Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit

C. U. Lei, A. J. Weinstein, J. Suh, E. E. Wollman, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab

Phys. Rev. Lett. 117, 100801 – Published 30 August 2016

Abstract

We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction-evading measurement to directly quantify the squeezing, we observe $4.7 \pm 0.9 dB$ of squeezing below the zero-point level surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of squeezing obtained in the experiment.

Received 27 May 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.100801

Physics Subject Headings (PhySH)

Optomechanics Quantum correlations, foundations & formalism Quantum information processing with continuous variables Quantum metrology Squeezing of quantum noise Weak values & weak measurements

Micromechanical devices

Gravitation, Cosmology & AstrophysicsGeneral PhysicsAtomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

C. U. Lei¹, A. J. Weinstein¹, J. Suh², E. E. Wollman¹, A. Kronwald^3,4, F. Marquardt^3,4, A. A. Clerk⁵, and K. C. Schwab^1,*

¹Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
²Korea Research Institute of Standards and Science, Daejeon 305-340, Republic of Korea
³Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstrasse 7, D-91058 Erlangen, Germany
⁴Max Planck Institute for the Science of Light Günther-Scharowsky-Straße 1/Bau 24, D-91058 Erlangen, Germany
⁵Department of Physics, McGill University, Montreal, Quebec, H3A 2T8 Canada

^*schwab@caltech.edu

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Vol. 117, Iss. 10 — 2 September 2016

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Images

Figure 1
(a) Optical micrograph of the device. The gray region is aluminum; the blue region is silicon. The square at the center is a parallel plate capacitor which is coupled to a spiral inductor to form a microwave resonator. The top gate of the capacitor is a compliant membrane whose fundamental motion is being studied. (b) Schematic of the pumps (red and blue arrows) and probes (purple arrows) relative to the cavity resonance. The inset shows the schematic of the BAE probe sideband spectrum. (c) The squeezed quadrature variances (circles) and antisqueezed quadrature variances (squares) inferred from the output spectra. The red (blue) symbols represent the squeezed states achieved at $n_{p}^{tot} = 1.35 \times 1 0^{4}$ ( $n_{p}^{tot} = 1.85 \times 1 0^{5}$ ). The blue shaded region indicates sub-zero-point squeezing. The blue curves are the predictions from Eq. (4) with constant cavity and mechanical occupations at $n_{p}^{+} / n_{p}^{-} = 0$ . The orange curves are the predictions from Eq. (4) including cavity heating effect extracted from the experiment. (d) The cavity occupation $n_{c}^{th}$ extracted from the output spectra; the orange line is a linear fit of the pump ratio dependent heating. (e) The phonon bath heating rate $Γ_{m} n_{m}^{th}$ extracted from the output spectra. (f),(g) The output spectra normalized by the transmitted power of the red-detuned pump. The upper panel is the normalized noise spectrum of the mechanical sideband, the lower panel is the noise spectrum of the cavity resonance. (f) The normalized output spectra correspond to the solid red circle in Fig. 1. (g) The normalized output spectra correspond to the solid blue circle in Fig. 1.
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Figure 2
(a) Schematic of dissipative mechanical squeezing. The gray circle represents the initial thermal state in phase space. The engineered reservoir generates phase-dependent dissipation that relaxes the mechanics into a squeezed state, which is represented by the blue ellipse. The gray dashed circle represents the zero-point level. (b) Mechanical quadrature variance as a function of probe phase. The blue shaded region indicates sub-zero-point squeezing. The red (blue) circles are the quadrature variances of the weakly (strong) squeezed state as measured using the BAE technique. The solid curves are the quadrature variances inferred from the corresponding output spectra assuming no mechanical parametric drive. The dashed curves are the predictions of an optomechanical model including the mechanical parametric effect. The insets are the mechanical quadrature spectra of the strong squeezed state with phase $ϕ$ at $- 70 °$ (red), $- 50 °$ (green), $- 20 °$ (yellow), 0° (blue). The gray Lorentzian in the lower inset represents the spectrum with quadrature variance equal to half of the zero-point fluctuation (the 3 dB limit). (c) Mechanical quadrature linewidth as a function of probe phase. The red (blue) circles are the measured mechanical quadrature linewidths of the weakly (strong) squeezed state. The solid lines are the theoretical predictions from the ideal optomechanical model. The dashed curves are the fits with the optomechanical model including the mechanical parametric interaction.
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