Signatures of the single particle mobility edge in the ground state properties of Tonks-Girardeau and non-interacting Fermi gases in a bichromatic potential

TL;DR

This paper investigates how the single particle mobility edge manifests in the ground state properties of Tonks-Girardeau and non-interacting Fermi gases in a bichromatic potential, bridging the gap between tight-binding and continuous regimes.

Contribution

It demonstrates that signatures of the mobility edge are observable in many-body properties, including momentum distribution, even with strong interactions.

Findings

Mobility edge position depends on potential strength.

Signatures of localization transition appear in ground state properties.

Momentum distribution reveals the mobility edge in experiments.

Abstract

We explore the ground state properties of cold atomic gases, loaded into a bichromatic lattice, focusing on the cases of non-interacting fermions and hard-core (Tonks-Girardeau) bosons, trapped by the combination of two potentials with incommensurate periods. For such systems, two limiting cases have been thoroughly established. In the tight-binding limit, the single-particle states in the lowest occupied band show a localization transition, as the strength of the second potential is increased above a certain threshold. In the continuous limit, when the tight-binding approximation does not hold anymore, a mobility edge is found, whose position in energy depends upon the strength of the second potential. Here, we study how the crossover from the discrete to the continuum behavior occurs, and prove that signatures of the localization transition and mobility edge clearly appear in the generic many-body properties of the systems. Specifically, we evaluate the momentum distribution, which is a routinely measured quantity in experiments with cold atoms, and demonstrate that, even in the presence of strong boson-boson interactions, the single particle mobility edge can be observed in the ground state properties.