Observation of tunable mobility edges in generalized Aubry-Andr\'{e} lattices

TL;DR

This paper experimentally observes tunable mobility edges in generalized Aubry-Andre9 lattices using laser-coupled atomic momentum modes, revealing interaction effects on localization properties and mobility edge behavior.

Contribution

It demonstrates the realization of a family of quasiperiodic models with an analytical mobility edge and investigates interaction effects on localization in these systems.

Findings

Observation of energy-dependent mobility edges.

Deviations from single-particle predictions due to interactions.

Enhanced localization of low-energy states and inhibited localization of high-energy states.

Abstract

Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one-dimensional tight-binding models can be viewed as a generalization of the well-known Aubry-Andr\'{e} (AA) model, with an energy-dependent self duality condition that constitutes an analytical mobility edge relation. By adiabatically preparing the lowest and highest energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the model's tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of the highest energy state due to screening. This study paves the way for quantitative studies of interaction effects on self duality induced mobility edges.