Atomic interaction via diffractive light coupling

Transversely pumped cavities have been a workhorse for mediating global coupling between atoms and recent progress has been made towards multi-mode situations with more localized coupling [1]. However, in transversely pumped cavities, symmetries will be always constrained by the pump and cavity axes whereas in a system with a single distinguished axis the translational and rotational symmetries in the 2D transverse plane can be broken spontaneously. Recent work demonstrated that in a feedback system (Fig. 1a) using coupling to external degrees of freedom or internal spin degrees of freedom [2-4]. In this contribution, we are giving a generalized treatment of this coupling and show how the different light degrees of freedom on the Poincaré sphere can be utilized to address different atomic moments. We also investigate the transfer of this concept to longitudinally pumped cavities.