Measurement-based control of a mechanical oscillator at its thermal decoherence rate

Abstract

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.

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Figure 1: Measuring and controlling the position of a nanomechanical beam using a near-field optomechanical transducer.
Figure 2: Measurement imprecision and back action versus intracavity photon number.
Figure 3: Radiation-pressure feedback cooling to near the ground state.

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Acknowledgements

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.

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R.S., A.G. and D.J.W. contributed to the design and initial characterization of the device. R.S. developed, implemented and optimized the fabrication process. A.G. developed and implemented a numerical model to aid in device optimization. D.J.W., V.S. and N.P. conceived of, designed and performed the experiment. V.S. and D.J.W. analysed the data with support from N.P. V.S. developed the theoretical framework of the experiment with support from D.J.W. and N.P. V.S. wrote sections I and II of the Supplementary Information. R.S., V.S., D.J.W. and A.G. wrote section III of the Supplementary Information. D.J.W., N.P. and V.S. wrote sections IV and V of the Supplementary Information. D.J.W. wrote the main text with support from all other authors. T.J.K. oversaw all aspects of the work.

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Correspondence to T. J. Kippenberg.

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Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1–8, Supplementary Table 1 and additional references (see Contents for details). (PDF 5707 kb)

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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

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