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Advanced Quantum Technologies

Generation of Strong Mechanical–Mechanical Entanglement by Pump Modulation

Cheng‐Hua Bai, Dongyang Wang, Shou Zhang, Shutian Liu, Hong‐Fu Wang

Published Apr 6, 2021• 18 citations

Abstract

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.

DOI: 10.1002/qute.202000149

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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.

Abstract Different from the general schemes of two‐mode mechanical squeezing, a dissipative scheme to generate strong and robust two‐mode mechanical squeezing via frequency modulation of cavity modes in a cavity optomechanical system consisting of a modulated two‐mode optical cavity and two mechanical oscillators is proposed. It is shown that the strong mechanical squeezing, which is highly robust against the thermal noise, can be engineered by means of cavity dissipation. Moreover, the squeezing mechanism is explored via analytical approach and it is found that the squeezing direction is controlled by modulation amplitude. The scheme provides an alternative pathway to generate strong mechanical–mechanical entanglement.

We consider a dissipative cavity optomechanical system which couples to an auxiliary cavity with a high-quality factor and is driven by an amplitude-modulated laser field. Due to the introduction of the auxiliary cavity, we find that the steady-state mechanical squeezing can be enhanced compared to the case without an auxiliary cavity and the so-called 3 dB limit can also be broken in the resolved-sideband regime. Moreover, the squeezing can also be achieved even in the unresolved-sideband regime. We study the optomechanical entanglement in the presented system. It is found that the enhanced entanglement can be obtained by introducing the auxiliary cavity, and the entanglement can also be generated in the unresolved-sideband regime for appropriate system parameters. Numerical results show that the presented schemes have strong robustness against the thermal noise acting on the mechanical mode.

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.

Abstract We present a double-cavity optomechanical system with a mechanical oscillator, which is jointly driven by an amplitude-modulated laser field and a weak squeezed vacuum field, aiming to explore quantum entanglement effects under the unresolved-sideband regime. Within our proposed scheme, it is possible not only to surpass the limit of maximum steady-state entanglement ln2 for bipartite entanglement, achieving strong entanglement, but also to significantly enhance tripartite entanglement and improve the system’s robustness against thermal noise. Meanwhile, the introduction of the squeezed vacuum field plays a crucial role in entanglement control, enabling not only a several-fold enhancement of entanglement but also continuous and precise manipulation of its strength within specific ranges. The suggested method demonstrates exceptional flexibility and adaptability under a wide range of operating conditions, offering a new pathway for theoretical and experimental investigations of strong bipartite entanglement and tripartite entanglement.

We propose a scheme to generate strong squeezing of a mechanical oscillator in an optomechanical system through Lyapunov control. Frequency modulation of the mechanical oscillator is designed via Lyapunov control. We show that the momentum variance of the mechanical oscillator decreases with time evolution in a weak coupling case. As a result, strong mechanical squeezing is realized quickly (beyond 3 dB). In addition, the proposal is immune to cavity decay. Moreover, we show that the obtained squeezing can be detected via an ancillary cavity mode with homodyne detection.