Revealing Hidden Quantum Correlations in an Electromechanical Measurement

C. F. Ockeloen-Korppi, E. Damskägg, G. S. Paraoanu, F. Massel, and M. A. Sillanpää

Phys. Rev. Lett. 121, 243601 – Published 14 December 2018

Abstract

Under a strong quantum measurement, the motion of an oscillator is disturbed by the measurement backaction, as required by the Heisenberg uncertainty principle. When a mechanical oscillator is continuously monitored via an electromagnetic cavity, as in a cavity optomechanical measurement, the backaction is manifest by the shot noise of incoming photons that becomes imprinted onto the motion of the oscillator. Following the photons leaving the cavity, the correlations appear as squeezing of quantum noise in the emitted field. Here we observe such “ponderomotive” squeezing in the microwave domain using an electromechanical device made out of a superconducting resonator and a drumhead mechanical oscillator. Under a strong measurement, the emitted field develops complex-valued quantum correlations, which in general are not completely accessible by standard homodyne measurements. We recover these hidden correlations, using a phase-sensitive measurement scheme employing two local oscillators. The utilization of hidden correlations presents a step forward in the detection of weak forces, as it allows us to fully utilize the quantum noise reduction under the conditions of strong force sensitivity.

Received 29 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.243601

Physics Subject Headings (PhySH)

Optomechanics Quantum measurements Squeezing of quantum noise

General Physics

Authors & Affiliations

C. F. Ockeloen-Korppi¹, E. Damskägg¹, G. S. Paraoanu¹, F. Massel², and M. A. Sillanpää^1,*

¹Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 AALTO, Finland
²Department of Physics and Nanoscience Center, University of Jyväskylä, P.O. Box 35 (YFL), FI-40014 University of Jyväskylä, Finland

^*mika.sillanpaa@aalto.fi

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 121, Iss. 24 — 14 December 2018

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Detection of squeezing correlations. The signal is injected into a mixer that multiplies it with LO waveforms. (a) In the case of standard homodyne detection, the LO is a single sinusoid with frequency $ω_{0}$ and phase $θ$ , coinciding with the frequency of the pump used to create correlations in the resonator. This essentially sums up negative and positive frequencies $\pm ω$ with respect to $ω_{0}$ . (b) Bichromatic LO with two phases can detect complex quantum correlations that may be invisible in homodyne detection. (c) Sketch of the electromechanical experiment, where ponderomotive squeezing of microwaves is created in a sample comprising a micromechanical oscillator parametrically coupled to a microwave resonator.
Reuse & Permissions
Figure 2
Ponderomotive squeezing of microwaves. (a) Homodyne spectrum, Eq. (5), as referred to the input of the cryogenic amplifier. The phases of the sinusoidal local oscillator are written in the panels. (b) Detailed views of the phases around $π / 2$ that display the quantum squeezing. The thin black lines are theoretical fits. The experimental parameters are $G / 2 π ≃ 728 kHz$ , $n_{m}^{T} ≃ 517$ , $n_{c}^{T} ≃ 0.07$ , $Δ / 2 π ≃ - 620 kHz$ .
Reuse & Permissions
Figure 3
Squeezing eigenvalues. (a) Homodyne noise spectrum shown as a color map. We observe quantum squeezing (value below 0 dB) inside the white contours. (b) Maximum (red) and minimum (blue) envelope of the spectrum with respect to the local oscillator phase $θ$ from the data in (a). The black lines are theory predictions, and the red theory line is the lower eigenvalue of the correlation matrix.
Reuse & Permissions
Figure 4
Complex squeezing spectrum. The detuning of the two LOs are varied between $(ω_{s} - ω_{m}) / 2 π = [- 31, - 15, - 4.5, 1] kHz$ from top to bottom (magenta, green, blue, red). The phase is optimized in order to minimize the noise for each detuning value. Black lines are theoretical fits.
Reuse & Permissions
Figure 5
Mapping the correlation matrix. The solid symbols, with $2 σ$ error bars, denote the minimum of the complex squeezing spectrum at zero frequency as a function of the bi-LO detuning. This is compared to the theoretical prediction for the smallest eigenvalues of the correlation matrix (red line). The hidden quantum correlations are given by the data points falling below the lower homodyne envelope (blue trace) and the corresponding theory line (black), around zero detuning. The frequency axis for the homodyne data is given by the upper labels.
Reuse & Permissions

Physical Review Letters