Dissociation dynamics of ultracold atom-molecule mixtures in an optical lattice

We consider a gas of two-component fermionic atoms coupled to bosonic molecules via photoassociation in an optical lattice. The system consists initially of bosonic molecules only, assumed to be in a ground state corresponding to either a Mott-Insulator phase or a Superfluid phase. 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 show that the observation of Rabi-like oscillations between atomic and molecular populations detects the number statistics and coherence properties between different lattice sites, and then provides useful information on the many-body ground states and interactions in the system.