How to use the dispersion in the $\chi^{(3)}$ tensor for broadband generation of polarization-entangled photons

Polarization-entangled photon pairs are a widely used resource in quantum optics and technologies, and are often produced using a nonlinear process. Most sources based on spontaneous parametric downconversion have relatively narrow optical bandwidth because the pump, signal and idler frequencies must satisfy a phase-matching condition. Extending the bandwidth, for example to achieve spectral multiplexing, requires changing some experimental parameters such as temperature, crystal angle, poling period, etc. Here, we demonstrate broadband (tens of THz for each photon) generation of polarization-entangled photon pairs by spontaneous four-wave mixing in a diamond crystal, with a simple colinear geometry requiring no further optical engineering. Our approach leverages the quantum interference between electronic and vibrational contributions to the $\chi^{(3)}$ tensor. Entanglement is characterized in a single realization of a Bell test over the entire bandwidth using fiber dispersion spectroscopy and fast single-photon detectors. The results agree with the biphoton wavefunction predicted from the knowledge of the $\chi^{(3)}$ and Raman tensors and demonstrate the general applicability of our approach to other crystalline materials.