Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1309.3121 · Physical Review Letters

Feedback-Enhanced Parametric Squeezing of Mechanical Motion

Andrea Vinante, P. Falferi

Published Nov 13, 2013• 64 citations
arXivHTMLPDF

Abstract

We present a single-quadrature feedback scheme able to overcome the conventional 3 dB limit on parametric squeezing. The method is experimentally demonstrated in a micromechanical system based on a cantilever with a magnetic tip. The cantilever is detected at low temperature by a SQUID susceptometer, while parametric pumping is obtained by modulating the magnetic field gradient at twice the cantilever frequency. A maximum squeezing of 11.5 dB and 11.3 dB is observed, respectively, in the response to a sinusoidal test signal and in the thermomechanical noise. So far, the maximum squeezing factor is limited only by the maximum achievable parametric modulation. The proposed technique might be used to squeeze one quadrature of a mechanical resonator below the quantum noise level, even without the need for a quantum limited detector.

DOI
10.1103/physrevlett.111.207203

Related papers

Strong thermomechanical noise squeezing stabilized by feedback

Aida Mashaal, Lucio Stefan, Andrea Ranfagni +5 more

Squeezing the quadrature noise of a harmonic oscillator enhances its sensitivity. Stabilization of the antisqueezed quadrature can overcome the 3 dB squeezing limit by parametric modulation. Here, we apply this method to soft-clamped membrane resonators, which hold promise for both classical and quantum sensing applications. We compare piezoelectric and capacitive parametric modulation and observe thermomechanical squeezing by up to 17 and 21 dB, respectively. Finally, we provide a full quantum theory of combining this approach with quantum-limited motion measurement. We conclude that quantum squeezing is feasible at moderate cryogenic temperatures and realistic device parameters.

arXiv:2403.02328•Physical Review Research•Mar 17, 2025•5 citations

Deep feedback-stabilized parametric squeezing in an opto-electromechanical system

Menno Poot, King Yan Fong, Hong X. Tang

Using a stabilizing quadrature-feedback scheme the thermal motion of an on-chip opto-electromechanical resonator is squeezed far beyond the limit of classical parametric squeezing. It is shown that feedback on the Y quadrature by itself can already squeeze the thermal motion of the resonator, but the maximum achievable squeezing level is limited by the imprecision noise. By combining the feedback and parametric pumping a record of 15.1 dB of classical noise squeezing is demonstrated. This not only largely exceeds the 3 dB limit for regular squeezing, but is also deeper than ever can be achieved with feedback cooling. The detector-resonator interaction is analyzed within the semi-classical framework and it is shown that using this feedback-stabilized parametric pumping technique true quantum-squeezed states can be prepared when the resonator starts off close to its ground state, and that the ultimate amount of squeezing depends on the minimum detuning that can be achieved.

New Journal of Physics•Apr 27, 2015•23 citations

Generation of mechanical squeezing via magnetic dipoles on cantilevers

Hyojun Seok, Lukas F. Buchmann, Swati Singh +2 more

A scheme to squeeze the center-of-mass motional quadratures of a quantum mechanical oscillator below its standard quantum limit is proposed and analyzed theoretically. It relies on the dipole-dipole coupling between a magnetic dipole mounted on the tip of a cantilever to equally oriented dipoles located on a mesoscopic tuning fork. We also investigate the influence of several sources of noise on the achievable squeezing, including classical noise in the driving fork and the clamping noise in the oscillator. A detection of the state of the cantilever based on state transfer to a light field is considered. We investigate possible limitations of that scheme.

arXiv:1110.4935•Physical Review A•Mar 20, 2012•13 citations

Strong Thermomechanical Squeezing via Weak Measurement

Alex Szorkovszky, George A. Brawley, Andrew C. Doherty +1 more

We experimentally surpass the 3 dB limit to steady-state parametric squeezing of a mechanical oscillator. The localization of an atomic force microscope cantilever, achieved by optimal estimation, is enhanced by up to 6.2 dB in one position quadrature when a detuned parametric drive is used. This squeezing is, in principle, limited only by the oscillator Q factor. Used on low temperature, high frequency oscillators, this technique provides a pathway to achieve robust quantum squeezing below the zero-point motion. Broadly, our results demonstrate that control systems engineering can overcome well established limits in applications of nonlinear processes. Conversely, by localizing the mechanical position to better than the measurement precision of our apparatus, they demonstrate the usefulness of mechanical nonlinearities in control applications.

arXiv:1210.1657•Physical Review Letters•May 2, 2013•116 citations

Quantum dynamics of a cantilever under combined additive and parametric noise: Implications for squeezing and sensitivity control

Wael M. Al-Sawai

We present a comprehensive quantum framework to analyze the dynamics of a nanomechanical cantilever subjected to combined additive and parametric noise. Using the Wigner phase-space representation, we derive and numerically solve c-number stochastic differential equations that accurately capture the evolution of the quantum state under realistic noise conditions. This operator-to-c-number mapping makes the role of quadrature noise sources explicit and provides a transparent route to evaluating squeezing. Our simulations reveal distinct dynamical regimes, demonstrating a critical trade-off determined by the parametric drive strength g0. In the stable regime, parametric modulation suppresses quantum fluctuations, achieving squeezing of about −1.7 dB relative to the vacuum noise limit. For stronger parametric driving, transient squeezing levels approaching −5 dB are observed, but these gains are accompanied by rapid growth of the conjugate quadrature and eventual instability. We further connect these dynamics to effective quality factor enhancement, clarifying the implications for nano-cantilever sensor performance. An explicit check of the Heisenberg uncertainty relation confirms that our simulations remain physically consistent. Together, these results establish a unified framework that links fundamental quantum noise dynamics with practical benchmarks for quantum-enhanced sensing.

