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Communications in Theoretical Physics

Mechanical quantum cat-state generation in atom-optomechanical systems via parameter-controlled coherence engineering

Li Zheng, Jie Li, Jia-Cong ZHANG, Yu-Jie Liu

Published Jan 16, 2026• 0 citations
Publisher

Abstract

Abstract In this study, we propose an experimental scheme to generate macroscopic quantum cat states of a mechanical oscillator within a hybrid atom-optomechanical system. The system consists of a mechanical oscillator harmonically coupled to an optical cavity, where the atom-cavity interaction operates in the ultrastrong-coupling regime described by the Rabi–Stark model. The cavity photon and atom state measurements project the mechanical mirror into cat states, with the process enhanced by Fock-state initialization, nonlinear atom-field coupling and modulated mechanical tuning. Wigner-function analysis confirms nonclassicality. The key findings are: (1) higher initial photon number n increases coherent-state amplitudes and separations of the cat states; (2) smaller detuning improves distinguishability; (3) both the nonlinear atom-photon coupling term and stronger optomechanical coupling accelerate the generation of cat states. This approach provides a parameter-tunable framework for quantum coherence control.

DOI
10.1088/1572-9494/ae3956

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Abstract In this study, we propose an experimental scheme to generate macroscopic quantum cat states of a mechanical oscillator within a hybrid atom-optomechanical system. The system consists of a mechanical oscillator harmonically coupled to an optical cavity, where the atom-cavity interaction operates in the ultrastrong-coupling regime described by the Rabi–Stark model. The cavity photon and atom state measurements project the mechanical mirror into cat states, with the process enhanced by Fock-state initialization, nonlinear atom-field coupling and modulated mechanical tuning. Wigner-function analysis confirms nonclassicality. The key findings are: (1) higher initial photon number n increases coherent-state amplitudes and separations of the cat states; (2) smaller detuning improves distinguishability; (3) both the nonlinear atom-photon coupling term and stronger optomechanical coupling accelerate the generation of cat states. This approach provides a parameter-tunable framework for quantum coherence control.
In this paper, we propose a new theoretical scheme for generating a macroscopic Schrödinger cat state of a mechanical oscillator in a hybrid optomechanical system where a beam of two-level atoms passes through the cavity. In the model under consideration, the cavity field couples to the macroscopic mirror through the optomechanical interaction while it couples to the atom through a generalized Jaynes–Cummings interaction that involves the cavity-mode structure. The motion of the mirror modifies the cavity-mode function and therefore modulates the atom-field interaction, leading to the three-mode atom-field-mirror coupling or, equivalently, polariton-mirror coupling in a dressed picture. This interaction induces a controllable anharmonicity in the energy spectrum of the mechanical oscillator, which provides the possibility of generating a superposition of two time-dependent coherent states of the mechanical oscillator just by performing a conditional measurement on the internal states of the atoms exiting the optomechanical cavity. We also investigate the tripartite atom-field-mirror entanglement, which is controllable by adjusting the parameters of the system. In addition, we explore the effects of the mechanical dissipation and thermal noise on the tripartite quantum correlation in the system as well as the generated mechanical superposition state.
Abstract We propose an efficient scheme to generate a macroscopical quantum superposition state with a cavity optomechanical system, which is composed of a quantum Rabi-Stark model coupling to a mechanical oscillator. In a low-energy subspace of the Rabi-Stark model, the dressed states and then the effective Hamiltonian of the system are given. Due to the coupling of the mechanical oscillator and the atom-cavity system, if the initial state of the atom-cavity system is one of the dressed states, the mechanical oscillator will evolve into a corresponding coherent state. Thus, if the initial state of the atom-cavity system is a superposition of two dressed states, a coherent state superposition of the mechanical oscillator can be generated. The quantum coherence and their distinguishable properties of the two coherent states are exhibited by Wigner distribution. We show that the Stark term can enhance significantly the feasibility and quantum coherence of the generated macroscopic quantum superposition state of the oscillator.
We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom-cavity-oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, the proposed proposal consider the second order approximation on the Lamb-Dicke parameter, which is more universal in the experiment. Numerical simulations confirm the validity of our derivation.
In a nutshell, a cavity optomechanical system consists of a mechanical oscillator inside an optical cavity. Cavity optomechanics studies the interplay between the light-matter radiation-pressure interaction and the change in the cavity frequency induced by mechanical motion. By leveraging the tools of quantum optics and quantum measurement, cavity quantum optomechanics enables the engineering of nonclassical quantum states of bulk matter. In this thesis, I present protocols for engineering such nonclassical quantum states in Part II. First, I introduce a scheme to ‘grow’ a quantum kitten state of a mechanical oscillator into a macroscopic Schrödinger cat state using a series of nonlinear pulsed optomechanical interactions. Next, I detail our proposed schemes to generate and verify entanglement between two mechanical oscillators. Moving on from pulsed optomechanics, I describe the theory behind an experiment that achieved multi-phonon subtraction from a mechanical oscillator in a continuously driven Brillouin optomechanical system. In the final chapter of Part II, I provide a theoretical preview of an experiment that investigates the behaviour of the mechanical oscillator when no light is detected at the output. In Part III, I introduce a new framework for nonlinear cavity quantum optomechanics that incorporates the intrinsic nonlinearity of the radiation-pressure interaction, the nonlinearity from the cavity enhancement, and higher-order mechanical position terms in the expansion of the cavity frequency. I then propose a scheme for measuring mechanical position using general-dyne detection, applicable to pulsed and continuous measurements. This predicts a new regime of operation, the “stochastic Gaussian” regime. Finally, I discuss a protocol for deterministic mechanical squeezing that utilizes the cavity response.
It is quite important to enhance and control the optomechanically induced high-order sideband generation to achieve low-power optical comb and high-sensitivity sensing with an integrable structure. Here we present and analyze a proposal for enhancement and manipulation of optical nonlinearity and high-order sideband generation in a hybrid atom-cavity optomechanical system that is coherently driven by a bichromatic input field consisting of a control field and a probe field and that works beyond the perturbative regime. Our numerical analysis with experimentally achievable parameters confirms that robust high-order sideband generation and typical spectral structures with nonperturbative features can be created even under weak driven fields. The dependence of the high-order sideband generation on the atomic parameters are also discussed in detail, including the decay rate of the atoms and the coupling parameter between the atoms and the cavity field. We show that the cutoff order as well as the amplitude of the higher-order sidebands can be well tuned by the atomic coupling strength and the atomic decay rate. The proposed mechanism of enhancing optical nonlinearity is quite general and can be adopted to optomechanical systems with different types of cavity.
We show that an atom can be coupled to a mechanical oscillator via quantum vacuum fluctuations of a cavity field enabling energy transfer processes between them. In a hybrid quantum system consisting of a cavity resonator with a movable mirror and an atom, these processes are dominated by two pair-creation mechanisms: the counterrotating (atom-cavity system) and dynamical Casimir interaction terms (optomechanical system). Because of these two pair-creation mechanisms, the resonant atom-mirror coupling is the result of high-order virtual processes with different transition paths well described in our theoretical framework. We perform a unitary transformation to the atom-mirror system Hamiltonian, exhibiting two kinds of multiple-order transitions of the pair creation. By tuning the frequency of the atom, we show that photon frequency conversion can be realized within a cavity of multiple modes. Furthermore, when involving two atoms coupled to the same mechanical mode, a single vibrating excitation of the mechanical oscillator can be simultaneously absorbed by the two atoms. Considering recent advances in strong and ultrastrong coupling for cavity optomechanics and other systems, we believe our proposals can be implemented using available technology.