• Open Access

Appearance and Disappearance of Quantum Correlations in Measurement-Based Feedback Control of a Mechanical Oscillator

V. Sudhir, D. J. Wilson, R. Schilling, H. Schütz, S. A. Fedorov, A. H. Ghadimi, A. Nunnenkamp, and T. J. Kippenberg
Phys. Rev. X 7, 011001 – Published 6 January 2017

Abstract

Quantum correlations between imprecision and backaction are a hallmark of continuous linear measurements. Here, we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nanomechanical oscillator. Backaction imparted by the meter laser, due to radiation-pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e., feedback that suppresses measurement backaction, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to backaction arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits, of measurement-based feedback as a tool to manipulate quantum correlations.

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  • Received 5 May 2016

DOI:https://doi.org/10.1103/PhysRevX.7.011001

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)

Atomic, Molecular & Optical

Authors & Affiliations

V. Sudhir1, D. J. Wilson1, R. Schilling1, H. Schütz1, S. A. Fedorov1, A. H. Ghadimi1, A. Nunnenkamp2, and T. J. Kippenberg1,*

  • 1Institute for Condensed Matter Physics, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
  • 2Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom

  • *Corresponding author. tobias.kippenberg@epfl.ch

Popular Summary

Applying the conventional tools of control theory to steer quantum-mechanical systems poses a fundamental challenge because quantum mechanics dictates that the act of measurement itself randomly perturbs the system. However, if this measurement backaction is controlled, quantum feedback promises the ability to manipulate quantum-mechanical resources. Here, we perform an experiment in which feedback suppresses measurement backaction. We are able to manipulate subtle quantum correlations that are developed when a laser interacts with a mechanical oscillator.

Working at cryogenic temperatures (T=6K), we consider a glass nanostring whose position is measured via the frequency shift it induces on light circulating around a glass microdisk cavity. The vibrations of the nanostring, acting as a nonlinear optical medium, create correlations between the amplitude and phase of the light. We show that these correlations lead to either optical squeezing (i.e., a suppression of quantum fluctuations of the light) or sideband asymmetry (i.e., an imbalance in the power scattered by the nanostring). With an electro-optic feedback network, we demonstrate that the thermal and backaction fluctuations of the string are reduced, thereby enhancing the visibility of sideband asymmetry. We show that the ultimate source of noise in the feedback network—the quantum noise in the light used to perform the measurement—limits how well such a control strategy works.

Our observations demonstrate the possibilities and fundamental limits of measurement-based feedback control and pave the way for future applications of controlling systems in the quantum regime.

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Vol. 7, Iss. 1 — January - March 2017

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