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

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.

15 pages, 5 figures

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Measurement of the mobility edge for 3D Anderson localization
• Observation of Quantized Conductance in Neutral Matter
• Observing the Drop of Resistance in the Flow of a Superfluid Fermi Gas
• Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator
• Ordered structures in rotating ultracold Bose gases
• Symmetry breaking in small rotating cloud of trapped ultracold Bose atoms
• Superfluid Bloch dynamics in an incommensurate lattice
• Quasihole dynamics as a detection tool for quantum Hall phases

Cited by in corpus (5)

• Atomtronics-enabled Quantum Technologies
• Few strongly interacting ultracold fermions in one-dimensional traps of different shapes
• Evolution of an ultracold gas in a non-Abelian gauge fields: Finite temperature effect
• Emulation of magneto-optic Faraday effect using ultracold atoms
• Few-particle systems: An analysis of some strongly correlated states