Abstract
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 Schrödinger 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.
Highlights
Ongoing studies of atomic Bose-Einstein condensates (BECs) have contributed numerous fundamental insights in a wide range of phenomena [1, 2]
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 matterwave interferometry
We examine the soliton dynamics in the framework of the effectively 1D nonpolynomial Schrodinger equation (NPSE), which admits the collapse in a modified form, and in parallel we use the full 3D Gross-Pitaevskii equation (GPE)
Summary
Ongoing studies of atomic Bose-Einstein condensates (BECs) have contributed numerous fundamental insights in a wide range of phenomena [1, 2]. Collisions of 1D solitons with an attractive potential well, rather than the repulsive barrier, have been studied recently, revealing a fairly complex phenomenology The latter features alternating windows of transmission, reflection, and trapping with abrupt transitions between them as the potential depth varies [35, 36]. There exist significant differences between the dynamics described by the ordinary cubic 1D GPE and predictions of the full 3D equation, as the excitation of transverse oscillations (the feature which is obviously absent in the 1D description) becomes prominent for N → Nc. On the other hand, the quasi-1D NPSE is found to be in reasonable agreement with the 3D GPE both in regard to its static properties ( the stable branch of solutions at low N is captured more accurately than the unstable collapsing one of high N ) and to the dynamics of soliton-barrier interactions.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call