Resonant excitations of a Bose Einstein condensate in an optical lattice

We investigate experimentally a Bose Einstein condensate placed in a 1D optical lattice whose phase or amplitude is modulated in a frequency range resonant with the first bands of the band structure. More precisely, we study the effect of the strength of a weak extra external confinement superimposed to the lattice on the 1 and 2-phonon transitions. We identify lines immune or very sensitive to the external confinement despite many orders of magnitude of difference in strength compared to the lattice. We interpret those features and present 1D numerical simulations including atom-atom interactions consistent with the experimental observations. Using the band mapping technique, we also get a direct access to the populations that have undergone n -phonon transitions for each modulation frequency including for non-zero quasi-momentum.