Cold atoms are loaded into an optical cavity and pumped into two opposite Zeeman states of the cesium line. (top) An input light pulse with arbitrary polarization state is fed into the ensemble. Due to a spontaneous Raman process, the input superposition of right and left circularly polarization is converted to a single-collective-excitation superposition and a heralding photon is emitted into the resonator mode. (bottom) After a user-defined delay, a read beam converts the atomic state into a single photon, also into the resonator mode, with good efficiency and the same polarization as the input. These successive steps require rotating the atomic spin with a static magnetic field.