Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as effects of entanglement or equivalently in terms of interfering probability amplitudes, and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison we show that the Hong-Ou-Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized.
@article{arxiv.1705.06030,
title = {Entanglement, complementarity, and vacuum fields in spontaneous parametric down-conversion},
author = {Ralf Menzel and Axel Heuer and Peter W. Milonni},
journal= {arXiv preprint arXiv:1705.06030},
year = {2017}
}