Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions

TL;DR

This paper develops a method to construct multivalley dark soliton solutions in multicomponent Bose-Einstein condensates, revealing unique phase jump behaviors and collision dynamics, with implications for experimental observation.

Contribution

It introduces a Darboux transformation approach to generate multivalley dark solitons and analyzes their properties and interactions in multicomponent BECs.

Findings

Multivalley dark solitons exhibit width-dependent velocity and phase jump ranges.

Double-valley dark solitons have phase jumps in [0, 2π], differing from single-valley solitons.

Collision with single-valley dark solitons can transform double-valley solitons into breathers.

Abstract

We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation method. We demonstrate that the width-dependent parameters of solitons significantly affect the velocity ranges and phase jump regions of multivalley dark solitons, in sharp contrast to scalar dark solitons. For double-valley dark solitons, we find that the phase jump is in the range $[0,2\pi]$, which is quite different from that of the usual single-valley dark soliton. Based on our results, we argue that the phase jump of an $n$-valley dark soliton could be in the range $[0,n\pi]$, supported by our analysis extending up to five-component condensates. The interaction between a double-valley dark soliton and a single-valley dark soliton is further investigated, and we reveal a striking collision process in which the double-valley dark soliton is transformed into a breather after colliding with the single-valley dark soliton. Our analyses suggest that this breather transition exists widely in the collision processes involving multivalley dark solitons. The possibilities for observing these multivalley dark solitons in related Bose-Einstein condensates experiments are discussed.