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Optics Express

Manipulating bipartite and tripartite quantum correlations of mechanical oscillators via optomechanical interaction

Rui Peng, Zhen‐Biao Yang, Da‐Wei Wang, Ling Zhou

Published Sep 28, 2023• 6 citations
Publisher

Abstract

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.

DOI
10.1364/oe.500912

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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.
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 consider a three-mode optomechanical system in which two mechanical oscillators are independently coupled to a cavity mode driven by two controllable lasers. By controlling the two-tone driving, one can prepare the entanglement and Einstein-Podolsky-Rosen (EPR) steering of two mechanical modes, in which the cavity mode acts as a single reservoir to cool two Bogoliubov modes. We find that the direction of EPR steering can be manipulated effectively by adjusting the damping rates and the thermal noises of two mechanical modes. In addition, we show that the entanglement and EPR steering between two mechanical modes can be enhanced by adding a parametric amplifier (PA) into the cavity. The effects of the strength and phase of the PA on the mechanical entanglement and EPR steering are analyzed and discussed in detail. Meanwhile, the additional PA can also expand the region of the one-way steering and strengthen the robustness of the entanglement and EPR steering against the thermal noise. The present scheme may provide effective resources for quantum information processing.
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 theory of phase control of coherence, entanglement and quantum steering is developed for an optomechanical system composed of a single mode cavity containing a partially transmitting dielectric membrane and driven by short laser pulses. The membrane divides the cavity into two mutually coupled optomechanical cavities resulting in an effective three-mode closed loop system, two field modes of the two cavities and a mechanical mode representing the oscillating membrane. The closed loop in the coupling creates interfering channels which depend on the relative phase of the coupling strengths of the field modes to the mechanical mode. Populations and correlations of the output modes are calculated analytically and show several interesting phase dependent effects such as reversible population transfer from one field mode to the other, creation of collective modes, and induced coherence without induced emission. We find that these effects result from perfect mutual coherence between the field modes which is preserved even if one of the modes is not populated. The inseparability criterion for the output modes is also investigated and we find that entanglement may occur only between the field modes and the mechanical mode. We show that depending on the phase, the field modes can act on the mechanical mode collectively or individually resulting, respectively, in tripartite or bipartite entanglement. In addition, we examine the phase sensitivity of quantum steering of the mechanical mode by the field modes. Deterministic phase transfer of the steering from bipartite to collective is predicted and optimum steering corresponding to perfect EPR state can be achieved. These different types of quantum steering can be distinguished experimentally by measuring the coincidence rate between two detectors adjusted to collect photons of the output cavity modes. In particular, we find that the minima of the interference pattern of the coincidence rate signal the bipartite steering, while the maxima signal the collective steering.
We propose a novel scheme to generate and manipulate bipartite and tripartite entanglement and Bell nonlocality in a closed-loop three-mode optomechanical system, where two optical modes are simultaneously coupled to a mechanical mode via typical optomechanical interactions and also coupled to each other through field transmission. This configuration gives rise to a phase-sensitive coupling, in which the relative phase directly controls the population distribution between two optical modes, enabling coherent redistribution of quantum correlations. By tuning this relative phase, we achieve deterministic switching of bipartite entanglement between two optical-mechanical pairs, as well as tunable genuine tripartite entanglement among three modes. Employing the displaced-parity measurement, we construct both the bipartite and tripartite Bell inequalities in phase space and observe maximal violations of approximately 2.322.322.32 and 333, respectively, which coincide exactly with the values achievable for ideal bipartite and tripartite Einstein-Podolsky-Rosen states. Counterintuitively, we find that the tripartite Bell nonlocality can persist even when the genuine tripartite entanglement is absent, providing deeper insight into the relationship between these two types of quantum correlations. Furthermore, we systematically analyze the effects of mechanical dissipation and thermal noise, identifying the parameter regions where Bell violation survives under realistic experimental conditions. Our results establish a comprehensive framework for generating, controlling, and verifying multipartite quantum correlations, paving the way towards phase-tunable quantum networks and noise-resilient tests of quantum foundations.
We investigate in detail the properties of the stationary quantum steering of two mechanical modes, where the two mechanical modes interact with two coupling cavity modes, and two four-tone driving lasers are used to pump the two cavity modes. By controlling the pumping lasers, the two cavity modes can act as two engineered reservoirs to cool the two mechanical modes to a squeezed state. When the damping rates of the two mechanical modes are different, numerical simulation results show that there are parameter regions where the state of the two mechanical modes only has one-way quantum steering, which is the most prominent feature of quantum steering from quantum entanglement.