Fig. 1. (a) Schematic depicting coincidence measurement of two temporally separated CW-mode coherent photons via temporal post-selection. (b) Feynman diagrams depicting indistinguishable events of the TSPT states at the output stage.

Fig. 2. Schematic of experimental setup for HOM interference with a weak CW laser via temporal post-selection with the use of a polarization-based Michelson interferometer (M, mirror; PBS, polarizing beam splitter; IF, interference filter; HWP, half-wave plate; QWP, quarter-wave plate; SPD, single-photon detector).

Fig. 3. (a) Schematic for time-delayed coincidence measurement between D1 and D2 at both output ports of the PBS. (b) Normalized coincidence in different spatial modes in the three cases of Δt=0, 40, and 254 ns.

Fig. 4. (a) Schematic for time-delayed coincidence measurement of two photons in identical spatial modes upon performing two consecutive measurements with one SPD (D2). (b) Normalized coincidence in the same spatial modes in the case of Δt=60  ns.

Fig. 5. Analysis method for HOM fringe using photons temporally separated by the order of a day: one set (set A) of time-tagged data and another set (set B) are independently obtained after a long time delay ΔT, where D1 and D2 represent the time data of the detection events at D1 and D2, respectively, corresponding to the two spatial modes of the interferometer arms.

Fig. 6. HOM interference fringe of the TSPT state for ΔT=1 day. (a) HOM dip fringe (orange circles) of one-day-delayed coincidence counts between D1 data of set A and D2 data of set B; the red curve indicates the fitting of the HOM fringe with visibility of 50%±3%. (b) HOM peak fringe (blue circles) of one-day-delayed coincidence counts between D2 data of set A and D2 data of set B in the same spatial modes; the red curve indicates the fitting of the HOM peak fringe.