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Physical Review A

Dissipation-induced optomechanical entanglement with the assistance of Coulomb interaction

Rongxin Chen, Li-Tuo Shen, Shi‐Biao Zheng

Published Feb 20, 2015• 63 citations
Publisher

Abstract

We consider a hybrid three-mode optomechanical system where one mechanical oscillator couples to a second one via a Coulomb force and to a cavity mode via an optomechanical interaction. It is shown that stationary cavity-mechanical entanglement can be achieved by effectively cooling a Bogoliubov mode via the intermediate mode acting as an engineered reservoir. The entanglement can be maximized by carefully balancing the two confronting effects of the ratio of the effective couplings. Moreover, we analyze in detail the effects of the nonresonant terms. It is found that while the stability zone of the system shrinks in the parameter plane for large cooperativity, the maximal entanglement is not significantly reduced by the nonresonant terms. We numerically optimize the ratio in the stable region and obtain remarkably strong entanglement in the large cooperativity regime.

DOI
10.1103/physreva.91.022326

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We consider a hybrid three-mode optomechanical system where one mechanical oscillator couples to a second one via a Coulomb force and to a cavity mode via an optomechanical interaction. It is shown that stationary cavity-mechanical entanglement can be achieved by effectively cooling a Bogoliubov mode via the intermediate mode acting as an engineered reservoir. The entanglement can be maximized by carefully balancing the two confronting effects of the ratio of the effective couplings. Moreover, we analyze in detail the effects of the nonresonant terms. It is found that while the stability zone of the system shrinks in the parameter plane for large cooperativity, the maximal entanglement is not significantly reduced by the nonresonant terms. We numerically optimize the ratio in the stable region and obtain remarkably strong entanglement in the large cooperativity regime.
We propose an approach for generating steady-state mechanical entanglement in a coupled optomechanical system. By applying four-tone driving lasers with weighted amplitudes and specific frequencies, we obtain an effective Hamiltonian that couples the delocalized Bogoliubov modes of the two mechanical oscillators to the cavity modes via beam-splitter-like interactions. When the mechanical decay rate is small, the Bogoliubov modes can be effectively cooled by the dissipative dynamics of the cavity modes, generating steady-state entanglement of the mechanical modes. The mechanical entanglement obtained in the stationary regime is strongly dependent on the values of the ratio of the effective optomechanical coupling strengths. Numerical simulation with the full linearized Hamiltonian shows that significant amount of mechanical entanglement can indeed be obtained by balancing the opposing effects of varying the ratio and by carefully avoiding the system parameters that may lead to amplified oscillations of the mechanical mean values detrimental to the entanglement generation.
We propose an effective approach for generating highly pure and strong cavity-mechanical entanglement (or optical-microwave entanglement) in a hybrid modulated three-mode optomechanical system. By applying two-tone driving to the cavity and modulating the coupling strength between two mechanical oscillators (or between a mechanical oscillator and a transmission line resonator), we obtain an effective Hamiltonian where an intermediate mechanical mode acting as an engineered reservoir cools the Bogoliubov modes of two target system modes via beam-splitter-like interactions. In this way, the two target modes are driven to two-mode squeezed states in the stationary limit. In particular, we discuss the effects of cavity-driving detuning on the entanglement and the purity. It is found that the cavity-driving detuning plays a critical role in the goal of acquiring highly pure and strongly entangled steady states.
We show how strong steady-state entanglement can be achieved in a three-mode optomechanical system (or other parametrically coupled bosonic system) by effectively laser cooling a delocalized Bogoliubov mode. This approach allows one to surpass the bound on the maximum stationary intracavity entanglement possible with a coherent two-mode squeezing interaction. In particular, we find that optimizing the relative ratio of optomechanical couplings, rather than simply increasing their magnitudes, is essential for achieving strong entanglement. Unlike typical dissipative entanglement schemes, our results cannot be described by treating the effects of the entangling reservoir via a Linblad master equation.
We study reservoir-engineered entanglement for a cascaded bosonic system consisting of three modes, where the adjacent pairs couple to each other via both the beam-splitter interaction and the coherent parametric interaction with the interaction strengths being tunable. We focus on an optomechanical realization of the model by combining a nondegenerate parametric amplifier and an auxiliary cavity. A great steady-state cavity-mechanical entanglement can be achieved by optimizing the ratio of the interaction strengths, where the optomechanical cavity enacts the cold reservoir, simultaneously laser cooling the pair of hybrid modes delocalized over the auxiliary cavity and the mechanical oscillator. In comparison with the case of cooling a single delocalized mode, the dual-mode cooling approach allows one to obtain a greater amount of entanglement with higher cooling efficiencies and to explore strong entanglement in much broader parameter regions, where the rotating-wave approximation fails for the single-mode cooling case. Moreover, we show that the steady-state cavity-mechanical entanglement is robust to the mechanical thermal noise of the high temperature. The improved reservoir engineering approach can potentially be generalized to other bosonic systems with asymmetric beam-splitter and parametric interactions.
We discuss the generation of strong stationary mechanical squeezing and entanglement in the modulated two-and three-mode optomechanics. Following the reservoir engineering scheme, the beam-splitter and parametric optomechanical interactions can be simultaneously achieved through appropriately choosing the modulation frequency on mechanical motion, which is essential to strong squeezing and entanglement. In the two-mode modulated optomechanics, squeezing is tunable by the relative ratio of parametric and beam-splitter couplings, and also robust to thermal noise due to the simultaneously optically induced cooling process. In the three-mode modulated optomechanics, strong EPR-type entanglement is also attainable, which can surpass the 3dB limit of nondegenerate parametric interaction. However, the ideal entanglement is impossible since only one of mechanical Bogoliubov modes is cooled by the cavity mode, which also makes the entanglement fragile to the mechanical noise.
The generation and manipulation of highly pure and strongly entangled steady state in a quantum system are vital tasks in the standard continuous-variable teleportation protocol. Especially, the manipulation implemented in integrated devices is even more crucial in practical quantum information applications. Here we propose an effective approach for creating steady-state entanglement between two microwave fields in a four-mode hybrid cavity optomechanical system. The entanglement can be achieved by combining the processes of three beam-splitter interactions and two parametric-amplifier interactions. Due to the dissipation-driven and cavity cooling processes, the entanglement obtained can go far beyond the entanglement limit based on coherent parametric coupling. Moreover, our proposal allows the engineered bath to cool both Bogoliubov modes almost simultaneously. In this way, a highly pure and strongly entangled steady state of two microwave modes is obtained. Our finding may be significant for using the hybrid opto-electro-mechanical system fabricated on chips in various quantum tasks, where the strong and pure entanglement is an important resource.