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arXiv:1712.06755 · Physical Review A

Macroscopic quantum entanglement in modulated optomechanics

Mei Wang, Xin‐You Lü, Ying-Dan Wang, J. Q. You, Ying Wu

Published Nov 7, 2016• 108 citations
arXivHTMLPDF

Abstract

Quantum entanglement in mechanical systems is not only a key signature of macroscopic quantum effects but has wide applications in quantum technologies. Here we propose an effective approach for creating strong steady-state entanglement between two directly coupled mechanical oscillators (or a mechanical oscillator and a microwave resonator) in a modulated optomechanical system. The entanglement is achieved by combining the processes of a cavity cooling and the two-mode parametric interaction, which can surpass the bound on the maximal stationary entanglement from the two-mode parametric interaction. In principle, our proposal allows one to cool the system from an initial thermal state to an entangled state with high purity by a monochromatic driving laser. Also, the obtained entangled state can be used to implement the continuous-variable teleportation with high fidelity. Moreover, our proposal is robust against the thermal fluctuations of the mechanical modes under the condition of strong optical pumping.

DOI
10.1103/physreva.94.053807

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Quantum entanglement in mechanical systems is not only a key signature of macroscopic quantum effects but has wide applications in quantum technologies. Here we propose an effective approach for creating strong steady-state entanglement between two directly coupled mechanical oscillators (or a mechanical oscillator and a microwave resonator) in a modulated optomechanical system. The entanglement is achieved by combining the processes of a cavity cooling and the two-mode parametric interaction, which can surpass the bound on the maximal stationary entanglement from the two-mode parametric interaction. In principle, our proposal allows one to cool the system from an initial thermal state to an entangled state with high purity by a monochromatic driving laser. Also, the obtained entangled state can be used to implement the continuous-variable teleportation with high fidelity. Moreover, our proposal is robust against the thermal fluctuations of the mechanical modes under the condition of strong optical pumping.
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 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.
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 study the entanglement dynamics of two coupled mechanical oscillators, within a modulated optomechanical system. We find that, depending on the strength of the mechanical coupling, one could observe either a stationary or a dynamical behavior of the mechanical entanglement, which is extremely robust against the oscillator temperature. Moreover, we have shown that this entanglement dynamics is strongly related to the stability of the normal modes. Taking mechanical damping effects into account, an analytical expression corresponding to the critical mechanical coupling strength, where the transition from stationary to dynamical entanglement occurs, is also reported. The proposed scheme is analyzed with experimentally realistic parameters, making it a promising means to realize macroscopic quantum entanglement within current state-of-the-art experimental setups.
Abstract The implementation of strong quantum entanglement between two macroscopic mechanical oscillators is a longstanding pursued goal in fundamental research or applied science. Here, an effective scheme is proposed to generate strong mechanical–mechanical entanglement in a double‐oscillator optomechanical system via only introducing the sole amplitude‐modulated pattern into the pump field instead without the requirement of any extra techniques. Based on two mechanical oscillators with identical or different frequencies, a specific kind of amplitude‐modulated pump field is respectively designed, which successfully manipulates the mechanical oscillators into the highly entangled two‐mode squeezed state. The maximum value of the logarithmic negativity that quantifies the generated entanglement reaches about 9 ebits in the appropriate parameter regime, which greatly surpasses the bound 1 ebits on the maximal stationary entanglement from the two‐mode parametric interaction. Moreover, the obtained entanglement can be detected via resorting to an ancillary cavity mode with homodyne detection technique. Compared with the previous congeneric schemes, this scheme involves fewer modulation techniques and may provide a new perspective to effectively manipulate the mechanical quantum states in optomechanical systems utilizing the time‐dependent modulation.
We present a scheme for realizing phase-controlled entanglement in a microwave optomechanical system comprising two microwave cavities and two mechanical oscillators. Under specific driving conditions, we show that this optomechanical interface can be exploited to generate simultaneously the stationary cavity–cavity entanglement, mechanical–mechanical entanglement, and cavity–mechanical entanglement. Due to the closed loop interaction, we find that the entanglement can be controlled flexibly by tuning the phase difference between the optomechanical coupling strengths. The dependence of the entanglement on the amplitudes of the optomechanical coupling strengths is also explored in detail. Moreover, the bipartite entanglements are robust against temperature, and it is shown that the mechanical oscillators are cooled to the ground state in the parameter regimes for observing entanglement.