This paper is aimed at investigating the feasibility of generating quantum conditional entanglement between macroscopic mechanical mirrors in optomechanical systems while under continuous measurement and feedback control. We consider the squeezing of the states of the mechanical common and the differential motions of the mirrors by the action of measuring the common and the differential output light beams in the Fabry-P\'erot-Michelson interferometer. We carefully derive a covariance matrix for the mechanical mirrors in a steady state, employing the Kalman filtering problem with dissipative cavities. We demonstrate that Gaussian entanglement between the mechanical mirrors is generated when the states of the mechanical common and differential modes of the mirrors are squeezed with high purity in an asymmetric manner. Our results also show that quantum entanglement between 7-mg mirrors is achievable in the short term.
This paper is aimed at investigating the feasibility of generating quantum conditional entanglement between macroscopic mechanical mirrors in optomechanical systems while under continuous measurement and feedback control. We consider the squeezing of the states of the mechanical common and the differential motions of the mirrors by the action of measuring the common and the differential output light beams in the Fabry-P'erot-Michelson interferometer. We carefully derive a covariance matrix for the mechanical mirrors in a steady state, employing the Kalman filtering problem with dissipative cavities. We demonstrate that Gaussian entanglement between the mechanical mirrors is generated when the states of the mechanical common and differential modes of the mirrors are squeezed with high purity in an asymmetric manner. Our results also show that quantum entanglement between 7-mg mirrors is achievable in the short term.
We analyze the conditional quantum state of a mechanical mirror in an optomechanical system subject to continuous measurement, feedback control, and quantum filtering. We identify a parameter regime in which the mirror exhibits momentum squeezing beyond the standard quantum limit, achieved through an appropriate choice of the homodyne detection angle. In this regime, we show that optimal filtering effectively realizes a free-particle-like conditional state. When this mechanism is applied to a configuration consisting of two optomechanical systems, the resulting momentum squeezing significantly enhances the signal of gravity-induced entanglement. This enhancement arises because the momentum squeezing not only amplifies the distinction between the common and differential modes, but also, in the high-purity regime, increases the position uncertainty in accordance with the uncertainty principle, thereby enlarging the spatial extent of the quantum superposition. Our results provide insights into experimental strategies for probing the quantum nature of gravity using optomechanical platforms.
We report the feasibility of detecting the gravity-induced entanglement (GIE) with optomechanical systems, which is the first investigation that clarifies the feasible experimental parameters to achieve a signal-to-noise ratio of S/N=1. Our proposal focuses on GIE generation between optomechanical mirrors, coupled via gravitational interactions, under continuous measurement, feedback control, and Kalman filtering process, which matured in connection with the field of gravitational wave observations. We solved the Riccati equation to evaluate the time evolution of the conditional covariance matrix for optomechanical mirrors that estimated the minimum variance of the motions. The results demonstrate that GIE is generated faster than a well-known time scale without optomechanical coupling. The fast generation of entanglement is associated with quantum-state squeezing by the Kalman filtering process, which is an advantage of using optomechanical systems to experimentally detect GIE.
Abstract The ability to engineer entangled states that involve macroscopic objects is of particular importance for a wide variety of quantum‐enabled technologies, ranging from quantum information processing to quantum sensing. Here how to achieve coherent manipulation and enhancement of quantum entanglement in a hybrid optomechanical system, which consists of a Fabry–Pérot cavity with two movable mirrors, an optical parametric amplifier (OPA), and an injected squeezed vacuum reservoir is proposed. It is shown that the advantages of this system are twofold: 1) one can effectively regulate the light‐mirror interactions by introducing a squeezed intracavity mode via the OPA; 2) when properly matching the squeezing parameters between the squeezed cavity mode and the injected squeezed vacuum reservoir, the optical input noises can be suppressed completely. These peculiar features of this system allow the generation and manipulation of quantum entanglement in a coherent and controllable way. More importantly, it is also found that such controllable entanglement, under some specific squeezing parameters, can be considerably enhanced in comparison with those of the conventional optomechanical system. The work, providing a promising method to regulate and tailor the light‐mirror interaction, is poised to serve as a useful tool for engineering various quantum effects which are based on cavity optomechanics.
Entanglement and squeezing are two useful resources in quantum technologies. Recent studies have increasingly focused on generating these nonclassical features in macroscopic objects. However, establishing entanglement and squeezing in the degrees of freedom of mechanical motion of macroscopic objects is generally hindered by thermal fluctuations of their environments. Here, we propose a scheme to generate steady-state squeezing and entanglement between two rotating mirrors of a Laguerre-Gaussian cavity by quantum squeezed-reservoir engineering. It is revealed that, by injecting a broadband squeezed light into the cavity, stable squeezing in the relative momentum and entanglement between the two rotating mirrors are created. Compared to the previous work where only the entanglement between the two rotating mirrors appears under the condition of different angular frequencies, our result highlights the stable entanglement of the two mirrors with identical frequency and the simultaneous presence of the entanglement and squeezing of the two mirrors. Our finding deepens our understanding of macroscopic quantum phenomena of Laguerre-Gaussian cavity optomechanical system.
This study presents a detailed proposal for an optomechanical system consisting of two mechanical oscillators coupled to a common cavity, aimed at generating pure and entangled two-mode squeezed mechanical steady states. We found that the violation of Bell's measurement may not occur where the entanglement is maximum; rather, nonlocality can be observed for lower entangled states. A central result is that optomechanical coupling imperfections can enhance mechanical entanglement while simultaneously suppressing Bell nonlocality by reducing the purity of the mechanical state. To mitigate this trade-off, we introduce phase-dependent phonon hopping between the mechanical oscillators and show that Bell nonlocality can be selectively enhanced in specific dark-mode configurations, even when the overall entanglement is reduced. We trace this contrasting behaviorto changes in state purity associated with the imbalance of the Bogoliubov-mode occupations. Compatible with existing microwave cavity optomechanical platforms, the proposed architecture provides an experimentally accessible route for controlling nonlocal quantum correlations in multimode mechanical systems. Our proposed scheme serves as an attractive platform for the deployment of continuous-variable teleportation and high-fidelity quantum communication.
In this paper, we investigate the dynamics of quantum correlations for the continuous-variable bipartite optomechanical system in the presence of homodyne mediated quantum feedback. The system is constructed using the Fabry–Perot cavity and a mechanical oscillator. In detail, we have studied the quantum entanglement via logarithmic negativity, quantum discord, and quantum steering between the optical and mechanical modes. The results show that the maximum entanglement between the optical and mechanical modes occurred out of the resonance frequency at the steady-state region due to the presence of the optical feedback. We also employ quantum steering to see the steerability between the modes. It is observed that the quantum entanglement increases when the effective detuning frequency increases, however, the quantum discord and steering decrease when the effective detuning frequency increases for a given quantum feedback strength with other parameters of the system are to be fixed. Moreover, the presence of quantum feedback has an enhancement effect on the quantum correlations.