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Optics Express

Entanglement dynamics in double-cavity optomechanical systems

Zhi Xin Chen, Qing Lin, Bing He, Zhi Yang Lin

Published Jul 11, 2017• 34 citations
Publisher

Abstract

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.

DOI
10.1364/oe.25.017237

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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.
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.
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 give a theoretical study of a double-cavity system in which a mechanical resonator beam is coupled to two cavity modes on both sides through radiation pressures. The indirect coupling between the cavities via the resonator sets up a correlation in the optomechanical entanglements between the two cavities with the common resonator. This correlation initiates an entanglement transfer from the intracavity photon-phonon entanglements to an intercavity photon-photon entanglement. Using numerical solutions, we show two distinct regimes of the optomechanical system, in which the indirect entanglement either builds up and eventually saturates or undergoes a death-and-revival cycle, after a time lapse for initiating the cooperative motion of the left and right cavity modes.
A scheme for the generation of steady-state entanglement between optical and mechanical cavity modes in an optomechanical crystal nanobeam is proposed. Based on finite element simulation and the quantum Langevin equation, we explore the evolution of entanglement with optomechanical properties in various device configurations, and demonstrate the ability of optimal entanglement generation in both blue and red detuned optical pumps. The intrinsic relationship between optomechanical cooperativity and entanglement is further clarified for depicting a clear physical picture of optomechanical interaction. Our work expands the understanding of macroscopic quantum mechanics and is an important step for developing novel quantum optomechanical devices.
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.
In the field of optomechanics, one typically studies the interaction of a single mechanical resonator and a single optical cavity mode. In this thesis, we investigate collective quantum effects in optomechanical systems with two or more optical and mechanical modes. First, we study the generation and destruction of entanglement between two mechanical resonators effected by optical cavity fields. We also describe how the optomechanical interaction can be employed to mediate strong coherent coupling and entanglement between a micromechanical membrane and a single atom. Secondly, we show that a configuration with two optical and a single mechanical mode can lead to enhanced nonlinear interactions, which can be exploited for quantum non-demolition measurements of the phonon and photon numbers. Finally, we explore the quantum many-body dynamics of optomechanical arrays. In particular, we research into the transition from a disordered state due to quantum noise to a state with phasecoherent mechanical oscillations. As an intermediate step towards this study, we also investigate the nonlinear classical dynamics of single- and multi-mode optomechanical setups and compare theoretical predictions to experimental data.