Narrowband Biphotons with Polarization-Frequency Coupled Hyperentanglement

We demonstrate the generation of narrowband biphotons with polarization-frequency coupled hy- perentanglement from spontaneous four-wave mixing in cold atoms. The coupling between polariza- tion and frequency is realized through a frequency shifter and linear optics. When the polarization- frequency degrees of freedom are decoupled, it is robust to create polarization and frequency Bell states, confirmed by the polarization quantum-state tomography and the two-photon temporal quan- tum beating. Making use of the polarization-frequency coupling to transfer polarization phase retard to the entangled frequency modes, we produce a frequency Bell state with tunable phase difference between its two bases.