  We consider the photodissociation of ground-state bosonic molecules trapped
in an optical lattice potential into two-component fermionic atoms. The system
is assumed to be described by a one-band resonantly-coupled Bose-Fermi Hubbard
model. We show that in the strong fermion-fermion interaction limit the
dissociation dynamics is governed by a spin-boson lattice Hamiltonian. In the
framework of a mean-field analysis based on the Gutzwiller ansatz, we then
examine the crossover of the dissociation from a regime of independent
single-site dynamics to a regime of cooperative dynamics as the molecular
tunneling increases. We also identify two types of self-trapping transitions, a
{\it coherent} and an {\it incoherent} one, depending on the ratio of the
repulsive molecule-molecule interaction strength to molecular tunneling.
Finally, we show that in the limits of weak and strong intersite tunneling the
mean-field solutions agree well with the results from the quantum optical
Jaynes-Cummings and Tavis-Cummings models, respectively.
