Partially incoherent gap solitons in Bose-Einstein condensates

TL;DR

This paper constructs and analyzes the stability of incoherent gap solitons in Bose-Einstein condensates within optical lattices, revealing stable families and temperature effects on their properties.

Contribution

It introduces the first detailed construction and stability analysis of incoherent matter-wave gap solitons in a repulsive Bose gas with temperature considerations.

Findings

Intragap solitons are fully stable.

Intergap solitons may have small unstable eigenvalues but are stable in simulations.

Higher-order and bound solitons are also stable.

Abstract

We construct families of incoherent matter-wave solitons in a repulsive degenerate Bose gas trapped in an optical lattice (OL), i.e., gap solitons, and investigate their stability at zero and finite temperature, using the Hartree-Fock-Bogoliubov equations. The gap solitons are composed of a coherent condensate, and normal and anomalous densities of incoherent vapor co-trapped with the condensate. Both intragap and intergap solitons are constructed, with chemical potentials of the components falling in one or different bandgaps in the OL-induced spectrum. Solitons change gradually with temperature. Families of intragap solitons are completely stable (both in direct simulations, and in terms of eigenvalues of perturbation modes), while the intergap family may have a very small unstable eigenvalue (nevertheless, they feature no instability in direct simulations). Stable higher-order (multi-humped) solitons, and bound complexes of fundamental solitons are found too.