Spatial Resonance Overlap in Bose-einstein condensates in superlattice Potentials

We employ Chirikov’s overlap criterion to investigate interactions between subharmonic resonances of coherent structure solutions of the Gross–Pitaveskii (GP) equation governing the mean-field dynamics of cigar-shaped Bose–Einstein condensates in optical superlattices. We apply a standing wave ansatz to the GP equation to obtain a parametrically forced Duffing equation describing the BEC’s spatial dynamics. We then investigate analytically the dependence of spatial resonances on the depth of the superlattice potential, deriving an order-of-magnitude estimate for the critical depth at which spatial resonances with respect to different lattice harmonics first overlap. We also derive a formula for the size of resonance zones and examine changes in our estimates as the relative superlattice amplitudes corresponding to the different harmonics are adjusted. We investigate the onset of global chaos and support our analytical work with numerical simulations.