The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering1. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems2,3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback4. Successful implementations thus far include experiments on the level of optical and atomic systems5,6,7. Here we demonstrate real-time optimal control of the quantum trajectory8 of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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We thank J. M. Leitão for his introduction to optimal control, and P. Vezio, H. Hepach and T. Westphal for discussions and their help in the laboratory. L.M. thanks A. Rauschenbeutel for the discussion inspiring the confocal detection scheme. This project was supported by the European Research Council (grant agreement no. 649008, ERC CoG QLev4G), by the ERA-NET programme QuantERA under grants QuaSeRT (contract no. 11299191) and TheBlinQC (project no. 731473) (via the EC, the Austrian ministries BMDW and BMBWF and research promotion agency FFG), by the European Union’s Horizon 2020 research and innovation programme under grant no. 863132 (iQLev), and by the Austrian Science Fund (FWF, START Project TheLO, Y 952-N36). L.M. is supported by the Vienna Doctoral School of Physics (VDS-P) and by the FWF under project W1210 (CoQuS).
The authors declare no competing interests.
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Magrini, L., Rosenzweig, P., Bach, C. et al. Real-time optimal quantum control of mechanical motion at room temperature. Nature 595, 373–377 (2021). https://doi.org/10.1038/s41586-021-03602-3