Simulation of the quantum Hall effect in a staggered modulated magnetic field with ultracold atoms

Abstract

With ultracold atoms in an optical lattice, we propose an experimental scheme to simulate and detect the integer quantum Hall effect and a peculiar phase transition in a uniform magnetic field and an additional staggered magnetic field. The phase transition is characterized by the direct change from Hall plateau state $N\ensuremath{-}1$ to $\ensuremath{-}1$ due to Chern number redistribution when the staggered magnetic field is varied. We propose the possibility to observe the Hall conductivity and the phase transition by varying experimental parameters and measuring the number density of the ultracold atoms.