We expand the two-photon Hong-Ou-Mandel (HOM) effect onto a higher-dimensional set of spatial modes and introduce an effect that allows controllable redistribution of quantum states over these modes using directionally unbiased linear-optical four-ports without post-selection. The original HOM effect only allows photon pairs to exit in two directions in space. But when accompanied by beam splitters and phase shifters, the result is a directionally controllable two-photon HOM effect in four spatial modes, with direction controlled by changing the phases in the system. This controllable quantum amplitude manipulation also allows demonstration of a "delayed" HOM effect by exploiting phase shifters in a system of two connected multiport devices. By this means, both spatial and temporal control of the propagation of the two-photon superposition state through a network can be achieved.
@article{arxiv.2012.08745,
title = {Higher-dimensional Hong-Ou-Mandel effect and state redistribution with linear-optical multiports},
author = {Shuto Osawa and David S. Simon and Alexander V. Sergienko},
journal= {arXiv preprint arXiv:2012.08745},
year = {2020}
}