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Scientific Reports

Dissipative generation of significant amount of mechanical entanglement in a coupled optomechanical system

Rongxin Chen, Chang-Geng Liao, Xiu‐Min Lin

Published Oct 30, 2017• 16 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-017-15032-1

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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 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 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.
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.
We theoretically propose a scheme to generate strong genuine tripartite entanglement among three mechanical oscillators in a multimode optomechanical system. In our setup, each mechanical oscillator is independently coupled to three optical modes supported by a single optical cavity, with each optical mode driven by a six-tone driving field. By appropriately tailoring the amplitudes of the driving fields, the mechanical steady state can be engineered into a three-mode squeezed vacuum state exhibiting significant genuine tripartite entanglement. We further investigate the effects of mechanical thermal reservoirs and demonstrate that the entanglement generated by our scheme persists at a significant level even at dilution refrigerator temperatures. Our results offer a feasible route toward the generation and utilization of multipartite entanglement in quantum optomechanical platforms, with potential applications in quantum devices.
We propose an approach to generate strong quantum entanglement by the controllable four-wave-mixing mechanism in a single-cavity, weak-coupling optomechanical system. The optomechanical system is driven by a strong two-tone pump field and a weak signal field, simultaneously. The two-tone pump field consists of a lower and an upper sideband, which couple with the optical cavity and mechanical resonator, and generate the beam-splitter and two-mode squeezing interactions under the rotating-wave approximation. This interaction mechanism modifies the effective susceptibility of the optomechanical cavity and optomechanically induces a four-wave-mixing process. Strong quantum entanglement can be generated between the signal and four-wave-mixing fields in realistic optomechanical systems. The generation scheme of the quantum entanglement is quite robust against thermal-mechanical noise, and significant entanglement can persist at room temperature in the weak-coupling regime.