Quantum simulation of conductivity plateaux and fractional quantum Hall effect using ultracold atoms

TL;DR

This paper proposes a method to simulate and analyze the fractional quantum Hall effect and conductivity plateaux using ultracold atoms with impurities, providing insights into strongly correlated states and transport phenomena.

Contribution

It introduces a theoretical framework for observing quantum Hall effects and conductivity plateaux in ultracold atom systems with impurities, using exact diagonalization and dynamic analysis.

Findings

Identification of conductivity plateaux linked to particle localization transitions

Conditions for strongly correlated states to produce observable plateaux

Proposal for experimental detection of fractional quantum Hall states in ultracold gases

Abstract

We analyze the role of impurities in the fractional quantum Hall effect using a highly controllable system of ultracold atoms. We investigate the mechanism responsible for the formation of plateaux in the resistivity/conductivity as a function of the applied magnetic field in the lowest Landau level regime. To this aim, we consider an impurity immersed in a small cloud of an ultracold quantum Bose gas subjected to an artificial magnetic field. We consider scenarios corresponding to experimentally realistic systems with gauge fields induced either by rotation or by appropriately designed laser fields. Systems of this kind are adequate to simulate quantum Hall effects in ultracold atom setups. We use exact diagonalization for few atoms and, to emulate transport equations, we analyze the time evolution of the system under a periodic perturbation. We provide a theoretical proposal to detect the up-to-now elusive presence of strongly correlated states related to fractional filling factors in the context of ultracold atoms. We analyze the conditions under which these strongly correlated states are associated with the presence of the resistivity/conductivity plateaux. Our main result is the presence of a plateau in a region, where the transfer between localized and non-localized particles takes place, as a necessary condition to maintain a constant value of the resistivity/conductivity as the magnetic field increases.