Performing Hong-Ou-Mandel-type numerical experiments with repulsive condensates: The case of dark and dark-bright solitons

The Hong-Ou-Mandel experiment leads indistinguishable photons simultaneously reaching a 50:50 beam splitter to emerge on the same port through a two-photon interference. Motivated by this phenomenon, we consider numerical experiments of the same flavor for classical wave objects in the setting of repulsive condensates. We examine dark solitons interacting with a repulsive barrier, a case in which we find no significant asymmetries in the emerging waves after the collision, presumably due to their topological nature. We also consider case examples of two-component systems, where the dark solitons trap a bright structure in the second component (dark-bright solitary waves). For these, pronounced asymmetries upon collision are possible for the nontopological bright component. We also show an example of a similar phenomenology for ring dark-bright structures in two dimensions.