Fig. 2: Temporal two-photon probability.

a Histogram of the arrival times T_s, T_i of the signal, and idler photons. The arrival times are measured relative to an electronic trigger from the pump laser which serves as a global clock, and after adding an electronic delay of 70 ns to the idler detector to compensate for the chromatic delay between the signal and idler photons. The two off-diagonal peaks indicate that the two-photon state is not separable. We, therefore, conclude that the photons are correlated in the modal basis. The two peaks correspond to the occupation of modes \({\left|L{P}_{02}\right\rangle }_{s}{\left|L{P}_{01}\right\rangle }_{i}\) and \({\left|L{P}_{11}\right\rangle }_{s}{\left|L{P}_{11}\right\rangle }_{i}\), as verified by numerical computation of the fiber’s modal group delays. b, c Cross-sections of the two-dimensional histogram along the lines marked in (a), emphasizing the modal correlations. For example, post selecting events with an idler’s arrival time of \({T}_{i}^{(1)}=0.4\,\mathrm{ns}\) (green solid curve) shows localization of the signal photon at \({T}_{s}^{(2)}=3.5\,\mathrm{ns}\). In (b) the post-selection is on the signal photon, while in (c) it is on the idler photon. The measured delay between the two peaks is ΔT_s = 1 ns for the signal photons and ΔT_i = 0.5 ns for the idler photons.