Anisotropic spatial entanglement

The photon pairs generated through spontaneous parametric down-conversion (SPDC) possess strong correlations in their transverse position and momentum degrees of freedom. For such photon pairs, the transverse position correlation length depends on the crystal thickness and the pump wavelength. In contrast, the transverse momentum correlation length depends on the pump's beam waist and spatial coherence length. By controlling these parameters, it is possible to engineer spatial entanglement. Here, we utilize the circular asymmetry of the pump by using an elliptical-Gaussian beam to change the degree of entanglement in transverse directions, which we call anisotropic entanglement. We show the interrelation between the degree of anisotropic entanglement and the asymmetry in the beam width. In addition, we also show that for a highly asymmetric pump beam, the entanglement vanishes along the direction of the thinner beam width, while it remains intact in the direction of the broader beam width.