Breaking of reciprocity and the Pancharatnam-Berry phase for light scattered by a disordered cold-atom cloud

Collective effects on the light scattered by disordered media such as Anderson localization and coherent backscattering critically depend on the reciprocity between interfering optical paths. In this Letter, we explore the breaking of reciprocity for the light scattered by a disordered cold-atom setup, taking advantage of the noncommutation of optical elements that manipulate the polarization of the interfering paths. This breaking of symmetry manifests itself in the reduction of the fringes' contrast as the light scattered by the cloud interferes with that from its mirror image. We provide a geometrical interpretation in terms of the Pancharatnam-Berry phase, which we directly access from the fringe displacement. Our work paves the way toward the manipulation of path reciprocity and interference of light using atomic media, where it could be combined with collective and saturation effects.