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Photonics Research

Strong mechanical squeezing in an optomechanical system based on Lyapunov control

Biao Xiong, Xun Li, Shi‐Lei Chao, Zhen Yang, Wen-Zhao Zhang, Weiping Zhang, Ling Zhou

Published Jan 23, 2020• 43 citations
Publisher

Abstract

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.

DOI
10.1364/prj.8.000151

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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.
We propose a proposal to achieve strong mechanical squeezing in an optomechanical system through the joint effect of a weak squeezed vacuum field and Duffing nonlinearity. The squeezing of the cavity field induced by the squeezed vacuum field is transferred to the mechanical oscillator, which has already been squeezed via Duffing nonlinearity. This joint effect significantly enhances the degree of mechanical squeezing, enabling it to exceed the 3 dB strong mechanical squeezing limit. Moreover, the resulting mechanical squeezing exhibits remarkable robustness against thermal noise. The joint effect proposed in this scheme can be directly observed through homodyne detection of the cavity output field. This novel approach opens up a new avenue for generating a strong mechanical squeezed state and provides a promising pathway for the applications of macroscopic quantum control in quantum sensing and quantum information processing.
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.
In this paper, we first consider the generation of mechanical squeezing in a dispersively or dissipatively coupled optomechanical system by continuously homodyning the output field of the optomechanical cavity. It is found that strong steady-state mechanical squeezing beyond the 3 dB limit can be achieved in both of the optomechanical systems. The properties of the squeezing are quite different for the two types of systems and the reasons for the differences are analyzed. We next consider the achievement of optomechanical steering in the dispersive or dissipative optomechanical system via continuously monitoring the position of the mechanical oscillator. It is revealed that the monitoring can lead the steady-state optomechanical entanglement to be enhanced considerably such that strong steerable correlations can be achieved between the mechanical oscillator and the cavity field. The effects of thermal phonons are studied and it is shown that the generated squeezing and steering are quite robust against the thermal fluctuations.
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.
The dissipative squeezing mechanism is an effective method to generate the strong squeezing, which is important in the precision metrology. Here, we propose a practical method to achieve arbitrary bosonic squeezing via introducing frequency modulation into the coupled harmonic resonator model. We analyze the effect of frequency modulation and give the analytical and numerical squeezing results, respectively. To measure the accurate dynamic squeezing in our proposal, we give a more general defination of the relative squeezing degree. Finally, the proposed method is extended to generate the strong mechanical squeezing (>3 dB) in a practical optomechanical system consisting of a graphene mechanical oscillator coupled to a superconducting microwave cavity. The result indicates that the strong mechanical squeezing can be effectively achieved even when the mechanical oscillator is not initially in its ground state. The proposed method expands the study on nonclassical state and does not need the bichromatic microwave driving technology.
Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.