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arXiv:2411.03719 · Optics Express

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

Ke-Xiong Yan, Yuan Qiu, Yang Xiao, Jie Song, Ye‐Hong Chen, Yan Xia

Published Jul 24, 2025• 7 citations
arXivHTMLPDF

Abstract

When the mechanical oscillator is initially in an excited state, its free evolution, driven by the dynamical Casimir effect (DCE), leads to the generation of radiation in the vacuum, analogous to the spontaneous emission of an excited atom. In the regime where the loss rates are lower than the corresponding frequency splittings, reversible energy exchange can occur between the excited mechanical oscillator and the vacuum cavity field (i.e., vacuum Casimir-Rabi oscillations). By using the quantum trajectory approach, we show that n -photon/ n -phonon emission can be achieved by opening dissipative channels for these Casimir-Rabi oscillations. Simulation results from 10 5 quantum trajectories demonstrate that the purities of two-photon emission, two-phonon emission, and three-phonon emission can reach 0.92, 0.94, and 0.95, respectively. These values are observed in Casimir-Rabi oscillations between the three-phonon state and the two-photon state in a weak optomechanical coupling. This phenomenon could provide insights into the physical characteristics of photon and phonon emission in the DCE.

DOI
10.1364/oe.563278

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When the mechanical oscillator is initially in an excited state, its free evolution, driven by the dynamical Casimir effect (DCE), leads to the generation of radiation in the vacuum, analogous to the spontaneous emission of an excited atom. In the regime where the loss rates are lower than the corresponding frequency splittings, reversible energy exchange can occur between the excited mechanical oscillator and the vacuum cavity field (i.e., vacuum Casimir-Rabi oscillations). By using the quantum trajectory approach, we show that n -photon/ n -phonon emission can be achieved by opening dissipative channels for these Casimir-Rabi oscillations. Simulation results from 10 5 quantum trajectories demonstrate that the purities of two-photon emission, two-phonon emission, and three-phonon emission can reach 0.92, 0.94, and 0.95, respectively. These values are observed in Casimir-Rabi oscillations between the three-phonon state and the two-photon state in a weak optomechanical coupling. This phenomenon could provide insights into the physical characteristics of photon and phonon emission in the DCE.
When a two-level atom interacts resonantly with a coherent electromagnetic field, the polarizability of the atom can be modulated due to the Rabi oscillations between atomic levels. We show that in the quantum vacuum, such a time-dependent atomic polarizability can lead to a resonant generation of photon pairs, a phenomenon reminiscent of photon emission in the dynamical Casimir effect (DCE). Specifically, we employ a dressing transformation to obtain an effective Hamiltonian which uncovers a polarizability-dependent parametric interaction corresponding to DCE. We determine the photon emission rate and indicate features of DCE photon pairs distinguishable from regular fluorescence photons.
We propose an experimentally feasible optomechanical system (OMS) that is dispersively driven and operates in the reversed dissipation regime (RDR), where the mechanical damping rate far exceeds the cavity decay rate. We demonstrate that coherent, fast-time modulation of the driving laser frequency on time scales longer than the mechanical decoherence time allows for adiabatic elimination of the mechanical mode, resulting in strong parametric amplification of quantum vacuum fluctuations of the intracavity field. This mechanism, known as the parametric dynamical Casimir effect (parametric-DCE), leads to the generation of Casimir photons. In the dispersive RDR, we find that the total system Hamiltonian-including the DCE term-is intrinsically modified by a generalized optomechanical Kerr-type nonlinearity. This nonlinearity not only saturates the mean number of radiated Casimir photons on short time scales, even without dissipation, but also induces oscillatory behavior in their dynamics and quantum characteristics. Remarkably, the presence of the Kerr nonlinearity causes the generated DCE photons to exhibit nonclassical features, including simultaneous sub-Poissonian statistics and negative Wigner function, as well as quadrature squeezing, which can be controlled by adjusting the system parameters. Surprisingly, the controllable simultaneous nonclassical dynamics in the same physical parameter regime, which is induced by the optomechanical Kerr nonlinearity to the parametric DCE cannot occur in the standard DCE or Kerr-type systems. The proposed nonclassical microwave radiation source possesses the potential to be applied in quantum information processing, quantum computing as well as microwave quantum sensing.
The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuations of an electromagnetic field. The verification of such an effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way to an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of the DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.
We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.
In this work we study radiation-matter interaction in the limit of a single excitation when nano-mechanical effects act on the single photon emitted by a qubit. In particular, we use two different models. In the first model, we consider an opto-mechanical cavity with an oscillating mirror in front of a qubit, initially in its excited state. A photon is emitted and reflected by the mirror so it can re-excite the qubit and so continue a process of controlled emission. The qubit interacts with a continuous bath of harmonic oscillators with which energy can be partially exchanged. Results show that the time-dependent dynamics of light emission can be Markovian or non-Markovian. In both cases, the frequency spectrum exhibits sideband photons associated with nano-mechanical oscillations. In the second model, in addition to the opto-mechanical cavity, the qubit is located on an optical nano-cavity. In this picture we have two couplings, while the first one acts between the qubit and the single mode of the optical nano-cavity, the second one acts between the external modes of the opto-mechanical and the single mode of optical nano-cavity. The results of the time-dependent dynamics in the qubit-nanocavity, show that this system is capable of exchanging its only coherent excitation due to feedback produced by the mirror, even if the first coupling is weak. The energy exchange with the external modes produces a type-like Rabi oscillation, in which the system behaves as if it were in the strong coupling regime. The low amplitude of these oscillations shows that energy is partially exchanged between the external modes and the optical nano-cavity. Finally, we show that if we change the state of motion of the mirror, the entire structure of external modes does also change, causing a damping in the Rabi oscillations over time.
We study the coherent dynamics of an excited two-level atom in a vacuum optomechanical cavity and find that the original atom-cavity Rabi oscillation is sinusoidally modulated by the light-mechanics coupling as the Rabi splitting is on resonance with the mechanical mode. We develop an analytic model in a three-dimensional Hilbert subspace to explain this phenomenon and employ numerical simulations of the density-matrix master equation to confirm our analysis. We also show that the modulated Rabi oscillation survives in presence of dissipations and other non-ideal factors.