Fractional quantum Hall effect with cold atoms

Abstract

This work presents an introduction to the simulation of the Fractional Quantum Hall Effect with cold neutral atoms. In order to do this we perform the study of the energy spectrum of a neutral particle moving in a two dimensional square lattice. First, we analyse the Hamiltonian in absence of magnetic Feld. Then, we observe how the Hamiltonian changes undergoing artifcial and uniform magnetic feld, the so-called Hofstadter model. Finally, we reach the famous energy spectrum given by Hofstadter butterfly[1]