Formation of matter-wave soliton molecules

TL;DR

This paper introduces a method to create matter-wave soliton molecules by preparing two solitons with specific initial conditions, supported by numerical simulations and an analytical interaction model.

Contribution

It presents a novel approach for forming soliton molecules using phase and separation control, supported by an exact interaction energy derivation.

Findings

Bound soliton pairs form under specific initial conditions.

The interaction energy is described by a Morse potential.

The model applies to soliton gas and Toda lattice problems.

Abstract

We propose a method of forming matter-wave soliton molecules that is inspired by the recent experiment of Dris {\it et al.}. In the proposed set-up we show that if two solitons are initially prepared in phase and with a sufficiently small separation and relative velocity, a bound pair will always form. This is verified by direct numerical simulation of the Gross-Pitaevskii equation and by the derivation of the exact interaction energy of two solitons, which takes the form of a Morse potential. This interaction potential depends not only on the separation but also on the relative phase of the solitons and is essential for an analytical treatment of a host of other problems, such as the soliton gas and the Toda lattice of solitons.