We theoretically propose a method to generate tripartite entanglement of three mechanical oscillators in an optomechanical array. We consider a system comprised of three bichromatically driven optomechanical systems which are coupled to each other via Coulomb interaction of the mechanical oscillators. We show that, for small Coulomb coupling strength, steady tripartite entanglement of the three mechanical oscillators with time periodicity can be generated due to the combined effect of the two-tone drivings and the Coulomb coupling. At large Coulomb coupling strength, the tripartite entanglement exhibits steady entanglement sudden death and revival. The duration of entanglement death during one period can be controlled by the Coulomb coupling strength. The tripartite entanglement is robust against the mechanical thermal noise. Our paper provides us a route for exploring and exploiting controllable and robust multipartite entanglement among macroscopic mechanical oscillators.
We theoretically propose a method to generate tripartite entanglement of three mechanical oscillators in an optomechanical array. We consider a system comprised of three bichromatically driven optomechanical systems which are coupled to each other via Coulomb interaction of the mechanical oscillators. We show that, for small Coulomb coupling strength, steady tripartite entanglement of the three mechanical oscillators with time periodicity can be generated due to the combined effect of the two-tone drivings and the Coulomb coupling. At large Coulomb coupling strength, the tripartite entanglement exhibits steady entanglement sudden death and revival. The duration of entanglement death during one period can be controlled by the Coulomb coupling strength. The tripartite entanglement is robust against the mechanical thermal noise. Our paper provides us a route for exploring and exploiting controllable and robust multipartite entanglement among macroscopic mechanical oscillators.
We theoretically propose a scheme to generate strong genuine tripartite entanglement among three mechanical oscillators in a multimode optomechanical system. In our setup, each mechanical oscillator is independently coupled to three optical modes supported by a single optical cavity, with each optical mode driven by a six-tone driving field. By appropriately tailoring the amplitudes of the driving fields, the mechanical steady state can be engineered into a three-mode squeezed vacuum state exhibiting significant genuine tripartite entanglement. We further investigate the effects of mechanical thermal reservoirs and demonstrate that the entanglement generated by our scheme persists at a significant level even at dilution refrigerator temperatures. Our results offer a feasible route toward the generation and utilization of multipartite entanglement in quantum optomechanical platforms, with potential applications in quantum devices.
The entanglement of macroscopic mechanical oscillators is always an interesting domain. How to entangle multiple mechanical oscillators is still not well answered. In this paper, we investigate the bipartite and tripartite quantum correlations among three distinct mechanical oscillators interacting with one cavity pumped by a multi-tone driving laser. Floquet cavity modes, resulting from different frequency components of the multi-tone driven cavity, are used to construct channels for quantum correlations between mechanical oscillators. By modulating the effective optomechanical coupling, we can manipulate the mechanical entanglement and EPR steering. The numerical results show that the two-tone driving widely employed is not enough to generate tripartite entanglement, while three- and four-tone driving can be employed to generate and enhance genuine tripartite entanglement. All bipartite entanglement can also be modulated. In addition, we demonstrate the monogamous relation of tripartite EPR steering and manipulate the asymmetry of steering. This work provides a method for manipulating the quantum correlation among multiple macroscopic objects.
This paper investigates the deterministic generation and coherent control of continuous-variable bipartite and tripartite entanglement within a multi-mirror electro-optomechanical ring cavity. The proposed architecture integrates radiation pressure with tunable Coulomb interactions, governed by external gate voltages, to establish quantum correlations between an intracavity optical field and a collective of four mechanical oscillators. We perform a rigorous stability analysis of the system, identifying the operational regimes across a broad range of free parameters, and evaluate the generation of tripartite entanglement within two distinct subsystems. Our numerical results demonstrate that while standard coherent driving combined with Coulomb coupling can generate entanglement, it is restricted to narrow detuning regions. In contrast, the introduction of squeezed light dramatically enhances quantum correlations, facilitating entanglement over a significantly wider range of normalized detuning without compromising the stability of the optomechanical system. A central finding is that the fixed charged body serves as a dynamic control parameter rather than a static component; by effectively tuning the mechanical susceptibility, it enables the generation of optomechanical entanglement that is both stronger and more resilient to thermal noise than the mechanical–mechanical entanglement mediated by direct Coulomb interaction. Furthermore, the external gate voltage provides a reliable mechanism for the continuous tuning of mechanical coupling strengths. From a practical perspective, the ability of the Coulomb coupling to act as a quantum switch for activating or suppressing entanglement suggests significant potential for quantum information control and state transfer within hybrid quantum architecture networks.
