Oscillations of Bose-Einstein condensates in a one-dimensional optical superlattice

Oscillations of atomic Bose-Einstein condensates in a 1D optical lattice with a two-point basis is investigated. In the low-frequency regime, four branches of modes are resolved, that correspond to the transverse in-phase and out-of-phase breathing modes, and the longitudinal acoustic and optical phonon modes of the condensates. Dispersions of these modes depend intimately on the values of two intersite Josephson tunneling strengths, J1 and J2, and the on-site repulsion U between the atoms. Observation of these mode dispersions is thus a direct way to access them.