Nonlinear Scattering of a Bose-Einstein Condensate on a Rectangular Barrier

TL;DR

This paper investigates how nonlinear interactions in a Bose-Einstein condensate affect its scattering on a rectangular barrier, revealing complex bifurcation phenomena and new control mechanisms for soliton formation.

Contribution

It demonstrates the existence of infinite bifurcations in transmission resonances and shows how barrier width influences nonlinear scattering, unlike in linear quantum mechanics.

Findings

Infinite bifurcations in transmission resonances

Near-perfect resonance regions where the barrier is invisible

Barrier width controls transmission more than height

Abstract

We consider the nonlinear scattering and transmission of an atom laser, or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several new physical features beyond the well-known picture from single-particle quantum mechanics. We find numerical evidence for a denumerably infinite string of bifurcations in the transmission resonances as a function of nonlinearity and chemical potential, when the potential barrier is wide compared to the wavelength of oscillations in the condensate. Near the bifurcations, we observe extended regions of near-perfect resonance, in which the barrier is effectively invisible to the BEC. Unlike in the linear case, it is mainly the barrier width, not the height, that controls the transmission behavior. We show that the potential barrier can be used to create and localize a dark soliton or dark soliton train from a phonon-like standing wave.