  We theoretically investigated the biphoton state generated by spontaneous
four wave mixing (SpFWM) in ultrathin nonlinear films. The expression of the
biphoton state is obtained by perturbation method, in which the longitudinal
phase mismatch term is eliminated due to the ultra-small nonlinear interactive
length. As a result of the relaxation of the longitudinal phase match
condition, frequency bandwidth of the biphoton state could be very large. The
correlation function of the biphoton state is analyzed, showing that the space
and time in the biphoton correlation of this state are factorable. The
calculations of the frequency purity further indicate that the temporal and
spatial degrees of freedom in this biphoton state are separable. The spatial
Schmidt numbers of the biphoton state are also calculated, showing that this
state supports high dimensional transverse entanglement. These results shows
that SpFWM in ultrathin nonlinear films is promising in generating biphoton
states for applications involving hyper-entanglement and high-dimensional
entanglement.
