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

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.