In real-time quantum feedback protocols1,2, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen successful applications of these protocols in a variety of well-isolated micro-systems, including microwave photons3 and superconducting qubits4. However, stabilizing the quantum state of a tangibly massive object, such as a mechanical oscillator, remains very challenging: the main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, 4.3-megahertz nanomechanical oscillator in the timescale of its thermal decoherence, a basic requirement for real-time (Markovian) quantum feedback control tasks, such as ground-state preparation. The sensor is based on evanescent optomechanical coupling to a high-Q microcavity5, and achieves an imprecision four orders of magnitude below that at the standard quantum limit for a weak continuous position measurement6—a 100-fold improvement over previous reports7,8,9—while maintaining an imprecision–back-action product that is within a factor of five of the Heisenberg uncertainty limit. As a demonstration of its utility, we use the measurement as an error signal with which to feedback cool the oscillator. Using radiation pressure as an actuator, the oscillator is cold damped10 with high efficiency: from a cryogenic-bath temperature of 4.4 kelvin to an effective value of 1.1 ± 0.1 millikelvin, corresponding to a mean phonon number of 5.3 ± 0.6 (that is, a ground-state probability of 16 per cent). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of mechanical oscillators as practical subjects for measurement-based quantum control.
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.
Wiseman, H. M. Quantum theory of continuous feedback. Phys. Rev. A 49, 2133–2150 (1994); erratum 49, 5159 (1994)
Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge Univ. Press, 2009)
Sayrin, C. et al. Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 73–77 (2011)
Vijay, R. et al. Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature 490, 77–80 (2012)
Anetsberger, G. et al. Near-field cavity optomechanics with nanomechanical oscillators. Nature Phys. 5, 909–914 (2009)
Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010)
Teufel, J. D., Donner, T., Castellanos-Beltran, M. A., Harlow, J. W. & Lehnert, K. W. Nanomechanical motion measured with an imprecision below that at the standard quantum limit. Nature Nanotechnol. 4, 820–823 (2009)
Anetsberger, G. et al. Measuring nanomechanical motion with an imprecision below the standard quantum limit. Phys. Rev. A 82, 061804(R) (2010)
Westphal, T. et al. Interferometer readout noise below the standard quantum limit of a membrane. Phys. Rev. A 85, 063806 (2012)
Cohadon, P. F., Heidmann, A. & Pinard, M. Cooling of a mirror by radiation pressure. Phys. Rev. Lett. 83, 3174–3177 (1999)
LIGO. Scientific Collaboration. Observation of a kilogram-scale oscillator near its quantum ground state. New J. Phys. 11, 073032 (2009)
Bushev, P. et al. Feedback cooling of a single trapped ion. Phys. Rev. Lett. 96, 043003 (2006)
D’Urso, B., Odom, B. & Gabrielse, G. Feedback cooling of a one-electron oscillator. Phys. Rev. Lett. 90, 043001 (2003)
Hatridge, M. et al. Quantum back-action of an individual variable-strength measurement. Science 339, 178–181 (2013)
Caves, C. M. Quantum-mechanical radiation-pressure fluctuations in an interferometer. Phys. Rev. Lett. 45, 75–79 (1980)
Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014)
Courty, J.-M., Heidmann, A. & Pinard, M. Quantum limits of cold damping with optomechanical coupling. Eur. Phys. J. D 17, 399–408 (2001)
Szorkovszky, A., Doherty, A. C., Harris, G. I. & Bowen, W. P. Mechanical squeezing via parametric amplification and weak measurement. Phys. Rev. Lett. 107, 213603 (2011)
Mancini, S., Vitali, D. & Tombesi, P. Optomechanical cooling of a macroscopic oscillator by homodyne feedback. Phys. Rev. Lett. 80, 688–691 (1998)
Genes, C., Vitali, D., Tombesi, P., Gigan, S. & Aspelmeyer, M. Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes. Phys. Rev. A 77, 033804 (2008); erratum 79, 039903 (2009)
Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011)
Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011)
Verhagen, E., Deléglise, S., Weis, S., Schliesser, A. & Kippenberg, T. J. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63–67 (2012)
Wiseman, H. M. Using feedback to eliminate back-action in quantum measurements. Phys. Rev. A 51, 2459–2468 (1995)
Purdy, T. P., Peterson, R. W. & Regal, C. A. Observation of radiation pressure shot noise on a macroscopic object. Science 339, 801–804 (2013)
Murch, K. W., Moore, K. L., Gupta, S. & Stamper-Kurn, D. M. Observation of quantum-measurement backaction with an ultracold atomic gas. Nature Phys. 4, 561–564 (2008)
Gavartin, E., Verlot, P. & Kippenberg, T. J. A hybrid on-chip optomechanical transducer for ultrasensitive force measurements. Nature Nanotechnol. 7, 509–514 (2012)
Poggio, M., Degen, C., Mamin, H. & Rugar, D. Feedback cooling of a cantilever’s fundamental mode below 5 mK. Phys. Rev. Lett. 99, 017201 (2007)
Li, T., Kheifets, S. & Raizen, M. G. Millikelvin cooling of an optically trapped microsphere in vacuum. Nature Phys. 7, 527–530 (2011)
Jacobs, K., Nurdin, H. I., Strauch, F. W. & James, M. Comparing resolved-sideband cooling and measurement-based feedback cooling on an equal footing: analytical results in the regime of ground-state cooling. Phys. Rev. A 91, 043812 (2015)
We acknowledge nanofabrication advice from E. Gavartin in the early stages of the project. All samples were fabricated at the CMi (Center for Micro-Nanotechnology) at EPFL. Research was funded by an ERC Advanced Grant (QuREM), by the DARPA/MTO ORCHID programme, the Marie Curie Initial Training Network ‘Cavity Quantum Optomechanics’ (cQOM), the Swiss National Science Foundation and through support from the NCCR of Quantum Engineering (QSIT). N.P. and D.J.W. acknowledge support from the European Commission through Marie Skodowska-Curie Fellowships: IEF project 303029 and IIF project 331985, respectively.
The authors declare no competing financial interests.
About this article
Cite this article
Wilson, D., Sudhir, V., Piro, N. et al. Measurement-based control of a mechanical oscillator at its thermal decoherence rate. Nature 524, 325–329 (2015). https://doi.org/10.1038/nature14672
Physical Review A (2020)
Physical Review Research (2020)
Topological phase induced by distinguishing parameter regimes in a cavity optomechanical system with multiple mechanical resonators
Physical Review A (2020)
New Journal of Physics (2020)
International Journal of Modelling and Simulation (2020)