Bright solitary waves of trapped atomic Bose-Einstein condensates

TL;DR

This paper investigates the stability and dynamics of bright solitary waves in trapped Bose-Einstein condensates, revealing that phase differences critically influence collapse and longevity, with detailed simulations aligning with experimental observations.

Contribution

The study provides a theoretical analysis of phase-dependent stability of bright solitary waves in BECs, including collapse thresholds and long-term dynamics, supported by numerical simulations.

Findings

In-phase waves are highly unstable and prone to collapse.

π-phase difference stabilizes solitary waves, matching experimental results.

Intermediate phase differences cause population asymmetries leading to collapse.

Abstract

Motivated by recent experimental observations, we study theoretically multiple bright solitary waves of trapped Bose-Einstein condensates. Through variational and numerical analyses, we determine the threshold for collapse of these states. Under $\pi$-phase differences between adjacent waves, we show that the experimental states lie consistently at the threshold for collapse, where the corresponding in-phase states are highly unstable. Following the observation of two long-lived solitary waves in a trap, we perform detailed three-dimensional simulations which confirm that in-phase waves undergo collapse while a $\pi$-phase difference preserves the long-lived dynamics and gives excellent quantitative agreement with experiment. Furthermore, intermediate phase differences lead to the growth of population asymmetries between the waves, which ultimately triggers collapse.