Performing Hong-Ou-Mandel-type Numerical Experiments with Repulsive Condensates: The case of Dark and Dark-bright Solitons

TL;DR

This paper explores classical wave analogs of the Hong-Ou-Mandel effect in repulsive condensates, analyzing dark and dark-bright soliton interactions and their asymmetries post-collision.

Contribution

It introduces numerical experiments of wave objects in condensates, revealing topological and non-topological collision behaviors and extending to two-dimensional structures.

Findings

Dark solitons show no significant asymmetries after collision.

Dark-bright solitons can exhibit pronounced asymmetries.

Similar phenomena are observed in ring dark-bright structures in 2D.

Abstract

The Hong-Ou-Mandel experiment leads indistinguishable photons simultaneously reaching a 50:50 beam splitter to emerge on the same port through two-photon interference. Motivated by this phenomenon, we consider numerical experiments of the same flavor for classical, {\it 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 {\it are} possible for the non-topological bright component. We also show an example of a similar phenomenology for ring dark-bright structures in two dimensions.