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

By Núria Barberán Falcón, D. Dagnino, M. A. Garcia-March, Andrea Trombettoni, Josep Taron i Roca and M. Lewenstein

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 by rotation of the trapping parabolic potential. 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

Topics: Càlcul fraccional, Efecte Hall quàntic, Transport biològic, Àtoms, Fractional calculus, Quantum Hall effect, Biological transport, Atoms
Publisher: Institute of Physics Pub.
Year: 2016
DOI identifier: 10.1088/1367-2630
OAI identifier: oai:diposit.ub.edu:2445/100382
Journal:

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