Bloch-Landau-Zener Oscillations in Moiré Lattices

Abstract

We develop a theory of two-dimensional Bloch-Landau-Zener (BLZ) oscillations of wavepackets in incommensurate moiré lattices under the influence of a weak linear gradient. 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. We derive a multimode model describing BLZ oscillations in the linear regime and analyze how both attractive and repulsive nonlinearities affect their dynamics. The proposed framework can be readily extended to other physical systems, including cold atoms and Bose-Einstein condensates in aperiodic potentials.

References in corpus (15)

• Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at micrometer scale
• Optical soliton formation controlled by angle twisting in photonic moiré lattices
• Control of Interaction-Induced Dephasing of Bloch Oscillations
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Atomic Bose-Einstein condensate in a twisted-bilayer optical lattice
• Two-dimensional Thouless pumping of light in photonic moiré lattices
• Resonant tunneling of Bose-Einstein condensates in optical lattices
• Observation of linear and nonlinear light localization at the edges of moiré lattices
• Time-resolved measurement of Landau--Zener tunneling in different bases
• Wannier-Stark states and Bloch oscillations in the honeycomb lattice
• Bias driven coherent carrier dynamics in a two-dimensional aperiodic potential
• Wannier-Stark states in double-periodic lattices II: two-dimensional lattices
• Dimers and discrete breathers in Bose-Einstein condensates in a quasi-periodic potential
• Bloch-Landau-Zener oscillations in a quasi-periodic potential
• Irregular Bloch Zener oscillations in two-dimensional flat-band Dirac materials