Solitary Matter Waves in Combined Linear and Nonlinear Potentials: Detection, Stability, and Dynamics

TL;DR

This paper investigates the existence, stability, and dynamics of solitary matter waves in Bose-Einstein condensates with spatially varying interactions, combining analytical and computational methods to reveal how inhomogeneities affect wave stability.

Contribution

It introduces a novel experimental setup with compensating linear and nonlinear potentials and provides a detailed analytical and computational analysis of solitary wave stability in inhomogeneous BECs.

Findings

Dark solitary waves are unstable for all step widths.

Bright solitary waves can become stable via a symmetry-breaking bifurcation.

The study combines effective-potential theory and Bogoliubov-de Gennes analysis.

Abstract

We study statically homogeneous Bose-Einstein condensates with spatially inhomogeneous interactions and outline an experimental realization of compensating linear and nonlinear potentials that can yield constant-density solutions. We illustrate how the presence of a step in the nonlinearity coefficient can only be revealed dynamically and consider, in particular, how to reveal it by exploiting the inhomogeneity of the sound speed with a defect-dragging experiment. We conduct computational experiments and observe the spontaneous emergence of dark solitary waves. We use effective-potential theory to perform a detailed analytical investigation of the existence and stability of solitary waves in this setting, and we corroborate these results computationally using a Bogoliubov-de Gennes linear stability analysis. We find that dark solitary waves are unstable for all step widths, whereas bright solitary waves can become stable through a symmetry-breaking bifurcation as one varies the step width. Using phase-plane analysis, we illustrate the scenarios that permit this bifurcation and explore the dynamical outcomes of the interaction between the solitary wave and the step.