Squeezing of Quantum Noise of Motion in a Micromechanical Resonator

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Squeezing of Quantum Noise of Motion in a Micromechanical Resonator

J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää

Phys. Rev. Lett. 115, 243601 – Published 7 December 2015

See Viewpoint: Quantum Squeezing of Micromechanical Motion

Abstract

A pair of conjugate observables, such as the quadrature amplitudes of harmonic motion, have fundamental fluctuations that are bound by the Heisenberg uncertainty relation. However, in a squeezed quantum state, fluctuations of a quantity can be reduced below the standard quantum limit, at the cost of increased fluctuations of the conjugate variable. Here we prepare a nearly macroscopic moving body, realized as a micromechanical resonator, in a squeezed quantum state. We obtain squeezing of one quadrature amplitude $1.1 \pm 0.4 dB$ below the standard quantum limit, thus achieving a long-standing goal of obtaining motional squeezing in a macroscopic object.

Received 15 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.243601

Physics Subject Headings (PhySH)

Mechanical effects of light on material media Optomechanics

Cooling & trapping

Atomic, Molecular & Optical

Viewpoint

Quantum Squeezing of Micromechanical Motion

Published 7 December 2015

The act of a quantum measurement reduces the uncertainty in the motion of a vibrating membrane below the fundamental quantum limit.

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Authors & Affiliations

J.-M. Pirkkalainen¹, E. Damskägg¹, M. Brandt¹, F. Massel², and M. A. Sillanpää^1,*

¹Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
²Department of Physics, Nanoscience Center, University of Jyväskylä, P.O. Box 35 (YFL), Jyväskylä FI-40014, Finland

^*Mika.Sillanpaa@aalto.fi

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Issue

Vol. 115, Iss. 24 — 11 December 2015

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Images

Figure 1
Setup of the microwave optomechanical squeezing experiment. (a) Idea of dissipative squeezing. The initial fluctuation amplitudes of the quadratures are marked with dashed lines, and the final ones with solid lines. The gray circles denote the quantum ground state. In sideband cooling (left), the initial fluctuations uniformly cool towards the ground state. In a suitably engineered system (right), cooling can be quadrature dependent, hence leading to one quadrature becoming squeezed. (b, c) Optical micrographs of the micromechanical device and of the cavity. There are two drum resonators connected to the cavity; however, only one of them (within the dashed rectangle) operates. The cavity is asymmetrically coupled to the input port (left) and to the output port (right) for transmission measurements. (d) The frequencies involved in the scheme. The cavity is pumped by two nonequal-amplitude microwave tones at the sideband frequencies $ω_{\pm} = ω_{c} \pm ω_{m}$ . (e) Example of the thermal motion signal measured at the refrigerator base temperature, with the coupling $G_{-} / 2 π ≃ 1.3 kHz$ .
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Figure 2
Cooling the Bogoliubov mode. In all the panels, black refers to regular sideband cooling (i.e., $G_{+} = 0$ ) used as calibration, whereas green refers to the BG mode experiment. (a) Thermalization in equilibrium. The left scale gives $n_{m}^{T}$ , as well as the area of both the sideband cooling peaks, and of the BG mode peaks (both in a.u.), whereas the right-hand side scale is $n_{BG}^{T}$ . (b–e) Output spectrum during sideband cooling (black) or under BG mode conditions (green). The solid lines are theoretical curves. The $n_{m}$ values refer to the $G_{+} = 0$ case.
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Figure 3
Squeezing inferred from the quadrature spectra. In all panels, blue and red refer to the cold and hot quadratures $X_{1}$ and $X_{2}$ , respectively. Black and green refer to the regular sideband cooling and the BG mode, respectively. The solid lines are theory curves. The pump powers are increased from (a) to (d) as marked in the panels, while the $G_{-} / G_{+} ≃ 1.43$ ratio is kept constant. The variances $Δ X_{1}^{2}$ are marked, and a value less than 1 implies squeezing below vacuum. The amplitudes of parametric modulation to the cavity are $ε_{c} / 2 π ≃ 35$ , 48, 49, 56 kHz from (a) to (d).
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Figure 4
Tomography and final results. (a) The quadrature data similar to Fig. 3, plotted at different LO phase values at $π / 10$ steps from 0 to $π / 2$ , from bottom to top. (b) The $X_{1}$ quadrature variance as a function of pump power. The blue region signifies squeezing below the quantum limit. The inset shows the quadrature variance from the data in (a).
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