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.

arXiv comment8 pages (with Supplemental Material), 4 figures

References in corpus (20)

• A spin-orbit coupled Bose-Einstein condensate
• Synthetic magnetic fields for ultracold neutral atoms
• Light-induced gauge fields for ultracold atoms
• Spin-orbit coupling in quantum gases
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Historical roots of gauge invariance
• A synthetic electric force acting on neutral atoms
• Spin-orbit coupling effects on quantum transport in lateral semiconductor dots
• Tunable Spin-Orbit Coupling via Strong Driving in Ultracold Atom Systems
• Solitons in Bose-Einstein Condensates with Helicoidal Spin-Orbit Coupling
• Tunable spin-orbit coupling synthesized with a modulating gradient magnetic field
• Probing variations of the Rashba spin-orbit coupling at the nanometer scale
• Diffusive and precessional spin dynamics in a two-dimensional electron gas with disorder: a gauge theory view
• Bose-Einstein condensates with localized spin-orbit coupling: soliton complexes and spinor dynamics
• A method to generate complex quasi-nondiffracting optical lattices
• Theory of spin noise in nanowires
• Self-trapping under the two-dimensional spin-orbit-coupling and spatially growing repulsive nonlinearity
• Generation of arbitrary complex quasi-non-diffracting optical patterns
• Macroscopic random Paschen-Back effect in ultracold atomic gases

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• Stable two-dimensional soliton complexes in Bose-Einstein condensates with helicoidal 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
• Spin-orbit-coupled spinor gap solitons in Bose-Einstein condensates
• Quenching dynamics of the bright solitons and other localized states in spin-orbit coupled Bose-Einstein condensates
• Stationary and moving bright solitons in Bose-Einstein condensates with spin-orbit coupling in a Zeeman field
• Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling
• Four-wave mixing in spin-orbit coupled Bose-Einstein condensates
• Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning
• Spin-dependent localization of spin-orbit and Rabi-coupled Bose-Einstein condensates in a random potential
• Superexponential amplification, power blowup, and solitons sustained by non-Hermitian gauge potentials