Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

TL;DR

This paper investigates the transition to localization and superfluidity in a weakly interacting quasi-1D Bose gas within a quasiperiodic potential, using numerical methods to analyze how interactions and lattice ratios influence the transition.

Contribution

It provides a detailed numerical analysis of the localization transition in a weakly interacting Bose gas under quasiperiodic potentials, highlighting the effects of lattice incommensurability and weak interactions.

Findings

Transition sharper at maximally incommensurate ratios

Weak repulsive interactions shift the transition to higher lattice strengths

Results relate to recent experimental observations

Abstract

Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach, we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.