• Open Access

Spectral Evidence of Squeezing of a Weakly Damped Driven Nanomechanical Mode

J. S. Huber, G. Rastelli, M. J. Seitner, J. Kölbl, W. Belzig, M. I. Dykman, and E. M. Weig
Phys. Rev. X 10, 021066 – Published 23 June 2020
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Abstract

Because of the broken time-translation symmetry, in periodically driven vibrational systems fluctuations of different vibration components have different intensities. Fluctuations of one of the components are often squeezed, whereas fluctuations of the other component, which is shifted in phase by π/2, are increased. Squeezing is a multifaceted phenomenon; it attracts much attention from the perspective of high-precision measurements. Here we demonstrate a new and hitherto unappreciated side of squeezing: its direct manifestation in the spectra of driven vibrational systems. With a weakly damped nanomechanical resonator, we study the spectrum of thermal fluctuations of a resonantly driven nonlinear mode. In the attained sideband-resolved regime, we show that the asymmetry of the spectrum directly characterizes the squeezing. This opens a way to deduce squeezing of thermal fluctuations in strongly underdamped resonators, for which a direct determination by a standard homodyne measurement is impeded by frequency fluctuations. The experimental and theoretical results are in excellent agreement. We further extend the theory to also describe the spectral manifestation of squeezing of quantum fluctuations.

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  • Received 19 May 2019
  • Revised 21 April 2020
  • Accepted 28 April 2020

DOI:https://doi.org/10.1103/PhysRevX.10.021066

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

J. S. Huber1, G. Rastelli1, M. J. Seitner1, J. Kölbl1,*, W. Belzig1, M. I. Dykman2,†, and E. M. Weig1,‡

  • 1Department of Physics, University of Konstanz, 78457 Konstanz, Germany
  • 2Michigan State University, East Lansing, Michigan 48824, USA

  • *Present address: Department of Physics, University of Basel, 4056 Basel, Switzerland.
  • dykmanm@msu.edu
  • eva.weig@uni-konstanz.de

Popular Summary

Fluctuations are omnipresent in nature, limiting the resolution of quantum as well as classical signals. The technique employed to increase the resolution of oscillating signals, laser radiation being an example, is squeezing fluctuations in one of the components of the signal and then using this component for applications. The price to pay is increased fluctuations in another, unused, component. Detecting and characterizing squeezed fluctuations is therefore of broad interest. In this article, we demonstrate a conceptually new and radically simple technique to probe squeezed fluctuations.

So far, squeezing has been conventionally quantified in phase-sensitive measurements tracking the fluctuations in phase space. By contrast, we characterize the squeezed state through a single spectral measurement. To this end, we employ a nanomechanical resonator of extremely high quality, operated in the classical regime. Its thermal fluctuations are squeezed by driving it into a nonlinear regime. The measured power spectrum exhibits two clearly resolved satellite peaks around the drive frequency. Theoretical analysis shows that the peaks’ heights encode the squeezing parameter, which can hence be directly extracted from the power spectrum.

Our results demonstrate that, in driven systems, squeezing can be revealed and characterized in a single-shot measurement of the power spectrum. The concept is generic and is not limited to the presented case of a classical resonator but fully applies in the quantum regime as well. It provides a new perspective on the squeezing of fluctuations and thus should further extend its important applications, including high-resolution sensing and signal processing.

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Vol. 10, Iss. 2 — April - June 2020

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