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Advanced Quantum Technologies

Squeezing of a Mechanical Oscillator in a Dissipative Optomechanical System with Duffing Nonlinearity

Sumei Huang, Li Deng, Aixi Chen

Published Mar 1, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1002/qute.202500713

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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 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 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.
We propose a scheme for producing the phase squeezing of the output light in a dissipative optomechanical coupling system. This is achieved by applying a degenerate parametric drive on the mechanical oscillator. We also show that this scheme is capable of generating the stationary entanglement between an optical cavity field and a macroscopic mechanical oscillator. The effects of the strength of the mechanical parametric drive, the power of the input laser, the temperature of the environment on the output phase squeezing, and the optomechanical entanglement are investigated. For a temperature of 20 mK, we find that up to 9 dB of the output phase squeezing and the large optomechanical entanglement can be achieved.
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 theoretically demonstrate that an especially tuned degenerate optical parametric amplifier (OPA) inside a cavity can lead to the momentum squeezing of a moving membrane in a dissipative optomechanical system. The momentum squeezing of the membrane depends on the parametric gain and the parametric phase of the OPA, the power of the external laser driving the cavity, and the temperature of the environment. The best achievable momentum squeezing is about 2.53 dB, which is limited by the OPA. Moreover, we show that the momentum squeezing of the membrane can be detected by directly measuring the cavity output field. In addition, we find that the mechanical squeezing can be enhanced to about 10.36 dB under the joint effect of the OPA and an input broadband squeezed vacuum field.
In this paper, we consider the generation of mechanical squeezed states and single-phonon Fock states, respectively, by homodyne detection and photon subtraction in a dissipative or dispersive optomechanical system under the situation that the cavity linewidth ${\ensuremath{\kappa}}_{c}$ is much larger than the mechanical frequency ${\ensuremath{\omega}}_{m}$. We at first show that strong mechanical squeezing beyond the 3-dB limit can be achieved by homodyning the filtered cavity output field in a purely dispersive or purely dissipative optomechanical system for ${\ensuremath{\kappa}}_{c}\ensuremath{\gg}{\ensuremath{\omega}}_{m}$, while the combination of the two kinds of coupling can also effectively enhance the mechanical squeezing. We next show that in these optomechanical systems, mechanical single-phonon states with high fidelity can be generated via photon subtraction on the filtered cavity output field in the regimes of weak optomechanical entanglement and ${\ensuremath{\kappa}}_{c}\ensuremath{\gg}{\ensuremath{\omega}}_{m}$. It is found that the single-phonon Fock state via purely dissipative optomechanical coupling is attainable in the blue-detuned regime, whereas it is present in the red-detuned regime by purely dispersive optomechanical coupling. In addition, the effects of thermal fluctuations on the mechanical squeezing and the negativity of the Wigner function of the mechanical single-phonon states are also studied. It is shown that the Gaussian squeezing is much more robust against decohering thermal fluctuations than the non-Gaussian nonclassicality.