Year: 2025
Type: article
Abstract: A theory of two‐dimensional Bloch–Landau–Zener (BLZ) oscillations of wavepackets in incommensurate moiré lattices under the influence of a weak linear gradient is developed. Unlike periodic systems, aperiodic lattices lack translational symmetry and therefore do not exhibit a conventional band‐gap structure. Instead, they feature a mobility edge, above which (in the optical context) all modes become localized. When a linear gradient is applied to a moiré lattice, it enables energy transfer between two or several localized modes, leading to the oscillatory behavior referred to as BLZ oscillations. This phenomenon represents simultaneous tunneling in real space and propagation constant (energy) space, and it arises when quasi‐resonance condition for propagation constants and spatial proximity of interacting modes (together constituting a selection rule) are met. The selection rule is controlled by the linear gradient, whose amplitude and direction play a crucial role in determining the coupling pathways and the resulting dynamics. A multimode model describing BLZ oscillations in the linear regime is derived, and effects of both attractive and repulsive nonlinearities on their dynamics are analyzed. The proposed framework can be readily extended to other physical systems, including cold atoms and Bose–Einstein condensates in aperiodic potentials.
Source: Fortschritte der Physik
DOI: 10.1002/prop.70039
Language: English
Topic: Nonlinear Photonic Systems
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,460
OpenAlex ID: W4415201602