  We investigate the many-body dissipative dynamics of fermionic atoms in an
optical lattice in the presence of incoherent light scattering. Deriving and
solving a master equation to describe this process microscopically for many
particles, we observe contrasting behaviour in terms of the robustness against
this type of heating for different many-body states. In particular, we find
that the magnetic correlations exhibited by a two-component gas in the Mott
insulating phase should be particularly robust against decoherence from light
scattering, because the decoherence in the lowest band is suppressed by a
larger factor than the timescales for effective superexchange interactions that
drive coherent dynamics. Furthermore, the derived formalism naturally
generalizes to analogous states with SU(N) symmetry. In contrast, for typical
atomic and laser parameters, two-particle correlation functions describing
bound dimers for strong attractive interactions exhibit superradiant effects
due to the indistinguishability of off-resonant photons scattered by atoms in
different internal states. This leads to rapid decay of correlations describing
off-diagonal long-range order for these states. Our predictions should be
directly measurable in ongoing experiments, providing a basis for
characterising and controlling heating processes in quantum simulation with
fermions.
