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arXiv:1401.1384 · Physical Review A

Entangling two macroscopic mechanical mirrors in a two-cavity optomechanical system

Jie‐Qiao Liao, WU Qin-Qin, Franco Nori

Published Jan 10, 2014• 172 citations
arXivHTMLPDF

Abstract

We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime.

DOI
10.1103/physreva.89.014302

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We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime.
Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct mechanical superposition states in a two-mode optomechanical system. Photon hopping between the two cavity modes is modulated sinusoidally. The modulated photon tunneling enables an ultrastrong radiation-pressure force acting on the mechanical resonator, and hence significantly increases the mechanical displacement induced by a single photon. We study systematically the generation of the Yurke-Stoler-like states in the presence of system dissipations. We also discuss the experimental implementation of this scheme.
We present a proposal to generate robust tripartite optomechanical entanglement with a single-cavity optomechanical system driven by a single input laser field. The produced stationary tripartite entanglement among two longitudinal cavity modes and a mirror oscillation mode via radiation pressure force exhibits robustness to the variation of the environment temperature when the cavity free spectral range is close to the mechanical oscillation frequency. The present optomechanical system can serve as an alternative intermediary for quantum-state exchange between two microwave (or optical) fields as well as between photons and the macroscopic mechanical oscillator, and may be potentially useful for quantum information processing and quantum networks.
We report an efficient mechanism to generate mechanical entanglement in a two-cascaded cavity optomechanical system with optical parametric amplifiers (OPAs) inside the two coupled cavities. We use the especially tuned OPAs to squeeze the hybrid mode composed of two mechanical modes, leading to strong macroscopic entanglement between the two movable mirrors. The squeezing parameter as well as the effective mechanical damping are both modulated by the OPA gains. The optimal degree of mechanical entanglement therefore depends on the balanced process between coherent hybrid mode squeezing and dissipation engineering. The mechanical entanglement is robust to strong cavity decay, going beyond simply resolved sideband regime, and is resistant to reasonable high thermal noise. The scheme provides an alternative way for generating strong macroscopic entanglement in cascaded optomechanical systems.
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Quantum entanglement and quantum superposition are fundamental properties of quantum mechanics, which underline quantum information and quantum computation. Preparing quantum states in the macroscopic level is both conceptually interesting for extending quantum physics to a broader sense and fundamentally important for testing the validity of quantum mechanics. In this dissertation, schemes of preparing macroscopic entanglement and macroscopic superposition states in cavity optomechanics are studied using the unitary evolution method in the nonlinear regime or Lyapunov equation in the linearized regime. Quantum entanglement and quantum superposition states can be realized using experimentally feasible parameters with the proposals in this dissertation.\nFirstly, a scheme of entangling two movable end mirrors in a Fabry-Perot cavity that are coupled to a common single photon superposition state is studied. It is shown that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.\nSecondly, a scheme of entangling two movable end mirrors, that are coupled to two-mode entangled fields generated from a correlated-emission laser is investigated. By tuning the input driving laser frequencies at the Stokes sidebands of the cavity, the radiation-pressure coupling can be linearized as an effective beam-splitter-like interaction. Hence entanglement can be transferred from the two-mode fields to the two mechanical mirrors. Macroscopic entanglement between macroscopic mirrors persists at temperature ~ 1K.\nThirdly, a scheme of creating macroscopic quantum superpositions of a mechanical mirror via periodically flipping a photonic qubit is proposed. Quantum superposition states of a mechanical mirror can be obtained via the nonlinear radiation coupling with a single-photon superposition state. However, the difference between two superposed mechanical states is very small due to the weak single-photon coupling rate available in experiment. By periodically flipping the photonic qubit state, the difference can be magnified. It is shown in detail that this scheme is experimentally feasible under current technology.
We propose a scheme to generate the macroscopic entangled Schrödinger cat state of two mechanical resonators in a hybrid optomechanical system by introducing modulated photon-hopping interaction between two cavities. We show that the obtained entangled cat state possesses large average phonon number and the two base vectors of which are nearly orthogonal, thus causing the high degree of entanglement. To justify the robust of the scheme, the dissipation of the system and the noise from the environment are considered. It shows that the high fidelity between the obtained state and the target state can be achieved in the presence of dissipation and thermal noise within our parameter regions, which suggests that our state-generation proposal is feasible.