  We investigate the cavity optomechanical properties of an antiferromagnetic
Bose-Einstein con- densate, where the role of the mechanical element is played
by spin-wave excitations. We show how this system can be described by a single
rotor that can be prepared deep in the quantum regime under realizable
experimental conditions. This system provides a bottom-up realization of
dispersive rotational optomechanics, and opens the door to the direct
observation of quantum spin fluctuations.
