Stable symmetry-protected 3D embedded solitons in Bose-Einstein condensates

TL;DR

This paper demonstrates the theoretical existence and stability of three-dimensional embedded solitons in Bose-Einstein condensates within optical lattices, highlighting their robustness and potential for experimental realization.

Contribution

It introduces the first demonstration of stable 3D embedded solitons in Bose-Einstein condensates protected by symmetry, expanding the understanding of nonlinear localized structures in quantum gases.

Findings

Stable 3D embedded solitons exist in BECs with optical lattices.

These solitons are robust against weak perturbations.

The study suggests potential for experimental observation of matter-wave embedded solitons.

Abstract

Embedded solitons are rare self-localized nonlinear structures that, counterintuitively, survive inside a continuous background of resonant states. While this topic has been widely studied in nonlinear optics, it has received almost no attention in the field of Bose-Einstein condensation. In this work, we consider experimentally realizable Bose-Einstein condensates loaded in one-dimensional optical lattices and demonstrate that they support continuous families of stable three-dimensional (3D) embedded solitons. These solitons can exist inside the resonant continuous Bloch bands because they are protected by symmetry. The analysis of the Bogoliubov excitation spectrum as well as the long-term evolution after random perturbations proves the robustness of these nonlinear structures against any weak perturbation. This may open up a way for the experimental realization of stable 3D matter-wave embedded solitons as well as for monitoring the gap-soliton to embedded-soliton transition.