2 research outputs found
Interactions of solitons with a Gaussian barrier: splitting and recombination in quasi-one-dimensional and three-dimensional settings
The interaction of matter–wave solitons with a potential barrier
is a fundamentally important problem, and the splitting and subsequent
recombination of the soliton by the barrier is the essence of soliton matter–wave
interferometry. We demonstrate the three-dimensional (3D) character of the
interactions in the case relevant to ongoing experiments, where the number of
atoms in the soliton is relatively close to the collapse threshold. We examine
the soliton dynamics in the framework of the effectively one-dimensional (1D)
nonpolynomial Schr¨odinger equation (NPSE), which admits the collapse in a
modified form, and in parallel we use the full 3D Gross–Pitaevskii equation
(GPE). Both approaches produce similar results, which are, however, quite different from those produced in recent work that used the 1D cubic GPE. Basic
features, produced by the NPSE and the 3D GPE alike, include (a) an increase
in the first reflection coefficient for increasing barrier height and decreasing
atom number; (b) large variation of the secondary reflection/recombination
probability versus barrier height; (c) pronounced asymmetry in the oscillation
amplitudes of the transmitted and reflected fragments; and (d) enhancement of
the transverse excitations as the number of atoms is increased. We also explore
effects produced by variations of the barrier width and outcomes of the secondary
collision upon phase imprinting on the fragment in one arm of the interferometer