Matter-wave solitons with a periodic, piecewise-constant nonlinearity

TL;DR

This paper investigates the existence and stability of matter-wave solitons in Bose-Einstein condensates with a spatially modulated, piecewise-constant nonlinearity, providing analytical approximations and numerical validation.

Contribution

It introduces a stitching method to analytically approximate soliton solutions in BECs with periodic, piecewise-constant nonlinearity and analyzes their stability properties.

Findings

Solitons exist only at the centers of constant nonlinearity regions.

Bright solitons can be stable or unstable depending on parameters.

All dark solitons are found to be unstable.

Abstract

Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a ``stitching'' approach to analytically approximate the pertinent solutions of the underlying nonlinear Schr\"odinger equation by matching the wavefunction and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that solitons can only exist at the centers of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.