Multi-solitonic states in a Bose-Einstein Condensate mixture
G. Brochier
Once its phase-space density is high enough, an interacting dilute Bose gas can be described by a macroscopic wave function obeying nonlinear dynamics. Ultracold Bose gases thus form coherent quantum fluids whose behavior becomes particularly rich in one dimension, where interactions and integrability tightly guide the evolution. In this thesis, we study a two-component weakly interacting 1D Bose gas that maps onto the attractive nonlinear Schrödinger equation (NLSE) in a certain limit, and more generally onto the Landau-Lifshitz equation (LLE), governing spin-chains. This correspondence enables the controlled preparation and exploration of multi-soliton solutions of both models. We first realize NLSE multi-solitons and characterize their dynamics, including their distinctive breathing behavior. Using the full LLE mapping, we then extend this implementation to multi-solitons with arbitrary depletion, thereby accessing a broader family of solitons and revealing features intrinsic to the underlying spin-chain description. Finally, we investigate weak integrability breaking and show that it drives the decomposition of multi-solitons into their constituents, rendering their encoded scattering data experimentally accessible. This provides a controlled pathway to probe integrable structures, opening prospects for studying soliton gases, interacting nonlinear waves, and the emergence of complex dynamics from nearly integrable systems.
•Mar 13, 2026•0 citations