frequencies exceeding currently available technology. Our improved theoretical analysis shows that this is not the case.
We analyzed the DCE in cavity optomechanical systems, using quantum-mechanical descriptions of both the cavity field and the vibrating mirror. Our fully quantum approach describes the DCE without introducing a time-dependent light-matter interaction; we show that the DCE can even be described without considering any time-dependent Hamiltonian. Vacuum emission can originate from the free evolution of an initial pure mechanical excited state, in analogy with the spontaneous emission from excited atoms.
Our analysis demonstrates that optomechanical systems with coupling strengths in reach of current experiments, and with vibrating mirrors working in the gigahertz spectral range, can be used to observe light emission from mechanical motion. We also found that the oscillating mirror can evolve into a state that is entangled with the radiation emitted by the mirror itself.
