  Quantum simulations of Fermi-Hubbard models have been attracting considerable
efforts in the optical lattice research, with the ultracold anti-ferromagnetic
atomic phase reached at half filling in recent years. An unresolved issue is to
dope the system while maintaining the low thermal entropy. Here we propose to
achieve the low temperature phase of the doped Fermi-Hubbard model using
incommensurate optical lattices through adiabatic quantum evolution. In this
theoretical proposal, we find that one major problem about the adiabatic doping
that shows up is atomic localization in the incommensurate lattice, potentially
causing exponential slowing down of the adiabatic procedure. We study both one-
and two-dimensional incommensurate optical lattices, and find that the
localization prevents efficient adiabatic doping in the strong lattice regime
for both cases. With density matrix renormalization group calculation, we
further show that the slowing down problem in one dimension can be circumvented
by considering interaction induced many-body delocalization, which is
experimentally feasible using Feshbach resonance techniques. This protocol is
expected to be efficient as well in two dimensions where the localization
phenomenon is less stable.
