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Nanometre-scale displacement sensing using a single electron transistor

Abstract

It has been a long-standing goal to detect the effects of quantum mechanics on a macroscopic mechanical oscillator1,2,3. Position measurements of an oscillator are ultimately limited by quantum mechanics, where ‘zero-point motion’ fluctuations in the quantum ground state combine with the uncertainty relation to yield a lower limit on the measured average displacement. Development of a position transducer, integrated with a mechanical resonator, that can approach this limit could have important applications in the detection of very weak forces, for example in magnetic resonance force microsopy4 and a variety of other precision experiments5,6,7. One implementation that might allow near quantum-limited sensitivity is to use a single electron transistor (SET) as a displacement sensor8,9,10,11: the exquisite charge sensitivity of the SET at cryogenic temperatures is exploited to measure motion by capacitively coupling it to the mechanical resonator. Here we present the experimental realization of such a device, yielding an unequalled displacement sensitivity of 2 × 10-15 m Hz-1/2 for a 116-MHz mechanical oscillator at a temperature of 30 mK—a sensitivity roughly a factor of 100 larger than the quantum limit for this oscillator.

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Figure 1: The device used in the experiment.
Figure 2: Magnetomotive measurements of the beam resonance.
Figure 3: Single electron transistor measurement of the beam motion.
Figure 4: Noise and quantum limits for the device.

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Acknowledgements

We thank C. Yung, D. Schmidt and S. Aldridge for conversations, and B. Hill for processing support. We acknowledge support provided by the National Science Foundation XYZ-On-A-Chip programme, by the Army Research Office, and by the Office of Naval Research/DARPA SPINS programme.

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Correspondence to Andrew N. Cleland.

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Knobel, R., Cleland, A. Nanometre-scale displacement sensing using a single electron transistor. Nature 424, 291–293 (2003). https://doi.org/10.1038/nature01773

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