Fig. 1: Scheme of the SFWM source and basic characteristics of generated biphotons.

a shows a simplified excitation geometry realized with a single laser frequency with counter-propagating collimated pump (P) and coupling (C) beams. Distance d is defined between the center of the intersection of excitation and observation spatial modes and the cell output viewport along the pump beam propagation direction. The optical pumping (OP) beam effectively covers the interaction area. The Stokes (S) and anti-Stokes (AS) fields are selected by a combination of Fabry–Pérot cavities, Glan–Thompson polarizers, and optical cut-off filters, marked together as F_S and F_AS, respectively. Spatial modes are set by the coupling into single-mode fibers (SMF) in two opposite directions. The energy level scheme of ⁸⁷Rb depicts the SFWM process corresponding to the emission of off-resonant Stokes and near-resonant anti-Stokes fields for the excitation laser set close to the 5S_1/2(F = 2) ↔ 5P_1/2(F = 2) transition. The graphs in (b) show basic characteristics of generated biphotons including two-photon coupling efficiency η_2ph and maxima of the intensity correlation function \({g}_{{{{\rm{S,AS}}}}}^{(2)}(0)\) between single-photon avalanche diodes (SPAD) in the heralding—anti-Stokes and in the signal—Stokes channels. The inset shows an example of \({g}_{{{{\rm{S,AS}}}}}^{2}(\tau )\). Stokes M_S, anti-Stokes M_AS, and coincidence C photodetection rates in kilo-counts/s are shown as red, blue, and magenta data points, respectively. For comparison, QNG marks an area of expectable observability of QNG features. Error bars correspond to a single standard deviation and, where not illustrated, their size is smaller than the size of the corresponding plot symbols.