Interaction of solitons in one-dimensional dipolar Bose-Einstein condensates and formation of soliton molecules

Abstract

The interaction between two bright solitons in a one-dimensional dipolar Bose-Einstein condensate (BEC) is investigated, with the aim of finding the regimes where they form a stable bound state, known as the soliton molecule. To study soliton interactions in BECs we employed a method similar to that used in experimental investigation of the interaction between solitons in optical fibers. The idea consists in creating two solitons at some spatial separation from each other at initial time ${t}_{0}$ and then measuring the distance between them at a later time ${t}_{1}>{t}_{0}$. Depending on whether the distance between solitons has increased, decreased, or remained unchanged, compared to its initial value at ${t}_{0}$, we conclude that the soliton interaction was repulsive, attractive, or neutral, respectively. We propose an experimentally viable method for estimating the binding energy of a soliton molecule, based on its dissociation at critical soliton velocity. Our theoretical analysis is based on the variational approach, which appears to be quite accurate in describing the properties of soliton molecules in dipolar BECs, as reflected in the good agreement between the analytical and the numerical results.