Nonlinear waves in a cylindrical Bose-Einstein condensate

TL;DR

This paper investigates solitary wave solutions in a cylindrical Bose-Einstein condensate, revealing a transition from quasi-1D solitons to complex vortex ring hybrids as interaction strength increases, with implications for understanding nonlinear excitations.

Contribution

It provides a comprehensive analysis of solitary waves in a cylindrical BEC, highlighting the emergence of vortex ring hybrids at higher couplings beyond simple 1D models.

Findings

Weak couplings are well-described by 1D models.

Stronger couplings produce hybrid solitons and vortex rings.

Energy-momentum dispersion shows Lieb mode and roton-like features.

Abstract

We present a complete calculation of solitary waves propagating in a steady state with constant velocity v along a cigar-shaped Bose-Einstein trap approximated as infinitely-long cylindrical. For sufficiently weak couplings (densities) the main features of the calculated solitons could be captured by effective one-dimensional (1D) models. However, for stronger couplings of practical interest, the relevant solitary waves are found to be hybrids of quasi-1D solitons and 3D vortex rings. An interesting hierarchy of vortex rings occurs as the effective coupling constant is increased through a sequence of critical values. The energy-momentum dispersion of the above structures is shown to exhibit characteristics similar to a mode proposed sometime ago by Lieb within a strictly 1D model, as well as some rotonlike features.