Dynamics of Macroscopic Tunneling in Elongated BEC

TL;DR

This paper studies the macroscopic tunneling behavior of elongated Bose-Einstein condensates, revealing shock waves and soliton formations through analytical and numerical methods.

Contribution

It introduces a new formalism for analyzing tunneling in elongated BECs and presents numerical results showing shock waves and soliton trains.

Findings

Observation of a 'blip' in particle density traveling with shock velocity

Revealed dispersive shock wave patterns inside the BEC

Found trains of bright solitons near the boundary in attractive cases

Abstract

We investigate macroscopic tunneling from an elongated quasi 1-d trap, forming a 'cigar shaped' BEC. Using recently developed formalism we get the leading analytical approximation for the right hand side of the potential wall, i.e. outside the trap, and a formalism based on Wigner functions, for the left side of the potential wall, i.e. inside the BEC. We then present accomplished results of numerical calculations, which show a 'blip' in the particle density traveling with an asymptotic shock velocity, as resulted from previous works on a dot-like trap, but with significant differences from the latter. Inside the BEC a pattern of a traveling dispersive shock wave is revealed. In the attractive case, we find trains of bright solitons frozen near the boundary.