  We present a proposal for a probing scheme utilizing Dicke superradiance to
obtain information about ultracold atoms in optical lattices. A probe photon is
absorbed collectively by an ensemble of lattice atoms generating a Dicke state.
The lattice dynamics (e.g., tunneling) affects the coherence properties of that
Dicke state and thus alters the superradiant emission characteristics -- which
in turn provides insight into the lattice (dynamics). Comparing the
Bose-Hubbard and the Fermi-Hubbard model, we find similar superradiance in the
strongly interacting Mott insulator regime, but crucial differences in the
weakly interacting (superfluid or metallic) phase. Furthermore, we study the
possibility to detect whether a quantum phase transition between the two
regimes can be considered adiabatic or a quantum quench.
