A proposed signature of Anderson localization and correlation-induced delocalization in an N-leg optical lattice

TL;DR

This paper proposes a cold atom optical lattice setup to observe Anderson localization and correlation-induced delocalization, identifying critical energies and symmetry-dependent signatures in momentum distributions.

Contribution

It introduces N-leg optical lattice models exhibiting multiple delocalization energies and analyzes their localization properties and symmetry effects.

Findings

Multiple delocalization energies depend on Hamiltonian symmetry.

Dips in momentum distribution signal localization-delocalization transitions.

N-leg systems show similarities and differences with 1D models.

Abstract

We propose a realization of the one-dimensional random dimer model and certain N-leg generalizations using cold atoms in an optical lattice. We show that these models exhibit multiple delocalization energies that depend strongly on the symmetry properties of the corresponding Hamiltonian and we provide analytical and numerical results for the localization length as a function of energy. We demonstrate that the N-leg systems possess similarities with their 1D ancestors but are demonstrably distinct. The existence of critical delocalization energies leads to dips in the momentum distribution which serve as a clear signal of the localization-delocalization transition. These momentum distributions are different for models with different group symmetries and are identical for those with the same symmetry.