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Frontiers of Physics

Multiphonon-resonance quantum Rabi model and adiabatic passage in a cavity-optomechanical system

Zhi‐Rong Zhong, Lei Chen, Jianqi Sheng, Li-Tuo Shen, Shi‐Biao Zheng

Published Jul 18, 2021• 9 citations
Publisher

Abstract

In this paper, we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system. In the scheme, when the driving bichromatic laser beam is adjusted to the off-resonant j -order red- and blue-sideband, the interaction between the cavity and mechanical oscillator leads to a j -phonon resonance quantum Rabi model. Moreover, we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system. As a typical example, we theoretically analyze the two-phonon resonance quantum Rabi model, and derive an effective Hamiltonian of the six-phonon coupling. Finally, we present a method of six-phonon generation based on adiabatic passage across the resonance. Numerical simulations confirm the validity of the proposed scheme. Theoretically, the proposed scheme can be extended to the realization of 3 j -phonon state.

DOI
10.1007/s11467-021-1092-7

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In this paper, we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system. In the scheme, when the driving bichromatic laser beam is adjusted to the off-resonant j -order red- and blue-sideband, the interaction between the cavity and mechanical oscillator leads to a j -phonon resonance quantum Rabi model. Moreover, we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system. As a typical example, we theoretically analyze the two-phonon resonance quantum Rabi model, and derive an effective Hamiltonian of the six-phonon coupling. Finally, we present a method of six-phonon generation based on adiabatic passage across the resonance. Numerical simulations confirm the validity of the proposed scheme. Theoretically, the proposed scheme can be extended to the realization of 3 j -phonon state.
We investigate theoretically the quantum Rabi model in the large-detuning regime. When the frequency of the cavity field is near one-third of the atomic transition frequency, we show that there exists a resonant three-photon coupling via intermediate states connected by counter-rotating processes. We derive an effective Hamiltonian of the three-photon coupling, which determines the magnitude of the energy splitting and the position of the resonance analytically. In addition, we present a scheme of three-photon generation based on adiabatic passage across the resonance.
The multiphonon state plays an important role in quantum information processing and quantum metrology. Here we propose a scheme to realize dynamical emission of phonon pairs based on the technique of stimulated Raman adiabatic passage in a single-cavity optomechanical system, where the optical cavity is driven by two Gaussian pulse lasers. By exploring quantum trajectories of the state populations and the average phonon number, we find that the dynamical phonon-pair emission can be realized under the appropriate parameter conditions and is tunable by controlling the time interval between the consecutive pulses of pump lasers. In particular, the numerical results for the standard and generalized second-order correlation functions of the mechanical mode show that the system can behave as an antibunched phonon-pair emitter. Our proposal can be extended to achieve an antibunched nnn-phonon emitter, which has potential applications for on-chip quantum communication.
We propose a scheme to realize the two-phonon blockade effect in a quadratically coupled optomechanical system. We consider the case that the optical cavity is simultaneously driven by a strong pumping field and a weak driving field. By strongly driving the optical cavity, the nonlinear interaction between the optical mode and the mechanical resonator can be significantly enhanced and an effective second-order nonlinearity between photons and phonons is induced. Based on this effectively strong nonlinearity, the two-phonon blockade effect can be achieved when a weak driving field is applied into the optical cavity. By contrast, we study the case of weakly driving the mechanical resonator. In this case, the single-phonon blockade is generated, while the two-phonon blockade cannot be observed. By numerically calculating the second-order and third-order correlation function, we investigate the statistical characteristics of phonons. In addition, we also study the influence of the thermal noise on the achieved two-phonon blockade effect. Our work provides an alternative approach for implementing multiphonon blockade and has potential applications in quantum information processing.
We propose a scheme to realize antibunched multiple-photon bundles based on phonon blockade in a quadratically coupled optomechanical system. Through adjusting the detunings to match the conditions of phonon blockade in the photon sidebands, we establish super-Rabi oscillation between zero-photon state and multiple-photon states with adjustable super-Rabi frequencies under appropriate single-phonon resonant conditions. Taking the system dissipation into account, we numerically calculate the standard and generalized second-order functions of the cavity mode as well as the quantum trajectories of the state populations with Monte Carlo simulation to confirm that the emitted photons form antibunched multiple-photon bundles. Interestingly, the desirable n-photon states are reconstructed after a direct phonon emission based on phonon blockade, and thus the single-phonon emission heralds the cascade emission of n-photon bundles. Our proposal shows that the optomechanical system can simultaneously behave as antibunched multiple-photon emitter and single-phonon gun. Such a nonclassical source could have potential applications in quantum information science.
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 ability to prepare a macroscopic mechanical resonator into a quantum superposition state is an outstanding goal of cavity optomechanics. Here, we propose a technique to generate cat states of motion using the intrinsic nonlinearity of a dispersive optomechanical interaction. By applying a bichromatic drive to an optomechanical cavity, our protocol enhances the inherent second-order processes of the system, inducing the requisite two-phonon dissipation. We show that this nonlinear sideband cooling technique can dissipatively engineer a mechanical resonator into a cat state, which we verify using the full Hamiltonian and an adiabatically reduced model. While the fidelity of the cat state is maximized in the single-photon, strong-coupling regime, we demonstrate that Wigner negativity persists even for weak coupling. Finally, we show that our cat state generation protocol is robust to significant thermal decoherence of the mechanical mode, indicating that such a procedure may be feasible for near-term experimental systems.