All-optical polarimetric generation of mixed-state single-photon geometric phases

We report robust polarimetric measurements of mixed-state geometric phases. An all-optical setup was used to generate geometric phases with great versatility, thereby extending the scope of analogous methods used in neutron polarimetry. Our method allows us to explore geometric phases generated by unitarily evolving mixed states. These are realized as partially polarized single-photon states whose degree of polarization and normalized Stokes vector can be fixed independently of one another. The geometric phases correspond to both open and closed trajectories in Poincaré space. By exploiting the gauge invariance of geometric phases we nullify their dynamical part, thereby making the geometric phase coincide with the total (Pancharatnam) phase, which can be directly addressed by employing standard techniques.