Stationary entangled radiation from micromechanical motion

Abstract

Mechanical systems facilitate the development of a hybrid quantum technology comprising electrical, optical, atomic and acoustic degrees of freedom1, and entanglement is essential to realize quantum-enabled devices. Continuous-variable entangled fields—known as Einstein–Podolsky–Rosen (EPR) states—are spatially separated two-mode squeezed states that can be used for quantum teleportation and quantum communication2. In the optical domain, EPR states are typically generated using nondegenerate optical amplifiers3, and at microwave frequencies Josephson circuits can serve as a nonlinear medium4,5,6. An outstanding goal is to deterministically generate and distribute entangled states with a mechanical oscillator, which requires a carefully arranged balance between excitation, cooling and dissipation in an ultralow noise environment. Here we observe stationary emission of path-entangled microwave radiation from a parametrically driven 30-micrometre-long silicon nanostring oscillator, squeezing the joint field operators of two thermal modes by 3.40 decibels below the vacuum level. The motion of this micromechanical system correlates up to 50 photons per second per hertz, giving rise to a quantum discord that is robust with respect to microwave noise7. Such generalized quantum correlations of separable states are important for quantum-enhanced detection8 and provide direct evidence of the non-classical nature of the mechanical oscillator without directly measuring its state9. This noninvasive measurement scheme allows to infer information about otherwise inaccessible objects, with potential implications for sensing, open-system dynamics and fundamental tests of quantum gravity. In the future, similar on-chip devices could be used to entangle subsystems on very different energy scales, such as microwave and optical photons.

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Fig. 1: Schematic representation of the experiment.
Fig. 2: Experimental realization.
Fig. 3: Experimental results.

Data availability

The data that support the findings of this study are available from the corresponding authors on reasonable request.

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Acknowledgements

This work was supported by the Institute of Science and Technology Austria (IST Austria), the IST nanofabrication facility, the EU’s Horizon 2020 research and innovation programme under grant agreement number 732894 (FET Proactive HOT), and the European Research Council under grant agreement number 758053 (ERC StG QUNNECT). S.B. acknowledges support from Marie Skłodowska Curie fellowship number 707438 (MSC-IF SUPEREOM). G.A. is a recipient of a DOC fellowship of the Austrian Academy of Sciences at IST. We thank N. Kuntner and J. Jung for contributions to the digitizer software, M. Hennessey-Wesen for developing the thermal calibration source, and K. Fedorov, M. Kalaee, O. Painter, D. Vitali and M. Paternostro for discussions.

Author information

S.B. and J.M.F. conceived the ideas for the experiment and analysed the data. S.B. developed the theoretical model and performed the measurements. E.S.R. and S.B. fabricated the sample. S.B., E.S.R., M.P., M.W. and J.M.F. designed the microwave circuit and built the experimental setup. G.A. and M.W. performed finite-element method simulations. S.B., M.P. and D.P.L. developed the measurement software. S.B. and J.M.F. prepared the manuscript.

Correspondence to S. Barzanjeh or J. M. Fink.

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Extended data figures and tables

Extended Data Fig. 1 Finite-element method simulations.

a, Sample geometry. Important dimensions are indicated and the aluminium metallization is shown in yellow. b, Finite-element method simulated mechanical eigenfrequencies of the two fundamental in-plane nanobeam modes versus the tensile stress of the 65-nm-thick aluminium metallization. The insets show the displacement profile of the two modes. The dashed lines indicate the tensile stress corresponding to the two measured mechanical frequencies, ωm,1(2). c, Simulated modulated capacitance of a single beam as a function of the capacitor gap size. The dashed lines indicate the capacitor gap sizes obtained from d, and the resulting modulated capacitances consistent with the measured resonance frequencies ωc,1(2). The solid line shows a fit with \({C}_{{\rm{mod}}}\propto {x}_{0}^{-0.6}\). d, Simulated electromechanical coupling strength between mechanical mode 1 at ωm,1 and the two measured microwave resonators at ωc,1(2) as a function of the capacitor gap size. Dashed lines indicate the experimentally measured coupling strengths g0,1(2) and the two resulting capacitor gap sizes. Solid lines show fits with \({g}_{0}\propto {x}_{0}^{-1.5}\).

Extended Data Fig. 2 Quadrature measurements.

a, System calibration of output channel 1 (top) and 2 (bottom). The measured noise density in units of quanta, Si = (Ni/ζi) − nadd,i, is shown as a function of the temperature T of the 50-Ω load. The error bars indicate the standard deviation obtained from three measurements with 28,800 quadrature pairs each. The solid lines are fits to equation (5) in units of quanta, which yields the system gain and noise with the standard errors (95% confidence interval) stated in the main text. The insets show the phase space distribution with the pump tones turned off. These two-variable quadrature histograms are based on 604,800 measured quadrature pairs for each channel. b, Difference of the two-variable quadrature histograms with the pumps turned on and off for all quadrature-pair combinations in units of quanta (as calibrated in a), obtained using 216,000 pairs from both channels.

Extended Data Fig. 3 Dynamical back-action cooling.

Measured phonon occupation of the mechanical oscillator as a function of the red-detuned drive power Pd at the input of microwave resonator 1 (blue) and 2 (red). From the fits (coloured lines) we infer a phonon bath occupation of \({\bar{n}}_{{\rm{m}}}=77\) and an intrinsic mechanical dissipation rate of γm/2π = 4 Hz.

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Supplementary Information

This file contains a Theoretical Model A-E and References.

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