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arXiv:2408.06365 · Physical Review A

Effects of quadratic optomechanical coupling on bipartite entanglements, mechanical ground-state cooling, and mechanical quadrature squeezing in an electro-optomechanical system

N. Ghorbani, Ali Motazedifard, M. H. Naderi

Published Jan 22, 2025• 7 citations
arXivHTMLPDF

Abstract

We theoretically investigate the steady-state bipartite entanglements, mechanical ground-state cooling, and mechanical quadrature squeezing in a hybrid electro-optomechanical system where a moving membrane is linearly coupled to the microwave field mode of an LC circuit, while it simultaneously interacts both linearly and quadratically with the radiation pressure of a single-mode optical cavity. We show that by choosing a suitable sign and amplitude for the quadratic optomechanical coupling (QOC), one can achieve enhanced and thermally robust stationary bipartite entanglement between the subsystems, improved mechanical ground-state cooling, and $Q$-quadrature squeezing of the mechanical mode beyond the 3-dB limit of squeezing. In particular, we find that in the presence of QOC with negative sign and in the resolved sideband regime the bipartite optical-mechanical entanglement can be increased by about 2 orders of magnitude around the temperature of 1 mK, and it can be preserved against thermal noise up to the ambient temperature of 0.1 K. Furthermore, the QOC with positive sign can give rise to the enhancement of the mechanical ground-state cooling by about 1 order of magnitude in the optical and microwave red-detuned regime. We also find that for the positive sign of QOC and near the microwave resonance frequency the squeezing degree of the $Q$ quadrature of the mechanical mode can be amplified up to 15 dB. Such a hybrid electro-optomechanical system can serve as a promising platform to engineer an improved entangled source for quantum sensing as well as quantum information processing.

DOI
10.1103/physreva.111.013524

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We present a theoretical investigation of quantum entanglement enhancement in an electro-optomechanical system comprising a ring cavity with two Coulomb-coupled mechanical resonators and an embedded optical parametric amplifier (OPA). The system dynamics are governed by radiation pressure interactions between the optical field and mechanical modes, modified by both the Coulomb coupling and OPA-induced squeezing. Through a comprehensive quantum Langevin analysis and linearization approach, we demonstrate how these competing interactions can be exploited to generate and control entanglement. Our key finding is that the Coulomb interaction strength is fundamental for generating bipartite entanglement, both between directly coupled mechanical modes and, more remarkably, between optical and mechanical modes, thereby influencing the entire system. The OPA parameters, namely the gain and phase, provide powerful control knobs for entanglement optimization. Notably, the OPA enhances entanglement robustness against thermal noise, resulting in stronger quantum correlations. We quantify these effects through covariance matrix methods and logarithmic negativity measures. The study provides new insights into hybrid optomechanical entanglement generation, showing how combined charge-mediated coupling and optical squeezing can overcome typical limitations of purely optomechanical systems. These results offer practical guidelines for experimental implementations in quantum information processing and macroscopic quantum state engineering, particularly in systems where environmental noise and parameter stability are critical concerns.
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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 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 showcase 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.
Optomechanical generation of entangled optical beams is usually hindered by thermal noise. We present a theoretical study of low frequency entanglement generation between two optical harmonics emitted from a cavity optomechanical system operating in the resolved-sideband regime. The system comprises three nearly equidistant optical modes in a high-finesse cavity, with the central mode coherently driven. This configuration enables radiation-pressure interactions that generate strong quantum correlations between the two sideband modes. Remarkably, these correlations persist even at large numbers of thermal quanta if one properly engineers the optical cooling rate of the mechanical mode. Our findings demonstrate the feasibility of robust entanglement under ambient conditions, opening new avenues for hybrid quantum technologies based on mechanical interfaces and continuous-variable quantum information processing.
We theoretically investigate a quadratic optomechanical system comprising a single-mode optical cavity linearly coupled to one mechanical resonator and quadratically coupled to a second resonator. By tuning the cavity detuning and optomechanical coupling strengths, we demonstrate the transition from optical bistability to multistability with up to seven steady-state solutions. Notably, simultaneous ground-state cooling of both mechanical resonators occurs on the dynamically stable branch of the nonlinear steady-state solutions, offering new opportunities for combined nonlinear optical and quantum cooling functionalities. Beyond the multistable regime, we systematically study dual-mode ground-state cooling and find that robust simultaneous cooling can be achieved over a broad parameter range, except when the linear and quadratic couplings become comparable, where a dark-mode effect arises. In this case, tuning the second-order optomechanical-induced frequency shifts effectively suppresses dark-mode interference, enabling controllable and simultaneous ground-state cooling. Our results provide a versatile framework for engineering multimode quantum states in optomechanical systems and open new avenues for the development of multifunctional quantum devices, including ultra-sensitive sensors, scalable quantum memories, and integrated quantum networks.