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arXiv:1308.5932 · Physical Review A

Fully quantum approach to optomechanical entanglement

Qing Lin, Bing He, Roohollah Ghobadi, Christoph Simon

Published Aug 11, 2014• 36 citations
arXivHTMLPDF

Abstract

The radiation-pressure-induced coupling between an optical cavity field and a mechanical oscillator can create entanglement between them. In previous works this entanglement was treated as that of the quantum fluctuations of the cavity and mechanical modes around their classical mean values. Here we provide a fully quantum approach to optomechanical entanglement, which goes beyond the approximation of classical mean motion plus quantum fluctuation and applies to arbitrary cavity drive. We illustrate the real-time evolution of optomechanical entanglement under drive of arbitrary detuning to show the existence of high, robust, and stable entanglement in the blue-detuned regime and highlight the quantum noise effects that can cause entanglement sudden death and revival.

DOI
10.1103/physreva.90.022309

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Probing quantum entanglement with macroscopic objects allows us to test quantum mechanics in new regimes. One way to realize such behavior is to couple a macroscopic mechanical oscillator to a continuous light field via radiation pressure. In view of this, the system that is discussed comprises an optomechanical cavity driven by a coherent optical field in the unresolved sideband regime where we assume Gaussian states and dynamics. We develop a framework to quantify the amount of entanglement in the system numerically. Different from previous work, we treat non-Markovian noise and take into account both the continuous optical field and the cavity mode. We apply our framework to the case of the Advanced Laser Interferometer Gravitational-Wave Observatory and discuss the parameter regimes where entanglement exists, even in the presence of quantum and classical noises.
We present a detailed study of a double-cavity optomechanical system, focusing on the dynamics of the entanglement between the cavity and mechanical modes, as well as the entanglement between two cavity modes. The discussions are based on a complete quantum approach without the standard practice of fluctuation expansion. The entanglement evolutions for various combinations of two different drives, such as those of the same blue detuning, of the same red detuning, and one red detuning and one blue detuning, are investigated. The relation of the entanglement and the rate of photon hopping between two cavities is also discussed.
We study theoretically the dynamics of multiple mechanical oscillators coupled to a single cavity field mode via linear or quadratic optomechanical interactions. We focus specifically on the strong-coupling regime where the cavity decays much faster than the mechanical modes, and the optomechanical coupling is comparable to or larger than the mechanical frequency, so that both the optical and mechanical systems operate in the deep quantum regime. Using the examples of one and two mechanical oscillators, we show that the system can classically exhibit bistability and bifurcations, and we explore how these manifest themselves in interference, entanglement, and correlation in the quantum theory, while revealing the impact of decoherence of the mechanical system due to cavity fluctuations and coherent driving.
We investigate the quantum entanglement in a double-cavity optomechanical system consisting of an optomechanical cavity and an auxiliary cavity, where the optomechanical cavity mode couples with the mechanical mode via radiation-pressure interaction, and simultaneously couples with the auxiliary cavity mode via nonreciprocal coupling. We study the entanglement between the mechanical oscillator and the cavity modes when the two cavities are reciprocally or nonreciprocally coupled. The logarithmic negativity E n ( 1 ) ( E n ( 2 ) ) is adopted to describe the entanglement degree between the mechanical mode and the optomechanical cavity mode (the auxiliary cavity mode). We find that both E n ( 1 ) and E n ( 2 ) have maximum values in the case of reciprocal coupling. By using nonreciprocal coupling, E n ( 1 ) and E n ( 2 ) can exceed those maximum values, and a wider detuning region where the entanglement exists can be obtained. Moreover, the entanglement robustness with respect to the environment temperature is also effectively enhanced.