Double two-photon coalescence in a controlled propagation

The propagation, storage, and release of two quantized light fields in an optically dressed atomic medium in the tripod configuration are studied. Using the formalism of spinor dark-state polaritons, the probabilities are obtained of finding outgoing photons of two possible localizations and two possible types, i.e., having different frequencies or polarizations. An additional interaction at the storage stage is applied which modifies the atomic coherences due to the stored photons; this results in a modification of the states of the outgoing photons. The conditions are examined for the photons' spatial and type coalescence typical of the Hong-Ou-Mandel effect, i.e., a zero probability of finding the outgoing photons having not only different localizations but also types. These results can possibly be observed in rubidium vapors.