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Annalen der Physik

Strong Squeezing of Duffing Oscillator in a Highly Dissipative Optomechanical Cavity System

Biao Xiong, Xun Li, Shi‐Lei Chao, Zhen Yang, Rui Peng, Ling Zhou

Published Mar 9, 2020• 20 citations
Publisher

Abstract

Abstract In the conventional scheme of generating strong mechanical squeezing by the joint effect between mechanical parametric amplification and sideband cooling, the resolved sideband condition is required so as to overcome the quantum backaction heating. In the unresolved sideband regime, to suppress the quantum backaction, a χ(2) nonlinear medium is introduced to the cavity. The result shows that the quantum backaction heating effect caused by unwanted counter‐rotating term can be completely removed. Hence, the strong mechanical squeezing can be obtained even for the system far from the resolved‐sideband regime.

DOI
10.1002/andp.201900596

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Abstract In the conventional scheme of generating strong mechanical squeezing by the joint effect between mechanical parametric amplification and sideband cooling, the resolved sideband condition is required so as to overcome the quantum backaction heating. In the unresolved sideband regime, to suppress the quantum backaction, a χ(2) nonlinear medium is introduced to the cavity. The result shows that the quantum backaction heating effect caused by unwanted counter‐rotating term can be completely removed. Hence, the strong mechanical squeezing can be obtained even for the system far from the resolved‐sideband regime.
ABSTRACT The quadrature‐squeezed state of a macroscopic mechanical oscillator plays a key role in enhancing the precision of quantum measurements. Here, we theoretically demonstrate that the steady‐state displacement squeezing of a membrane in a purely dissipative optomechanical system can be generated via the Duffing nonlinearity of the membrane when the cavity is driven by a red‐detuned laser. The mechanical squeezing results from a combination of the Duffing nonlinearity and the cooling of the membrane induced by the red‐detuned laser. We find that the maximum achievable squeezing is over 6 dB at a temperature of 10 mK in the resolved‐sideband regime. We show that a larger Duffing nonlinear strength or a smaller cavity decay rate causes the strong displacement squeezing exceeding 3 dB to emerge at a lower input laser power. And the strong mechanical squeezing beyond 3 dB can be achieved at a temperature of 10 mK even outside the resolved sideband regime. The generated mechanical squeezing is robust against the thermal noise of the membrane. Moreover, we show that the mechanical squeezing can be detected directly through homodyning detection of the cavity output field.
We propose an alternative experimentally feasible approach to achieve high-efficiency ground-state cooling of a mechanical oscillator in an optomechanical system under the deeply unresolved sideband condition with the assistance of both intracavity and extracavity squeezing. In the scheme, a degenerate optical parametric amplifier is placed inside the optical cavity, generating the intracavity squeezing; in addition, the optical cavity is driven by the extracavity squeezed light, namely the extracavity squeezing. The quantum interference effect generated by intracavity squeezing and extracavity squeezing can completely suppress the nonresonant Stokes heating process while greatly enhancing the anti-Stokes cooling process. Therefore, the joint-squeezing scheme is capable of cooling the mechanical oscillators to their quantum ground state in a regime far away from the resolved sideband condition. Compared with other traditional optomechanical cooling schemes, the single-photon cooling rate in this joint-squeezing scheme can be tremendously enlarged by nearly three orders of magnitude. At the same time, the coupling strength required to achieve ground-state cooling can be significantly reduced. This scheme is promising for cooling large-mass and low-frequency mechanical oscillators, which provides a prerequisite for preparing and manipulating nonclassical states in macroscopic quantum systems and lays a significant foundation for quantum manipulation.
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.
ABSTRACT Narrow linewidth and macroscopically accessible mechanical microstructures make mechanical squeezing a promising platform for ultra‐high‐sensitivity detection and fundamental investigations of classical‐to‐quantum quantum effects. The conventional approaches to utilizing optomechanical interactions for generating mechanical squeezing are restricted to the resolved‐sideband regime, limiting their practical applicability. In this paper, we propose a scheme to generate a highly squeezed mechanical state in both resolved‐ and unresolved‐sideband optomechanical systems assisted by nitrogen‐vacancy ensembles (NVEs). By coupling two NVEs to the optical cavity, the detrimental counter‐rotating terms that degrade mechanical squeezing are efficiently suppressed via destructive quantum interference originating from the NVEs‐cavity coupling channels. Numerical results reveal that mechanical squeezing exhibits non‐monotonic behavior with respect to both the optomechanical coupling ratio and the cavity‐spin coupling strength. Moreover, the achievable degree of mechanical squeezing degrades as the initial thermal‐phonon occupation of the mechanical resonator and the dissipation rates of the NVEs increase. This work offers an alternative feasible pathway toward strong mechanical squeezing beyond the 3‐dB limit and broadens the application scope of hybrid solid‐state‐optomechanical quantum systems.
Abstract A novel and efficient method is proposed for generating mechanical squeezing in a double‐cavity optomechanical system by introducing an optical parametric amplifier (OPA) with pump modulation (PM). The combined effects of periodic amplitude modulation of the driving laser and the OPA enable mechanical squeezing in both the resolved‐sideband and unresolved‐sideband regimes, with significantly enhanced squeezing observed in the resolved‐sideband regime. The individual contributions of the OPA and PM to mechanical squeezing is systematically investigated, with results indicating that PM plays a more dominant role. Additionally, the proposed scheme demonstrates excellent robustness against environmental thermal noise. These findings highlight the potential of this approach for advancing quantum precision measurements and exploring macroscopic quantum phenomena.