# Heidelberg 2015 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 15: Poster: Quantum Optics and Photonics I

### Q 15.2: Poster

### Montag, 23. März 2015, 17:00–19:00, C/Foyer

**Matter-wave scattering from interacting ultracold bosons in optical lattices** — Klaus Mayer, •Alberto Rodriguez, and Andreas Buchleitner — Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg

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].
To understand the role of interactions in this process, 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. 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)

K. Mayer, A. Rodriguez, A. Buchleitner, PRA **90**, 023629 (2014)