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Coherent feedback stabilises a system towards a target state without the needof a measurement, thus avoiding the quantum backaction inherent tomeasurements. Here, we employ optical coherent feedback to remotely cool ananomechanical membrane using atomic spins as a controller. Direct manipulationof the atoms allows us to tune from strong-coupling to an overdamped regime.Making use of the full coherent control offered by our system, we performspin-membrane state swaps combined with stroboscopic spin pumping to cool themembrane in a room-temperature environment to ${T}={216}\,\mathrm{mK}$($\bar{n}_{m} = 2.3\times 10^3$ phonons) in ${200}\,\mathrm{{\mu}s}$. Wefurthermore observe and study the effects of delayed feedback on the coolingperformance. Starting from a cryogenically pre-cooled membrane, this methodwould enable cooling of the mechanical oscillator close to its quantummechanical ground state and the preparation of nonclassical states.

Coherent feedback cooling of a nanomechanical membrane with atomic spins