Two-body collisions in the time-of-flight dynamics of lattice Bose superfluids

We investigate two-body collisions occurring during the time-of-flight expansion of interacting three-dimensional lattice Bose superfluids. The number of collisions is extracted from the observed s-wave scattering halos located between the diffraction peaks of the superfluids. These faint halos can be monitored thanks to the large dynamical range in densities associated with detecting individual metastable Helium atoms. We monitor the number of collisions as a function of the total atom number and of the amplitude of the lattice, in a regime where the number of trapped atoms per lattice site is large. In addition, we introduce a classical model of collisions that quantitatively describes the experiment without adjustable parameters. Finally, the present work validates quantitatively the assumption of a ballistic expansion when investigating the Bose-Hubbard Hamiltonian with a unity occupation of the lattice.