Cold, macroscopic mechanical systems are expected to behave contrary to our usual classical understanding of reality; the most striking and counterintuitive predictions involve the existence of states in which the mechanical system is located in two places simultaneously. Various schemes have been proposed to generate and detect such states1,2, and all require starting from mechanical states that are close to the lowest energy eigenstate, the mechanical ground state. Here we report the cooling of the motion of a radio-frequency nanomechanical resonator by parametric coupling to a driven, microwave-frequency superconducting resonator. Starting from a thermal occupation of 480 quanta, we have observed occupation factors as low as 3.8 ± 1.3 and expect the mechanical resonator to be found with probability 0.21 in the quantum ground state of motion. Further cooling is limited by random excitation of the microwave resonator and heating of the dissipative mechanical bath. This level of cooling is expected to make possible a series of fundamental quantum mechanical observations including direct measurement of the Heisenberg uncertainty principle and quantum entanglement with qubits.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Armour, A., Blencowe, M. & Schwab, K. Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box. Phys. Rev. Lett. 88, 148301 (2002)
Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superposition of a mirror. Phys. Rev. Lett. 91, 130401 (2003)
Naik, A. et al. Cooling a nanomechanical resonator with quantum back-action. Nature 443, 193–196 (2006)
Courty, J. M., Heidmann, A. & Pinard, M. Quantum limits of cold damping with optomechanical coupling. Eur. Phys. J. D 17, 399–408 (2001)
Martin, I., Shnirman, A., Tian, L. & Zoller, P. Ground-state cooling of mechanical resonators. Phys. Rev. B 69, 125339 (2004)
Blencowe, M. P. & Buks, E. Quantum analysis of a linear dc SQUID mechanical displacement detector. Phys. Rev. B 76, 014511 (2007)
Marquardt, F., Chen, J. P., Clerk, A. A. & Girvin, S. M. Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys. Rev. Lett. 99, 093902 (2007)
Wilson-Rae, I., Nooshi, N., Zwerger, W. & Kippenberg, T. J. Theory of ground state cooling of a mechanical oscillator using dynamical backaction. Phys. Rev. Lett. 99, 093901 (2007)
Schliesser, A., Arcizet, O., Riviere, R., Anetsberger, G. & Kippenberg, T. J. Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit. Nature Phys. 5, 509–514 (2009)
Park, Y.-S. & Wang, H. Resolved-sideband and cryogenic cooling of an optomechanical resonator. Nature Phys. 5, 489–493 (2009)
Groblacher, S. et al. Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity. Nature Phys. 5, 485–488 (2009)
Day, P. K., LeDuc, H. G., Mazin, B. A., Vayonakis, A. & Zmuidzinas, J. A broadband superconducting detector suitable for use in large arrays. Nature 425, 817–821 (2003)
Regal, C. A., Teufel, J. D. & Lehnert, K. W. Measuring nanomechanical motion with a microwave cavity interferometer. Nature Phys. 4, 555–560 (2008)
Cleland, A. N. & Roukes, M. L. A nanometre-scale mechanical electrometer. Nature 392, 160–162 (1998)
Dykman, M. I. Heating and cooling of local and quasilocal vibrations by nonresonant eld. Sov. Phys. Solid State 20, 1306 (1978)
Linthorne, N. P., Veitch, P. J. & Blair, D. G. Interaction of a parametric transducer with a resonant bar gravitational radiation detector. J. Phys. D 23, 1–6 (1990)
Xue, F., Wang, Y. D., Liu, Y.-X. & Nori, F. Cooling a micromechanical beam by coupling it to a transmission line. Phys. Rev. B 76, 205302 (2007)
Diedrich, F., Bergquist, J. C., Itano, W. & Wineland, D. J. Laser cooling to the zero-point energy of motion. Phys. Rev. Lett. 62, 403–406 (1989)
Dobrindt, J. M., Wilson-Rae, I. & Kippenberg, T. J. Parametric normal-mode splitting in cavity optomechanics. Phys. Rev. Lett. 101, 263602 (2008)
Blair, D. G. et al. High sensitivity gravitational wave antenna with parametric transducer readout. Phys. Rev. Lett. 74, 1908–1911 (1995)
Teufel, J. D., Harlow, J. W., Regal, C. A. & Lehnert, K. W. Dynamical backaction of microwave fields on a nanomechanical oscillator. Phys. Rev. Lett. 101, 197203 (2008)
Teufel, J. D., Regal, C. A. & Lehnert, K. W. Prospects for cooling nanomechanical motion by coupling to a superconducting microwave resonator. New J. Phys. 10, 095002 (2008)
Stipe, B. C., Mamin, H. J., Stowe, T. D., Kenny, T. W. & Rugar, D. Noncontact friction and force fluctuations between closely spaced bodies. Phys. Rev. Lett. 87, 096801 (2001)
Poggio, M., Degen, C. L., Mamin, H. J. & Rugar, D. Feedback cooling of a cantilever’s fundamental mode below 5mk. Phys. Rev. Lett. 99, 017201 (2007)
Grajcar, M., Ashhab, S., Johansson, J. R. & Nori, F. Lower limit on the achievable temperature in resonator-based sideband cooling. Phys. Rev. B 78, 035406 (2008)
Shytov, A. V., Levitov, L. S. & Beenakker, C. W. J. Electromechanical noise in a diffusive conductor. Phys. Rev. Lett. 88, 228303 (2002)
Castellanos-Beltran, M. A., Irwin, K. D., Hilton, G. C., Vale, L. R. & Lehnert, K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Phys. 4, 929–931 (2008)
Utami, D. W. & Clerk, A. A. Entanglement dynamics in a dispersively coupled qubit-oscillator system. Phys. Rev. A 78, 042323 (2008)
Verbridge, S. S., Craighead, H. G. & Parpia, J. M. A megahertz nanomechanical resonator with room temperature quality factor over a million. Appl. Phys. Lett. 92, 013112 (2008)
Segev, E., Abdo, B., Shtempluck, O. & Buks, E. Thermal instability and self-sustained modulation in superconducting NbN stripline resonators. J. Phys. Condens. Matter 19, 096206 (2007)
We acknowledge conversations with M. Blencowe, M. Aspelmeyer, R. Ilic, M. Skvarla, M. Metzler and M. Shaw and assistance from M. Savva, S. Rosenthal and M. Corbett. This work has been supported by the Fundamental Questions Institute (http://fqxi.org) (RFP2-08-27) and the US National Science Foundation (NSF) (DMR-0804567). Device fabrication was performed at the Cornell Nanoscale Facility, a member of the US National Nanotechnology Infrastructure Network (NSF grant ECS-0335765).
Author Contributions T.R. and T.N. contributed equally to device fabrication and measurements. C.M. built key apparatus and assisted in experimental set-up. J.B.H. assisted in planning and analysis. A.A.C. provided theoretical analysis. K.C.S. initiated and oversaw the work.
The authors declare no competing financial interests.
About this article
Cite this article
Rocheleau, T., Ndukum, T., Macklin, C. et al. Preparation and detection of a mechanical resonator near the ground state of motion. Nature 463, 72–75 (2010). https://doi.org/10.1038/nature08681
The European Physical Journal Plus (2021)
Gain-type optomechanically induced absorption and precise mass sensor in a hybrid optomechanical system
Journal of Applied Physics (2021)
Nano Letters (2021)
Physical Review Research (2021)
Nano Letters (2020)