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Measuring nanomechanical motion with a microwave cavity interferometer

Abstract

A mechanical resonator is a physicist’s most tangible example of a harmonic oscillator. With the advent of micro and nanoscale mechanical resonators, researchers are rapidly progressing towards a tangible harmonic oscillator with motion that requires a quantum description. Challenges include freezing out the thermomechanical motion to leave only zero-point quantum fluctuations δ xzp and, equally importantly, realizing a Heisenberg-limited displacement detector. Here, we introduce a detector that can be in principle quantum limited and is also capable of efficiently coupling to the motion of small-mass, nanoscale objects, which have the most accessible zero-point motion. Specifically, we measure the displacement of a nanomechanical beam using a superconducting transmission-line microwave cavity. We realize excellent mechanical force sensitivity (3 aN Hz−1/2), detect thermal motion at tens of millikelvin temperatures and achieve a displacement imprecision of 30 times the standard quantum limit.

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Figure 1: Measurement schematic diagram.
Figure 2: Illustration of our device geometry.
Figure 3: Microwave cavity characterization.
Figure 4: Resonant response of an aluminium nanomechanical beam to an electrostatic drive at Tcryo=17 mK.
Figure 5: Integrated mechanical beam fluctuations in units of cavity resonance frequency shift δ ωc.
Figure 6: Imprecision temperature (blue open circles) and saturation temperature (red circles) as a function of incident microwave power.

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Acknowledgements

We acknowledge support from the National Science Foundation’s Physics Frontier Center for Atomic, Molecular and Optical Physics and from the National Institute of Standards and Technology; C.A.R. acknowledges support from the Fannie and John Hertz Foundation. The authors acknowledge R. J. Schoelkopf, S. M. Girvin, K. D. Irwin, D. Alchenberger, M. A. Castellanos-Beltran and N. E. Flowers-Jacobs for enlightening conversations and technical assistance.

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Correspondence to K. W. Lehnert.

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Regal, C., Teufel, J. & Lehnert, K. Measuring nanomechanical motion with a microwave cavity interferometer. Nature Phys 4, 555–560 (2008). https://doi.org/10.1038/nphys974

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