  We propose that negative absolute temperatures in ultracold atomic clouds in
optical lattices can be used to simulate quantum systems in new regions of
phase diagrams. First we discuss how the attractive SU(3) Hubbard model in
three dimensions can be realized using repulsively interacting 173-Yb atoms,
then we consider how an antiferromagnetic S=1 spin chain could be simulated
using spinor 87-Rb or 23-Na atoms. The general idea to achieve negative
absolute temperatures is to reverse the sign of the external harmonic
potential. Energy conservation in a deep optical lattice imposes a constraint
on the dynamics of the cloud, which can relax toward a T<0 state. As the
process is strongly non-adiabatic, we estimate the change of the entropy.