Journal of Applied Physics•Oct 22, 2025•3 citations

Strong quantum squeezing of mechanical resonator via parametric amplification and coherent feedback

Xiang You, Zongyang Li, Yongmin Li

A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.

Physical Review A•Dec 8, 2017•21 citations
We present a single-quadrature feedback scheme able to overcome the conventional 3 dB limit on parametric squeezing. The method is experimentally demonstrated in a micromechanical system based on a cantilever with a magnetic tip. The cantilever is detected at low temperature by a SQUID susceptometer, while parametric pumping is obtained by modulating the magnetic field gradient at twice the cantilever frequency. A maximum squeezing of 11.5 dB and 11.3 dB is observed, respectively, in the response to a sinusoidal test signal and in the thermomechanical noise. So far, the maximum squeezing factor is limited only by the maximum achievable parametric modulation. The proposed technique might be used to squeeze one quadrature of a mechanical resonator below the quantum noise level, even without the need for a quantum limited detector.
Squeezing the quadrature noise of a harmonic oscillator enhances its sensitivity. Stabilization of the antisqueezed quadrature can overcome the 3 dB squeezing limit by parametric modulation. Here, we apply this method to soft-clamped membrane resonators, which hold promise for both classical and quantum sensing applications. We compare piezoelectric and capacitive parametric modulation and observe thermomechanical squeezing by up to 17 and 21 dB, respectively. Finally, we provide a full quantum theory of combining this approach with quantum-limited motion measurement. We conclude that quantum squeezing is feasible at moderate cryogenic temperatures and realistic device parameters.
Using a stabilizing quadrature-feedback scheme the thermal motion of an on-chip opto-electromechanical resonator is squeezed far beyond the limit of classical parametric squeezing. It is shown that feedback on the Y quadrature by itself can already squeeze the thermal motion of the resonator, but the maximum achievable squeezing level is limited by the imprecision noise. By combining the feedback and parametric pumping a record of 15.1 dB of classical noise squeezing is demonstrated. This not only largely exceeds the 3 dB limit for regular squeezing, but is also deeper than ever can be achieved with feedback cooling. The detector-resonator interaction is analyzed within the semi-classical framework and it is shown that using this feedback-stabilized parametric pumping technique true quantum-squeezed states can be prepared when the resonator starts off close to its ground state, and that the ultimate amount of squeezing depends on the minimum detuning that can be achieved.
A scheme to squeeze the center-of-mass motional quadratures of a quantum mechanical oscillator below its standard quantum limit is proposed and analyzed theoretically. It relies on the dipole-dipole coupling between a magnetic dipole mounted on the tip of a cantilever to equally oriented dipoles located on a mesoscopic tuning fork. We also investigate the influence of several sources of noise on the achievable squeezing, including classical noise in the driving fork and the clamping noise in the oscillator. A detection of the state of the cantilever based on state transfer to a light field is considered. We investigate possible limitations of that scheme.
We experimentally surpass the 3 dB limit to steady-state parametric squeezing of a mechanical oscillator. The localization of an atomic force microscope cantilever, achieved by optimal estimation, is enhanced by up to 6.2 dB in one position quadrature when a detuned parametric drive is used. This squeezing is, in principle, limited only by the oscillator Q factor. Used on low temperature, high frequency oscillators, this technique provides a pathway to achieve robust quantum squeezing below the zero-point motion. Broadly, our results demonstrate that control systems engineering can overcome well established limits in applications of nonlinear processes. Conversely, by localizing the mechanical position to better than the measurement precision of our apparatus, they demonstrate the usefulness of mechanical nonlinearities in control applications.
We present a comprehensive quantum framework to analyze the dynamics of a nanomechanical cantilever subjected to combined additive and parametric noise. Using the Wigner phase-space representation, we derive and numerically solve c-number stochastic differential equations that accurately capture the evolution of the quantum state under realistic noise conditions. This operator-to-c-number mapping makes the role of quadrature noise sources explicit and provides a transparent route to evaluating squeezing. Our simulations reveal distinct dynamical regimes, demonstrating a critical trade-off determined by the parametric drive strength g0. In the stable regime, parametric modulation suppresses quantum fluctuations, achieving squeezing of about −1.7 dB relative to the vacuum noise limit. For stronger parametric driving, transient squeezing levels approaching −5 dB are observed, but these gains are accompanied by rapid growth of the conjugate quadrature and eventual instability. We further connect these dynamics to effective quality factor enhancement, clarifying the implications for nano-cantilever sensor performance. An explicit check of the Heisenberg uncertainty relation confirms that our simulations remain physically consistent. Together, these results establish a unified framework that links fundamental quantum noise dynamics with practical benchmarks for quantum-enhanced sensing.
A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.