Photon pair generation via direct and cascaded processes in a thin second-order nonlinear film

Pairs of entangled photons are crucial for photonic quantum technologies. The demand for integrability and multi-functionality suggests "flat" platforms-ultrathin layers and metasurfaces-as sources of photon pairs. With the success in demonstrating spontaneous parametric down-conversion (SPDC) from such sources, an alternative process to generate photon pairs, spontaneous four-wave mixing (SFWM), also attracts interest. In materials with nonzero second-order nonlinear susceptibility χ⁽²⁾, SFWM can generate photon pairs both directly, through the third-order nonlinear susceptibility χ⁽³⁾, and in a cascaded way, through second harmonic generation (SHG) followed by SPDC. Usually, the cascaded process is more efficient. Here, we show that in a thin layer, direct SFWM is likely to dominate, because the wavevector mismatch for SFWM is much smaller than for SHG or SPDC. To demonstrate this, we implement photon pair generation via SFWM in a second-order nonlinear material-a thin layer of lithium niobate (LN). The existence of both second- and third-order nonlinear processes offers broader opportunities for quantum state engineering.