Controlling a quantum system based on the observation of its dynamics is
inevitably complicated by the backaction of the measurement process. Efficient
measurements, however, maximize the amount of information gained per
disturbance incurred. Real-time feedback then enables both canceling the
measurement's backaction and controlling the evolution of the quantum state.
While such measurement-based quantum control has been demonstrated in the clean
settings of cavity and circuit quantum electrodynamics, its application to
motional degrees of freedom has remained elusive. Here we show
measurement-based quantum control of the motion of a millimetre-sized membrane
resonator. An optomechanical transducer resolves the zero-point motion of the
soft-clamped resonator in a fraction of its millisecond coherence time, with an
overall measurement efficiency close to unity. We use this position record to
feedback-cool a resonator mode to its quantum ground state (residual thermal
occupation n = 0.29 +- 0.03), 9 dB below the quantum backaction limit of
sideband cooling, and six orders of magnitude below the equilibrium occupation
of its thermal environment. This realizes a long-standing goal in the field,
and adds position and momentum to the degrees of freedom amenable to
measurement-based quantum control, with potential applications in quantum
information processing and gravitational wave detectors.Comment: New version with corrected detection efficiency as determined with a
NIST-calibrated photodiode, added references and revised structure. Main
conclusions are identical. 41 pages, 18 figure
