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arXiv:1406.7829 · Physical Review A

Bipartite and tripartite output entanglement in three-mode optomechanical systems

Ying-Dan Wang, Stefano Chesi, Aashish A. Clerk

Published Jan 5, 2015• 114 citations
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Abstract

We provide analytic insight into the generation of stationary itinerant photon entanglement in a three-mode optomechanical system. We identify the parameter regime of maximal entanglement and show that strong entanglement is possible even for weak many-photon optomechanical couplings. We also show that strong tripartite entanglement is generated between the photonic and phononic output fields; unlike the bipartite photon-photon entanglement, this tripartite entanglement diverges as one approaches the boundary of system stability.

DOI
10.1103/physreva.91.013807

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We provide analytic insight into the generation of stationary itinerant photon entanglement in a three-mode optomechanical system. We identify the parameter regime of maximal entanglement and show that strong entanglement is possible even for weak many-photon optomechanical couplings. We also show that strong tripartite entanglement is generated between the photonic and phononic output fields; unlike the bipartite photon-photon entanglement, this tripartite entanglement diverges as one approaches the boundary of system stability.
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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.
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In this paper, we study theoretically bipartite and tripartite continuous variable entanglement as well as normal-mode splitting in a single-atom cavity optomechanical system with intensity-dependent coupling. The system under consideration is formed by a Fabry-P\'erot cavity with a thin vibrating end mirror and a two-level atom in the Gaussian standing wave of the cavity mode. We first derive the general form of the Hamiltonian describing the tripartite intensity-dependent atom-field-mirror coupling due to the presence of the cavity mode structure. We then restrict our treatment to the first vibrational sideband of the mechanical resonator and derive a tripartite atom-field-mirror Hamiltonian. We show that when the optical cavity is intensely driven, one can generate bipartite entanglement between any pair in the tripartite system and that, due to entanglement sharing, atom-mirror entanglement is efficiently generated at the expense of optical-mechanical and optical-atom entanglement. We also find that in such a system, when the Lamb-Dicke parameter is large enough, one can simultaneously observe the normal mode splitting into three modes.
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