  Using exact diagonalization for a small system of cold bosonic atoms, we
analyze the emergence of strongly correlated states in the presence of an
artificial magnetic field. This gauge field is generated by a laser beam that
couples two internal atomic states, and it is related to Berry's geometrical
phase that emerges when an atom follows adiabatically one of the two
eigenstates of the atom--laser coupling. Our approach allows us to go beyond
the adiabatic approximation, and to characterize the generalized Laughlin wave
functions that appear in the strong magnetic field limit.
