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arXiv:1111.1869 · Physical Review A

Steady-state entanglement and normal-mode splitting in an atom-assisted optomechanical system with intensity-dependent coupling

Sh. Barzanjeh, M. H. Naderi, M. Soltanolkotabi

Published Dec 29, 2011• 38 citations
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Abstract

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.

DOI
10.1103/physreva.84.063850

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We theoretically investigate the entanglement properties in a hybrid system consisting of an optical cavity–array coupled to a mechanical resonator. We show that the steady state of the system presents bipartite continuous variable entanglement in an experimentally accessible parameter regime. The effects of the cavity–cavity coupling strength on the bipartite entanglements in the field–mirror subsystem and in the field–field subsystem are studied. We further find that the entanglement between the adjacent cavity and the movable mirror can be entirely transferred to the distant cavity and mirror by properly choosing the cavity detunings and the coupling strength in the two-cavity case. Surprisingly, such a remote macroscopic entanglement tends to be stable in the large coupling regime and persists for environment temperatures at above 25 K in the three-cavity case. Such optomechanical systems can be used for the realization of continuous variable quantum information interfaces and networks.
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ABSTRACT Hybrid optomechanical systems that combine a cavity field, mechanical motion, and intracavity atomic media offer a versatile platform for engineering normal‐mode structure and macroscopic quantum correlations. Most atom‐assisted systems rely on passive absorbing media, leaving the role of an inverted ensemble acting as a resonant intracavity gain element largely unexplored. Here, we investigate a driven optomechanical cavity containing a movable mirror and two resonant atomic ensembles, one prepared in its ground state and the other inverted, thereby realizing a combined absorptive–amplifying intracavity response. We find that the inverted ensemble acts as an active control resource: tuning the gain coupling reshapes the hybrid‐mode structure and produces resolved normal‐mode peaks in both the mechanical and optical spectra, while the absorbing ensemble independently sets the mode linewidths and relative peak amplitudes. The coupling parameters control and redistribute the bipartite and tripartite Gaussian entanglement shared among the optical, mechanical, and atomic modes, with the mechanical thermal occupation setting the robustness of the correlations. Formulated with experimentally feasible parameters of existing strong‐coupling optomechanics, the scheme provides a tunable route to controlling normal‐mode splitting and quantum correlations in hybrid quantum systems.