Delocalization and spreading in a nonlinear Stark ladder

Abstract

We study the evolution of a wave packet in a nonlinear Schrödinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. With increasing strength of nonlinearity we observe: (I) localization as a transient, with subsequent subdiffusion (weak mode-mode interactions); (II) immediate subdiffusion (strong mode-mode interactions); (III) single site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For single mode excitations and weak nonlinearities stability intervals are predicted and observed upon variation of the dc bias strength, which affect the short and long time dynamics.

4 pages, 5 figures

References in corpus (4)

• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at micrometer scale
• Control of Interaction-Induced Dephasing of Bloch Oscillations

Cited by in corpus (24)

• Localization from Hilbert space shattering: from theory to physical realizations
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Interaction induced fractional Bloch and tunneling oscillations
• Nonlinear lattice waves in heterogeneous media
• Bose-Einstein condensates on tilted lattices: coherent, chaotic and subdiffusive dynamics
• Realization of Discrete Quantum Billiard in 2D Optical Lattices
• Correlated metallic two particle bound states in quasiperiodic chains
• Wave interactions in localizing media - a coin with many faces
• Interacting Fermionic Atoms in Optical Lattices Diffuse Symmetrically Upwards and Downwards in a Gravitational Potential
• Quasiperiodic driving of Anderson localized waves in one dimension
• Many-body quantum dynamics of initially trapped systems due to a Stark potential --- thermalization vs. Bloch oscillations
• Nonlinear Lattice Waves in Random Potentials
• Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain
• Subdiffusion in classical and quantum nonlinear Schrödinger equations with disorder
• Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model
• Coexistence of insulating phases in confined fermionic chains with a Wannier-Stark potential
• Simulating DNLS models
• Nonequilibrium Nonlinear Effects and Dynamical Boson Condensation in a Driven-Dissipative Wannier-Stark Lattice
• Modulation stabilization of Bloch oscillations of two-component Bose-Einstein condensates in optical lattices
• Bloch oscillations sustained by nonlinearity
• Observation of asymmetric solitons in waveguide arrays with refractive index gradient
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems