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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Bocko, M. F. & Onofrio, R. On the measurement of a weak classical force coupled to a harmonic oscillator: Experimental progress. Rev. Mod. Phys. 68, 755–790 (1996)
Braginsky, V. B. & Khalili, F. Y. Quantum Measurement (Cambridge Univ. Press, Cambridge, 1992)
Cho, A. Researchers race to put the quantum in mechanics. Science 299, 36–37 (2002)
Sidles, J. A. et al. Magnetic resonance force microscopy. Rev. Mod. Phys. 67, 249–265 (1995)
Armour, A. D., Blencowe, M. P. & Schwab, K. C. Entanglement and decoherence of a micromechanical resonator via coupling to a cooper-pair box. Phys. Rev. Lett. 88, 148301 (2002)
Tobar, M. E. & Blair, D. G. Sensitivity analysis of a resonant-mass gravitational wave antenna with a parametric transducer. Rev. Sci. Instrum. 66, 2751–2759 (1995)
Long, J. C. et al. Upper limits to submillimetre-range forces from extra space-time dimensions. Nature 421, 922–925 (2003)
White, J. D. An ultra high resolution displacement transducer using the Coulomb blockade electrometer. Jap. J. Appl. Phys 2 32, L1571–L1573 (1993)
Blencowe, M. P. & Wybourne, M. N. Sensitivity of a micromechanical displacement detector based on the radio-frequency single-electron transistor. Appl. Phys. Lett. 77, 3845–3847 (2000)
Zhang, Y. & Blencowe, M. P. Intrinsic noise of a micro-mechanical displacement detector based on the radio-frequency single-electron transistor. J. Appl. Phys. 91, 4249–4255 (2002)
Knobel, R. & Cleland, A. N. Piezoelectric displacement sensing with a single-electron transistor. Appl. Phys. Lett. 81, 2258–2260 (2002)
Caves, C. M., Thorne, K. S., Drever, R. W. P., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. 1. Issues of principle. Rev. Mod. Phys. 52, 341–392 (1980)
Huang, X. M. H., Zorman, C. A., Mehregany, M. & Roukes, M. L. Nanoelectromechanical systems: Nanodevice motion at microwave frequencies. Nature 421, 496 (2003)
Abramovici, A. et al. Improved sensitivity in a gravitational wave interferometer and implications for LIGO. Phys. Lett. A 218, 157–163 (1996)
Mamin, H. & Rugar, D. Sub-attonewton force detection at millikelvin temperature. Appl. Phys. Lett. 79, 3358–3360 (2001)
Cleland, A. N. & Roukes, M. L. External control of dissipation in a nanometer-scale radiofrequency mechanical resonator. Sensors Actuators A 72, 256–261 (1999)
Beck, R. G. et al. GaAs/AlGaAs self-sensing cantilevers for low temperature scanning probe microscopy. Appl. Phys. Lett. 73, 1149–1151 (1998)
Schoelkopf, R. J., Wahlgren, P., Kozhevnikov, A. A., Delsing, P. & Prober, D. E. The radiofrequency single-electron transistor (rf-SET): A fast and ultrasensitive electrometer. Science 280, 1238–1242 (1998)
Devoret, M. H. & Schoelkopf, R. J. Amplifying quantum signals with the single-electron transistor. Nature 406, 1039–1046 (2000)
Cleland, A. N., Aldridge, J. S., Driscoll, D. C. & Gossard, A. C. Nanomechanical displacement sensing using a quantum point contact. Appl. Phys. Lett. 81, 1699–1701 (2002)
Fulton, T. A. & Dolan, G. J. Observations of single-electron charging effects in small tunnel junctions. Phys. Rev. Lett. 59, 109–112 (1987)
Knobel, R., Yung, C. S. & Cleland, A. N. Single-electron transistor as a radio-frequency mixer. Appl. Phys. Lett. 81, 532–534 (2002)
Martinis, J. M., Devoret, M. H. & Clarke, J. Experimental tests for the quantum behavior of a macroscopic degree of freedom: The phase difference across a Josephson junction. Phys. Rev. B 35, 4682 (1987)
Greywall, D. S., Yurke, B., Busch, P. A., Pargellis, A. N. & Willett, R. A. Evading amplifier noise in nonlinear oscillators. Phys. Rev. Lett. 72, 2992–2995 (1994)
Cleland, A. N. & Roukes, M. L. Fabrication of high frequency nanometer scale resonators from bulk Si crystals. Appl. Phys. Lett. 69, 2653 (1996)
Yang, J., Ono, T. & Esashi, M. Surface effects and high quality factors in ultrathin single-crystal silicon cantilevers. Appl. Phys. Lett. 77, 3860–3862 (2000)
Yasumura, K. Y. et al. Quality factors in micron- and submicron-thick cantilevers. J. Microelectromech. Syst. 9, 117–125 (2000)
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.
The authors declare that they have no competing financial interests.
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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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