Adiabatic Path to Fractional Quantum Hall States of a Few Bosonic Atoms

We propose a realistic scheme to create motional entangled states of a few bosonic atoms. It can experimentally be realized with a gas of ultra cold bosonic atoms trapped in a deep optical lattice potential. By simultaneously deforming and rotating the trapping potential on each lattice site it is feasible to adiabatically create a variety of entangled states on each lattice well. We fully address the case of N=2 and N=4 atoms per well and identify a sequence of fractional quantum Hall states: the Pfaffian state, the 1/2-Laughlin quasiparticle and the 1/2-Laughlin state. Exact knowledge of the spectrum has allowed us to design adiabatic paths to these states, with all times and parameters well within the reach of current experimental setups. We further discuss the detection of these states by measuring different properties as their density profile, angular momentum or correlation functions.