ABSTRACT Quantum entanglement is a crucial resource in quantum information science, applying to quantum key distribution, quantum sensing, and quantum teleportation. However, generating macroscopic quantum entanglement in multimode optomechanical systems, where an optical mode couples to multiple degenerate or near‐degenerate vibrational modes, is a challenging task, as the entanglement is suppressed by the dark‐mode effect. In this paper, we propose a scheme to generate both bipartite and genuine tripartite entanglement in the system via periodic modulation. First, we consider a two‐oscillator optomechanical system in which time‐varying voltages applied to the oscillators enable the engineering of coupling pathways between the bright and dark modes, thus breaking the dark‐mode effect. Thermal phonons can be extracted by the coupling channels, so that bipartite and tripartite entanglement can be achieved at a nonzero temperature. Furthermore, we extend this scheme to an optomechanical system with oscillators, where the degenerate vibrational modes can entangle with the optical mode. Notably, the macroscopic quantum entanglement we obtain exhibits greater robustness against thermal phonons.
This study investigates the generation and enhancement of quantum entanglement in an electro-optomechanical ring cavity system. The setup integrates two Coulomb-coupled mechanical resonators, which serve as the fundamental mechanism for the generation of bipartite and tripartite entanglement via charge mediated coupling. We then demonstrate the significant enhancement of this entanglement via a nonlinear parametric drive (an optical parametric amplifier, OPA), which injects a controllable nonlinearity into the cavity. We derive the system's Hamiltonian and the corresponding quantum Langevin equations, which are linearized around steady-state solutions to analyze Gaussian quantum fluctuations. Employing the covariance matrix formalism, we quantify bipartite entanglement via logarithmic negativity and tripartite entanglement via the minimum residual contangle. Our results unequivocally show that while the Coulomb interaction is indispensable for creating entanglement, the OPA acts as a powerful control tool, dramatically amplifying the degree of quantum correlations for all subsystems. We find that the strength of entanglement is highly sensitive to several parameters and can be optimized through the strategic selection of the OPA's gain and phase, the laser detuning, and the input power. A key finding is the existence of a trade-off, where parameters that maximize entanglement also constrain the stable operating regime of the system. Furthermore, thermal noise is shown to progressively degrade all quantum correlations, underscoring the necessity for low-temperature operation. These findings provide comprehensive guidance for parameter optimization, outlining a clear path from generation to enhancement, and highlight the potential of such hybrid systems as versatile platforms for controlling multipartite entanglement in quantum technologies.
We present a scheme for realizing phase-controlled entanglement in a microwave optomechanical system comprising two microwave cavities and two mechanical oscillators. Under specific driving conditions, we show that this optomechanical interface can be exploited to generate simultaneously the stationary cavity–cavity entanglement, mechanical–mechanical entanglement, and cavity–mechanical entanglement. Due to the closed loop interaction, we find that the entanglement can be controlled flexibly by tuning the phase difference between the optomechanical coupling strengths. The dependence of the entanglement on the amplitudes of the optomechanical coupling strengths is also explored in detail. Moreover, the bipartite entanglements are robust against temperature, and it is shown that the mechanical oscillators are cooled to the ground state in the parameter regimes for observing entanglement.