High harmonic spectroscopy of disorder-induced Anderson localization

TL;DR

This paper demonstrates that nonlinear optical responses can detect Anderson localization phase transitions by observing the emergence of symmetry-forbidden even-order harmonics in disordered quantum systems.

Contribution

It introduces a novel optical method to identify Anderson localization transitions through harmonic generation analysis in disordered Floquet lattices.

Findings

Emergence of even-order harmonics signals localization transition.

Harmonic intensity ratios map the phase transition.

Detection is possible even with minimal band structure changes.

Abstract

Exponential localization of wavefunctions in lattices, whether in real or synthetic dimensions, is a fundamental wave interference phenomenon. Localization of Bloch-type functions in space-periodic lattice, triggered by spatial disorder, is known as Anderson localization and arrests diffusion of classical particles in disordered potentials. In time-periodic Floquet lattices, exponential localization in a periodically driven quantum system similarly arrests diffusion of its classically chaotic counterpart in the action-angle space. Here we demonstrate that nonlinear optical response allows for clear detection of the disorder-induced phase transition between delocalized and localized states. The optical signature of the transition is the emergence of symmetry-forbidden even-order harmonics: these harmonics are enabled by Anderson-type localization and arise for sufficiently strong disorder even when the overall charge distribution in the field-free system spatially symmetric. The ratio of even to odd harmonic intensities as a function of disorder maps out the phase transition even when the associated changes in the band structure are negligibly small.