Bright matter-wave soliton collisions at narrow barriers

TL;DR

This paper analyzes how bright matter-wave solitons interact with narrow barriers, revealing phase-dependent outcomes and effects of barrier width, with implications for matter-wave interferometry.

Contribution

It provides a comprehensive analysis of soliton collisions at narrow barriers, including a quasi-analytic approach for delta barriers and numerical exploration of finite-width effects.

Findings

Outgoing wave norms depend sinusoidally on phase difference in high velocity limit

Finite barrier width introduces skew in phase dependence

Results applicable to bright matter-wave interferometry

Abstract

We study fast-moving bright solitons in the focusing nonlinear Schr\"odinger equation perturbed by a narrow Gaussian potential barrier. In particular, we present a general and comprehensive analysis of the case where two fast-moving bright solitons collide at the location of the barrier. In the limiting case of a delta-function barrier, we use a quasi-analytic method to show that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and to determine whether one, or both, of the outgoing waves are bright solitons. We show using numerical simulations that this quasi-analytic result is valid in the high velocity limit: outside this limit nonlinear effects introduce a skew to the phase-dependence, which we quantify. Finally, we numerically explore the effects of introducing a finite-width Gaussian barrier. Our results are particularly relevant, as they can be used to describe a range of interferometry experiments using bright solitary matter-waves.