Coherence and entanglement in a nano-mechanical cavity

Abstract

We examine the role of coherences on the creation of multi-mode entanglement in a nanomechanical cavity containing a finite size one-dimensional optical lattice. We show that, in general, the system is composed of three coupled modes and find that the presence of the first-order coherence between two modes of the system is equally effective in destroying entanglement between them. In the case of two modes coupled through an intermediate mode we show that there is no entanglement between the modes when both modes are coupled to the intermediate mode by the parametric interaction. We find that in order to effectively entangle the modes, one of the modes should be coupled to the intermediate mode by a parametric interaction but the other mode should be coupled by the linear-mixing interaction.