Entanglement in a Tripartite Cavity-Optomechanical System

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Entanglement in a Tripartite Cavity-Optomechanical System Ni Liu · Junqi Li · J.-Q. Liang

Received: 8 August 2012 / Accepted: 6 October 2012 / Published online: 27 October 2012 © Springer Science+Business Media New York 2012

Abstract We propose a scheme to prepare entangled-states in the tripartite optomechanicalsystem consisting of a two-level atom in a high-finesse optical cavity with a oscillating mirror at one end. In particular, a Greenberger-Horne-Zeilinger like state can be generated. It is shown that the spontaneous emission rate γ of the atom, mean photon-number n and the coupling strength k play an important role in entanglement generation. Moreover the interesting phenomena of entanglement sudden-death (ESD) and sudden-birth (ESB) can be displayed in the system considered. Keywords Cavity optomechanical system · Movable mirror · Negativity · Master equation

1 Introduction Cavity optomechanical systems in quantum engineering have recently received considerable attention with the goal of measuring and controlling mechanical objects at the quantum limit, using interactions with light. In these systems, an optical cavity with one movable end mirror [1–6] or with a micromechanical membrane is concerned with mechanical effects caused by light through radiation pressure [7–12]. It has been shown that, in recent experiment [12], the collective density excitation of a Bose-Einstein condensate can serve as the mechanical oscillator coupled to the cavity field. This pioneer experiment provides us an access to investigate the strong coupling regime of cavity optomechanics, in which the nonclassical state of the movable mirror and the mechanical Shrödinger cat state can be prepared. Recently, radiation pressure induced cavity cooling of a radio-frequency (57.8-MHz) micromechanical oscillator, which might provide a route to achieve ground-state cooling of a micromechanical oscillator using dynamical backaction, has been reported [11] and the existence of electromagnetically induced transparent (EIT) in optomechanical system was demonstrated theoretically in [4]. N. Liu () · J. Li · J.-Q. Liang Institute of Theoretical Physics, Shanxi University, Taiyuan, Shanxi 030006, China e-mail: [email protected]

Int J Theor Phys (2013) 52:706–715

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On the other hand, ultracold atoms in cavity coupled to mechanical oscillators represents a novel type of hybrid mechanical systems, which could enable readout, cooling, and coherent manipulation of mechanical systems via the well-developed tools of atomic physics [13–16]. In [17] a hybrid, strongly quantum-correlated system, formed of an atomic ensemble surrounded by a high-finesse optical cavity with a vibrating mirror, was prior proposed. Thereinto, the tripartite and bipartite continuous variable entanglement of the system’s steady state in experimentally accessible parameter regimes were given [17]. Moreover, using the same model as given by [17], [6] found that the collective excitations of the atoms are dressed by the cavity field and transformed into polaritons, causing