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arXiv:1107.4152 · Physical Review A

Entangling optical and microwave cavity modes by means of a nanomechanical resonator

Sh. Barzanjeh, David Vitali, Paolo Tombesi, Gerard J Milburn

Published Oct 31, 2011• 213 citations
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Abstract

We propose a scheme that is able to generate stationary continuous-variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a nanomechanical resonator. We show that when both cavities are intensely driven, one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and optomechanical entanglement.

DOI
10.1103/physreva.84.042342

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We propose a scheme that is able to generate stationary continuous-variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a nanomechanical resonator. We show that when both cavities are intensely driven, one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and optomechanical entanglement.
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The stationary continuous-variable entanglement between an optical cavity and a nanomechanical resonator beam is generated by their common interaction with a quantum dot. To deal with the quantum dot which is modeled as a two-level system, we do not use the low excitation limit approximation to bosonize the spin operators, but we keep them in the quantum Langevin equations. We linearize the quantum Langevin equations reasonably and investigate the stationary continuous-variable entanglement in detail, and finally we show that a high degree of entanglement can be achieved for experimentally feasible parameters.
We present a scheme for realizing phase-controlled entanglement in a microwave optomechanical system comprising two microwave cavities and two mechanical oscillators. Under specific driving conditions, we show that this optomechanical interface can be exploited to generate simultaneously the stationary cavity–cavity entanglement, mechanical–mechanical entanglement, and cavity–mechanical entanglement. Due to the closed loop interaction, we find that the entanglement can be controlled flexibly by tuning the phase difference between the optomechanical coupling strengths. The dependence of the entanglement on the amplitudes of the optomechanical coupling strengths is also explored in detail. Moreover, the bipartite entanglements are robust against temperature, and it is shown that the mechanical oscillators are cooled to the ground state in the parameter regimes for observing entanglement.
We propose a scheme for generation of the stationary continuous-variable entanglement and Einstein-Podolsky-Rosen (EPR) steering between an optical cavity mode and a nanomechanical resonator (NMR) mode. The cavity and the NMR are commonly coupled with two separated quantum dots (QDs), where the two QDs are driven simultaneously by a strong laser field. By adjusting the frequency of the strong laser field, the two QDs are nearly trapped on different dressed states, which is helpful to generate the entanglement between the cavity mode and the NMR mode. Due to the combined resonant interaction of the two QDs with the NMR-cavity subsystem, the photon and the phonon created and (or) annihilated are correlated. In this regime, the optimal entanglement of the two modes is obtained and the purity of the state of the NMR-cavity subsystem is near to 1. Furthermore, the coupling strength between the cavity and two QDs is different from the dot-NMR coupling strength, which leads to the different mean occupation numbers of the cavity and the NMR. In this case, one-way EPR steering is observed. In addition, through analyzing the purity, we find the conditions of the existence for the different types of EPR steering.