Coherent reconstruction of pump beams through recombination of entangled photon pairs

Abstract

In theoretical and experimental work, we consider the process in which an entangled photon pair recombines into a single photon in a nonlinear crystal, with particular interest in the amplitude distribution and coherence properties of the up-converted light. It is found that the up-converted state has perfect mutual coherence with the pump that originally produced the photon pair in another nonlinear crystal and that the amplitude has the spatiotemporal structure of the original pump mode, filtered by a linear transfer function. These conclusions are drawn from leading-order calculations performed in the interaction picture, with the multimodal nature of all fields being fully accounted for. In our experimental results, we observe the spatial similarity between the up-converted light and the original pump mode; their mutual coherence is demonstrated through observation of fringes with near-unit visibility. The effects studied here have potential applications in quantum information processing and also confirm that the principle of path indistinguishability holds even under unusually extreme conditions.