  Ultracold polar molecules provide an excellent platform to study quantum
many-body spin dynamics, which has become accessible in the recently realized
low entropy quantum gas of polar molecules in an optical lattice. To obtain a
detailed understanding for the molecular formation process in the lattice, we
prepare a density distribution where lattice sites are either empty or occupied
by a doublon composed of a bosonic atom interacting with a fermionic atom. By
letting this disordered, out-of-equilibrium system evolve from a well-defined
initial condition, we observe clear effects on pairing that arise from
inter-species interactions, a higher partial wave Feshbach resonance, and
excited Bloch-band population. When only the lighter fermions are allowed to
tunnel in the three-dimensional (3D) lattice, the system dynamics can be well
described by theory. However, in a regime where both fermions and bosons can
tunnel, we encounter correlated dynamics that is beyond the current capability
of numerical simulations. Furthermore, we show that we can probe the
microscopic distribution of the atomic gases in the lattice by measuring the
inelastic loss of doublons. These techniques realize tools that are generically
applicable to heteronuclear diatomic systems in optical lattices and can shed
light on molecule production as well as dynamics of a Bose-Fermi mixture.
