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Physical Review A

Entangled three-particle states and phonon pairs in an optomechanical system with quadratic mechanical-displacement coupling

Yan Liu, Zhentao Zhang, Zhenshan S. Yang

Published Nov 4, 2024• 1 citation
Publisher

Abstract

We study the generation of three-particle (one photon plus two phonons) states and phonon pairs in a cavity-waveguide system where the optomechanical coupling is quadratic in the mechanical displacement. Both the three-particle state and the phonon pair exhibit quantum entanglement in the continuous frequency domain, and the entanglement can be controlled by adjusting the pump-pulse spectral width. By introducing a phantom waveguide, we can analyze the impact of intrinsic cavity losses on the quantum-state generation, and we find that the cavity losses can actually enhance the entanglement in the successfully generated three-particle state or phonon pair.

DOI
10.1103/physreva.110.053501

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We study the generation of three-particle (one photon plus two phonons) states and phonon pairs in a cavity-waveguide system where the optomechanical coupling is quadratic in the mechanical displacement. Both the three-particle state and the phonon pair exhibit quantum entanglement in the continuous frequency domain, and the entanglement can be controlled by adjusting the pump-pulse spectral width. By introducing a phantom waveguide, we can analyze the impact of intrinsic cavity losses on the quantum-state generation, and we find that the cavity losses can actually enhance the entanglement in the successfully generated three-particle state or phonon pair.
Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.
Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.
Abstract We introduce a hybrid cavity optomechanical model capable of generating significant genuine tripartite interactions and entanglement among coherent degrees of freedom. However, realizing and controlling such tripartite interactions and their entanglement pose crucial challenges that remain largely unexplored. In this work, we predict a tripartite coupling mechanism within a hybrid quantum system consisting of a vibrating mechanical oscillator, a two-level atom and a single-frequency cavity field. We specifically propose a mechanism for tripartite and cross-Kerr nonlinear coupling through displacement and squeezing transformations. By adjusting the optical amplitude of the pump light, we can effectively enhance these nonlinear couplings, facilitating the manipulation of entangled and squeezed states. The resulting tripartite genuine entanglement exhibits distinct evolutionary characteristics. Notably, when the pump light amplitude is large, the tripartite entanglement persists for longer time. Additionally, the phonon displays characteristics of both cooling and squeezing. Our study presents a pathway for exploring and exploiting controllable multipartite entanglement, as well as achieving phonon cooling and squeezing with the assistance of a mesoscopic harmonic oscillator. This work underscores the innovative potential of our model in advancing the field of optomechanics and quantum entanglement.
Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for nondemolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. Subsequently, accounting for dissipation, we supply a numerical treatment using a master equation approach. We expect our results to be of use to optomechanical spectroscopy, state transfer, wave-function engineering, and entanglement generation.