Strongly correlated states of a small cold atomic cloud from geometric gauge fields

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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.