Events in Physics

Matter-wave scattering from interacting ultracold bosons in optical lattices

We study matter-wave scattering from ultracold bosons in a one-dimensional optical lattice described by a Bose-Hubbard Hamiltonian. The phase transition from the superfluid (SF) state to the Mott insulator (MI) is clearly displayed in the decay of the inelastic scattering cross-section for increasing onsite interaction U/J [1]. We obtain analytical expressions for the cross-section from a Bogoliubov expansion, valid in the regime of small condensate depletion, and from a strong-coupling expansion, valid in the regime of large interactions U/J. This allows for the description of the inelastic cross-section’s decay in the entire range of the relevant system parameters, excluding the vicinity of the critical point of the MI-SF phase transition. In the weak-interaction regime, the cross section is found to decay linearly, with a slope that is independent of the bosonic density and the system size [2]. In the strong-interaction regime, the decay is quadratic and vanishes only as U/J → ∞, resulting in a non-vanishing inelastic cross section throughout the entire Mott phase [3]. To support our analytical results, we present numerical studies obtained from exact diagonalization methods.

[1] S. Sanders, F. Mintert, E. Heller, PRL 105, 035301 (2010)
[2] K. Mayer, A. Rodriguez, A. Buchleitner, PRA 90, 023629 (2014)
[3] K. Mayer, A. Rodriguez, A. Buchleitner, PRA 91, 053633 (2015)