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

11 pages, 4 figures, 1 appendixWe 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 increasesWe acknowledge partial financial support from the DGI (Spain) Grant No. FIS2011-24154 and FIS2013-41757-P; the Generalitat de Catalunya Grant No 2009SGR-1003, 2014SGR940 and 2009SGR21. We acknowledge also support from EU grants OSYRIS (ERC-2013-AdG Grant No 339106), SIQS (FP7-ICT-2011-9 No 600645), EU STREP QUIC (H2020-FETPROACT- 2014 No 641122), EQuaM (FP7/2007–2013 Grant No 323714), Spanish Ministry grant FOQUS (FIS2013-46768-P), the Generalitat de Catalunya project 2014 SGR 874, and Fundació Cellex. J T is supported by grants FPA2013-46570, 2014-SGR-104 and Consolider grant CSD2007-00042 (CPAN). Financial support from the Spanish Ministry of Economy and Competitiveness, through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522) is acknowledgedPeer Reviewe