Ultracold atoms in a 1D optical lattice: Mott-Superfluid transition

Abstract

In this project, the transition between different quantum phases of ultracold bosonic systems trapped in an optical lattice is studied using the exact diagonalization method. First, the Mott Insulator to Superfluid transition is analyzed. Afterwards, the Density Wave phase is also considered. Specifically, a Julia programming language code is used to find the ground state of a system defined by a Bose-Hubbard Hamiltonian and the phase of this state is determined by means of specific observables derived from the occupation levels.