Modulation of spin-orbit coupled Bose-Einstein condensates: analytical characterization of acceleration-induced transitions between energy bands

Abstract: The effects of modulating spin-orbit coupled Bose-Einstein condensates are analytically studied. A sinusoidal driving of the coupling amplitude is shown to induce significant changes in the energy bands and in the associated spin-momentum locking. Moreover, in agreement with recent experimental results, gravitational acceleration of the modulated system is found to generate transitions between the modified energy bands. The applicability of the Landau-Zener (LZ) model to the understanding of the experimental findings is rigorously traced. Through a sequence of unitary transformations and the reduction to the spin space, the modulated Hamiltonian, with the gravitational potential incorporated, is shown to correspond to an extended version of the LZ scenario. The generalization of the basic LZ model takes place along two lines. First, the dimensionality is enlarged to combine the description of the external dynamics with the internal-state characterization. Second, the model is extended to incorporate two avoided crossings emerging from the changes induced in the energy bands by the modulation. Our approach allows a first-principle derivation of the effective model-system parameters. The obtained analytical results provide elements to control the transitions.