Experimental position-time entanglement with degenerate single photons

We report an experiment in which two-photon interference occurs between degenerate single photons that never meet. The two photons travel in opposite directions through our fiber-optic interferometer and interference occurs when the photons reach two different, spatially separated, two-by-two couplers at the same time. We show that this experiment is analogous to the conventional Franson-type entanglement experiment where the photons are entangled in position and time. We measure wave-function overlaps for the two photons as high as $94\ifmmode\pm\else\textpm\fi{}3%$.