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We demonstrate continuous measurement and coherent control of the collectivespin of an atomic ensemble undergoing Larmor precession in a high-finesseoptical cavity. The coupling of the precessing spin to the cavity field yieldsphenomena similar to those observed in cavity optomechanics, including cavityamplification, damping, and optical spring shifts. These effects arise fromautonomous optical feedback onto the atomic spin dynamics, conditioned by thecavity spectrum. We use this feedback to stabilize the spin in either its high-or low-energy state, where, in equilibrium with measurement back-actionheating, it achieves a steady-state temperature, indicated by an asymmetrybetween the Stokes and anti-Stokes scattering rates. For sufficiently largeLarmor frequency, such feedback stabilizes the spin ensemble in a nearly purequantum state, in spite of continuous measurement by the cavity field.

Cavity-assisted measurement and coherent control of collective atomic spin oscillators