1112.0171 (Li-hui Sun et al.)

First-order coherence versus entanglement in a nano-mechanical cavity    [PDF]

Li-hui Sun, Gao-xiang Li, Zbigniew Ficek

The coherence and correlation properties of effective bosonic modes of a
nano-mechanical 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 a suitable tuning of the mechanical
mode to the polariton mode frequencies. In the two-mode case, we find that the
occurrence of entanglement between one of the polariton modes and the
mechanical mode is highly sensitive to the presence of the first-order
coherence between the modes. In particular, the creation of the first-order
coherence among the modes is achieved at the expense of entanglement between
the modes. 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 the 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 the first-order
coherence between two independent thermal modes. A 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.

View original: http://arxiv.org/abs/1112.0171