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arXiv:1110.4935 · Physical Review A

Generation of mechanical squeezing via magnetic dipoles on cantilevers

Hyojun Seok, Lukas F. Buchmann, Swati Singh, S. K. Steinke, Pierre Meystre

Published Mar 20, 2012• 13 citations
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Abstract

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.

DOI
10.1103/physreva.85.033822

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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 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.
We investigate the coupling of a nanomechanical oscillator in the quantum regime with molecular (electric) dipoles. We find theoretically that the cantilever can produce single-mode squeezing of the center-of-mass motion of an isolated trapped molecule and two-mode squeezing of the phonons of an array of molecules. This work opens up the possibility of manipulating dipolar crystals, which have been recently proposed as quantum memory, and more generally, is indicative of the promise of nanoscale cantilevers for the quantum detection and control of atomic and molecular systems.
Quantum squeezing in macroscopic oscillator systems plays a critical role in bridging quantum mechanics with classical-scale phenomena, enabling high-precision measurements and fundamental tests of quantum physics. In this work, we investigate the effect of squeezing on the phonon state in a hybrid macroscopic mechanical system consisting of an ensemble of Rydberg atoms coupled to two macroscopic mechanical oscillators. We notice that the dipole–dipole coupling between atoms and mechanical oscillators can be transferred to the indirectly coupled mechanical interaction, and the nonlinear effective Hamiltonian can be solved to generate a squeezed effect on the mechanical mode. We also discuss the noise effects induced by amplitude and phase fluctuations on the squeezed quadratures of the system.
We study the quantum measurement of a cantilever using a parametrically coupled electromagnetic cavity which is driven at the two sidebands corresponding to the mechanical motion. This scheme, originally due to Braginsky et al (Braginsky V, Vorontsov Y I and Thorne K P 1980 Science 209 547), allows a back-action free measurement of one quadrature of the cantilever's motion, and hence the possibility of generating a squeezed state. We present a complete quantum theory of this system, and derive simple conditions on when the quantum limit on the added noise can be surpassed. We also study the conditional dynamics of the measurement, and discuss how such a scheme (when coupled with feedback) can be used to generate and detect squeezed states of the oscillator. Our results are relevant to experiments in optomechanics, and to experiments in quantum electromechanics employing stripline resonators coupled to mechanical resonators.
We demonstrate optical squeezing below the shot-noise level generated through the interaction of an optical cavity field with two center-of-mass modes of a levitated nanoparticle, simultaneously cooled to occupation numbers well below unity. By analyzing the quadrature fluctuations of the cavity output through heterodyne detection, we resolve the full spectral covariance matrix of the optical field and map regions of sub-shot-noise squeezing as a function of detection phase and frequency. Operating in the resolved sideband and strong coupling regime where mechanical modes hybridize with the optical mode, we observe consistent squeezing in the band 70-95 kHz with a lowest variance of 0.98 (2%\%% below vacuum fluctuations). We thus demonstrate optical squeezing mediated by multiple mechanical oscillators in their quantum ground state, bridging mechanical quantum control with non-classical light and establishing levitated optomechanics as a platform for multimode quantum interactions.
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.