Spontaneous emission in Casimir-Rabi oscillations through a weak optomechanical coupling

The dynamical Casimir effect (DCE) describes the energy conversion from a mechanical motion to the electromagnetic fields. When the mechanical oscillator is in a mechanically excited state, the free evolution due to the DCE produces radiation in the vacuum, in analogy with the spontaneous emission from an excited atom. In this manuscript, we investigate such a spontaneous radiation process by employing the quantum trajectory approach. When the dissipation rate of the system is very low, there can be a reversible energy exchange between the mirror in the excited state and the vacuum field, and this reversible exchange is called vacuum Casimir-Rabi oscillations. Multiple quantum trajectory simulations of this process show that the number of trajectories responsible for the generation of radiation can reach a significant value when the mechanical dissipation rate is less than the photon dissipation rate. We also find that two-photon (two/three-phonon) bundle emission occurs in photon (phonon) emission. In comparison to pure two-photon and three-phonon free dissipation, the probability of two-photon bundle emission and two-phonon bundle emission are observed to be marginally elevated as a consequence of the presence of the DCE. This pattern may assist in developing a deeper comprehension of the physical characteristics of photon and phonon emission in the DCE.