Constraints on downconversion in atomically thick films

Spontaneous parametric downconversion (SPDC) has been predicted in atomically thick crystals, though not yet observed. In this work we uncover physical and experimental constraints of photon-pair generation in such planar nonlinear films with a free-space illumination/collection geometry. We measure the material nonlinear response of monolayer tungsten diselenide via second harmonic generation and subsequently calculate the expected SPDC efficiency from appropriate quantum-classical relations. Energy and momentum conservation shape the wavevectors of photon pairs in free-space and allow us to calculate the loss and coincidence-to-accidental ratio in various configurations. This work improves the understanding of the nonlinear quantum optical potential of these crystals, guides their experimental validation, and provides a performance benchmark for these ultrathin materials.