Bright matter-wave soliton collisions at narrow barriers

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 $\ensuremath{\delta}$-function barrier, we use an 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 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.