Matter-wave scattering from ultracold atoms in an optical lattice.

We study matter-wave scattering from an ultracold, many-body atomic system trapped in an optical lattice. The angular cross section of the target lattice for a matter wave is determined and is demonstrated to have a strong dependence on the many-body phase, superfluid, or Mott insulator. Analytical approaches are employed deep in the superfluid and Mott-insulator regimes, while intermediate points in the phase transition are treated numerically. Matter-wave scattering offers a convenient method for nondestructively probing the quantum many-body phase transition of atoms in an optical lattice.