Chaos in one-dimensional lattices under intense laser fields

TL;DR

This paper explores how intense laser fields induce chaos in electron dynamics within one-dimensional lattices, revealing a transition from regular to chaotic behavior and analyzing quantum effects like energy band fluctuations.

Contribution

It introduces a combined classical and quantum model of electron-laser interactions in 1D lattices, highlighting the onset of chaos and universal spectral fluctuations under intense fields.

Findings

Electron motion is regular at low laser amplitudes.

Chaotic regions expand with increasing field strength.

Quantum energy bands exhibit universal random-matrix fluctuations.

Abstract

A model is investigated where a monochromatic, spatially homogeneous laser field interacts with an electron in a one-dimensional periodic lattice. The classical Hamiltonian is presented and the technique of stroboscopic maps is used to study the dynamical behavior of the model. The electron motion is found to be completely regular only for small field amplitudes, developing a larger chaotic region as the amplitude increases. The quantum counterpart of the classical Hamiltonian is derived. Exact numerical diagonalizations show the existence of universal, random-matrix fluctuations in the electronic energy bands dressed by the laser field. A detailed analysis of the classical phase space is compatible with the statistical spectral analysis of the quantum model. The application of this model to describe transport and optical absorption in semiconductor superlattices submitted to intense infrared laser radiation is proposed.