Lattice bosons in a quasi-disordered environment: The effects of a superlattice potential on single particle and many particle properties

TL;DR

This paper theoretically explores how a superlattice potential influences localization, mobility edges, and Bose-Einstein condensation in one-dimensional bosonic systems with Aubry-André disorder, revealing complex phase transitions and condensate depletion effects.

Contribution

It introduces a detailed analysis of the combined effects of superlattice potentials and disorder on bosonic localization and condensation in 1D lattices, highlighting re-entrant transitions and mobility edge development.

Findings

Re-entrant localization-delocalization transition observed.

Multiple mobility edges develop with superlattice strength.

Superlattice increases condensate depletion at low temperatures.

Abstract

In this paper we present a theoretical investigation of the effect of a superlattice potential on some properties of non-interacting bosons in one dimensional lattices with Aubry-And\'re disorder potential. In the first part, we investigate the single particle localization properties. We find a re-entrant localization-delocalization transition and the development of multiple mobility edges for a range of superlattice potential strengths. In the second part, we study the Bose-Einstein condensation with an additional harmonic trapping potential. We find that an increase in the superlattice potential leads to an increase in the depletion of the condensate in the low temperature limit.