Quantum optomechanics of a Bose-Einstein antiferromagnet.

We investigate the cavity optomechanical properties of an antiferromagnetic Bose-Einstein condensate, 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.