arXiv:1112.0171 · Physical Review A

First-order coherence versus entanglement in a nanomechanical cavity

Lihui Sun, Gao‐xiang Li, Z. Ficek

Published Feb 21, 2012• 32 citations

Abstract

The coherence and correlation properties of effective bosonic modes of a nanomechanical cavity composed of an oscillating mirror and containing an optical lattice of regularly trapped atoms are studied. The system is modeled as a three-mode system: two orthogonal polariton modes, representing the coupled optical lattice and the cavity mode, and one mechanical mode, representing the oscillating mirror. We examine separately the cases of two-mode and three-mode interactions, which are distinguished by suitable tuning of the mechanical mode to the polariton mode frequencies. In the two-mode case, we find that the occurrence of entanglement in the system is highly sensitive to the presence of first-order coherence between the modes. In particular, the creation of the first-order coherence among the polariton and mechanical modes is achieved at the expense of entanglement between them. In the three-mode case, we show that no entanglement is created between the independent polariton modes if both modes are coupled to the mechanical mode by the parametric interaction. There is no entanglement between the polaritons even if the oscillating mirror is damped by a squeezed vacuum field. The interaction creates first-order coherence between the polaritons, and the degree of coherence can, in principle, be as large as unity. This demonstrates that the oscillating mirror can establish first-order coherence between two independent thermal modes. Further analysis shows that two independent thermal modes can be made entangled in the system only when one of the modes is coupled to the intermediate mode by a parametric interaction and the other is coupled by a linear-mixing interaction.

DOI: 10.1103/physreva.85.022327

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