Enhanced entanglement from Ince-Gaussian pump beams in spontaneous parametric down-conversion

Spontaneous parametric down-conversion (SPDC) has been a reliable process for the generation of entangled photon pairs. In this process, a nonlinear quadratic crystal is pumped by a laser field in order to convert (high-energy) photons into correlated photon pairs whose efficient control plays an essential role in various applications of quantum information processing. In particular, the amount of entanglement has been successfully controlled by adjusting the spatial structure of the incident pump field. Here, we theoretically analyze how the entanglement of the down-converted two-photon state can be further enhanced by using Ince-Gaussian beams with well-defined ellipticity epsilon, i.e., solutions of the paraxial wave equation in elliptical coordinates. These spatially structured beams are quite universal as they include both the Laguerre-Gaussian beams for epsilon -> 0 as well as the Hermite-Gaussian beams for epsilon -> infinity. We demonstrate that the entanglement of the generated photon pairs in SPDC can be maximized by a proper choice of epsilon and that such an enhanced entanglement can be observed experimentally in terms of the Schmidt number.