Solitons in inhomogeneous gauge potentials: integrable and nonintegrable dynamics

Abstract

We introduce an exactly integrable nonlinear model describing the dynamics of spinor solitons in space-dependent matrix gauge potentials of rather general types. The model is shown to be gauge equivalent to the integrable system of vector nonlinear Schrödinger equations known as the Manakov model. As an example we consider a self-attractive Bose-Einstein condensate with random spin-orbit coupling (SOC). If Zeeman splitting is also included, the system becomes nonintegrable. We illustrate this by considering the random walk of a soliton in a disordered SOC landscape. While at zero Zeeman splitting the soliton moves without scattering along linear trajectories in the random SOC landscape, at nonzero splitting it exhibits strong scattering by the SOC inhomogeneities. For a large Zeeman splitting the integrability is recovered. In this sense the Zeeman splitting serves as a parameter controlling the crossover between two different integrable limits.

8 pages (with Supplemental Material), 4 figures

References in corpus (6)

• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Tunable Spin-Orbit Coupling via Strong Driving in Ultracold Atom Systems
• Solitons in Bose-Einstein Condensates with Helicoidal Spin-Orbit Coupling
• Bose-Einstein condensates with localized spin-orbit coupling: soliton complexes and spinor dynamics
• Macroscopic random Paschen-Back effect in ultracold atomic gases

Cited by in corpus (7)

• Quantum solitons in spin-orbit-coupled Bose-Bose mixtures
• Stable nonlinear modes sustained by gauge fields
• Multidimensional hybrid Bose-Einstein condensates stabilized by lower-dimensional spin-orbit coupling
• Fundamental and second-order dark soliton solutions of 2- and 3-component Manakov equations in the defocusing regime
• Flat-floor bubbles, dark solitons, and vortices stabilized by inhomogeneous nonlinear media
• Quenching dynamics of the bright solitons and other localized states in spin-orbit coupled Bose-Einstein condensates
• Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling