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arXiv:2108.09906 · Europhysics Letters (EPL)

Exact solvability and two-frequency Rabi oscillation in cavity-QED setup with moving emitter

Mingzhu Weng, Zhihai Wang

Published Dec 13, 2021• 2 citations
arXivHTMLPDF

Abstract

Abstract In this paper, we investigate the energy spectrum and coherent dynamical process in a cavity-QED setup with a moving emitter, which is subject to a harmonic potential. We find that the vibration of the emitter will induce the effective Kerr and optomechanical interactions. We generalize the Bogliubov operators approach which dealt with quantum Rabi model, to our cavity-emitter-vibration system and obtain the energy spectrum exactly. Furthermore, we show that the dynamics of the system exhibit a two-frequency Rabi oscillation behavior. We explain such behavior by optomechanical-interaction–induced quantum transition between emitter-cavity dressed states. We hope that the interaction between cavity mode and moving emitter will provide a versatile platform to explore more exotic effects and potential applications in cavity-QED scenario.

DOI
10.1209/0295-5075/ac4273

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Abstract In this paper, we investigate the energy spectrum and coherent dynamical process in a cavity-QED setup with a moving emitter, which is subject to a harmonic potential. We find that the vibration of the emitter will induce the effective Kerr and optomechanical interactions. We generalize the Bogliubov operators approach which dealt with quantum Rabi model, to our cavity-emitter-vibration system and obtain the energy spectrum exactly. Furthermore, we show that the dynamics of the system exhibit a two-frequency Rabi oscillation behavior. We explain such behavior by optomechanical-interaction–induced quantum transition between emitter-cavity dressed states. We hope that the interaction between cavity mode and moving emitter will provide a versatile platform to explore more exotic effects and potential applications in cavity-QED scenario.
We simulate an optomechanical system via a cavity QED scenario with a movable atom and investigate its application in the tiny mass sensing. We find that the steady-state solution of the system exhibits a multiple stability behavior, which is similar to that in the optomechanical system. We explain this phenomenon by the opto-mechanical interaction term in the effective Hamiltonian. Due to the dressed states formed by the effective coupling between the vibration degree of the atom and the optical mode in the cavity, we observe a narrow transparent window in the output field. We utilize this vibration induced transparency phenomenon to perform the tiny mass sensing. We hope our study will broaden the application of the cavity QED system to quantum technologies.
We study nonlinear dynamics in the fundamental cavity QED system, consisting of a point-like collection of two-level atoms moving through a single-mode cavity, with a spatially inhomogenous field. In the semiclassical, strong-coupling and rotating-wave approximations, the model is shown to be integrable with atoms moving at exact resonance through a cavity with an arbitrary spatial profile of the mode along the propagation axis. The general exact semiclassical solution is derived in an explicit form, in terms of Jacobian elliptic functions. Numerical simulation confirms that perturbations, which are produced by a modulation of the coupling between moving atoms and a cavity mode, provide, our of resonance, a mechanism responsible for Hamiltonian chaos. Taking into account the interatomic quantum correlations, we go beyond the semiclassical model and derive a dynamical system, which is able to describe vacuum Rabi oscillation with moving atoms. At resonance, this system is again shown to be integrable with a general semiquantum solution found. Out of resonance, it can demonstrate chaotic vacuum Rabi oscillations, which may be considered as a new kind of reversible spontaneous emission.
We propose a scheme to realize frequency conversion of photons, using a hybrid system with a qubit coupled to both a resonator cavity and an optomechanical cavity. In this system, a high-energy photon can be converted into a low-energy photon plus a phonon and vice versa; the qubit works as an intermediate medium with its states unchanged. Moreover, the process can be exquisitely tuned by changing the frequency of the qubit or the resonator mode, providing additional control for the conversion. We further analyze the system dynamics and demonstrate two Rabi oscillation behaviors with dissipations. With the state-of-the-art techniques in cavity quantum electrodynamics and optomechanical systems, our proposal would be implemented and an efficient and controllable quantum light source can be achieved.
The interaction of a two-level atom uniformly moving along a classical trajectory with a high-Q cavity quantum mode is analyzed. The dressed-state method is used to derive a recurrence formula for the transition probability of the atom with photon emission; the temporal dynamics of this probability qualitatively depends on the Doppler shift of the atomic transition frequency, on the Rabi frequency of the atom-field system, and on the detuning of the atomic transition frequency from the field mode frequency. The emission dynamics of a moving atom is very sensitive to the detuning. Rabi-type oscillations with a frequency equal to the Doppler shift can arise under certain conditions. At resonance, the emission probability of a moving atom can considerably exceed the emission probability of an atom at rest. A plane-parallel-mirror cavity and a confocal spherical-mirror cavity are considered. It is shown that the peculiarities of Doppler-Rabi oscillations must be taken into account in micromaser theory.
The interaction with a quantum mode of a high- Q cavity is considered for a two-level atom uniformly moving along the classical trajectory. The method of dressed states is employed to deduce the recursion relation for the probability of atomic transition with photon emission. It is shown that the dependence of the transition probability on the position of a moving atom in the cavity and the magnitude of this probability are qualitatively influenced by the ratio between the Doppler shift of transition frequency and the Rabi frequency of atom-field system.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.