Probing the energy bands of a Bose-Einstein condensate in an optical lattice

We simulate three experimental methods which could be realized in the laboratory to probe the band excitation energies and the momentum distribution of a Bose-Einstein condensate inside an optical lattice. The values of the excitation energies obtained in these different methods agree within the accuracy of the simulation. The meaning of the results in terms of density and phase deformations is tested by studying the relaxation of a phase-modulated condensate towards the ground state.