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.
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