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We theoretically investigated the biphoton state generated by spontaneousfour wave mixing (SpFWM) in ultrathin nonlinear films. The expression of thebiphoton state is obtained by perturbation method, in which the longitudinalphase mismatch term is eliminated due to the ultra-small nonlinear interactivelength. As a result of the relaxation of the longitudinal phase matchcondition, frequency bandwidth of the biphoton state could be very large. Thecorrelation function of the biphoton state is analyzed, showing that the spaceand time in the biphoton correlation of this state are factorable. Thecalculations of the frequency purity further indicate that the temporal andspatial degrees of freedom in this biphoton state are separable. The spatialSchmidt numbers of the biphoton state are also calculated, showing that thisstate supports high dimensional transverse entanglement. These results showsthat SpFWM in ultrathin nonlinear films is promising in generating biphotonstates for applications involving hyper-entanglement and high-dimensionalentanglement.

Spatiotemporally Separable Biphoton State Generated by Spontaneous Four Wave Mixing in Ultrathin Nonlinear Films