  There have been considerable research efforts devoted to quantum simulations
of Fermi-Hubbard model with ultracold atoms loaded in optical lattices. In such
experiments, the antiferromagnetically ordered quantum state has been achieved
at half filling in recent years. The atomic lattice away from half filling is
expected to host d-wave superconductivity, but its low temperature phases have
not been reached. In a recent work, we proposed an approach of incommensurate
quantum adiabatic doping, using quantum adiabatic evolution of an
incommensurate lattice for preparation of the highly correlated many-body
ground state of the doped Fermi-Hubbard model starting from a unit-filling band
insulator. Its feasibility has been demonstrated with numerical simulations of
the adiabatic preparation for certain incommensurate particle-doping fractions,
where the major problem to circumvent is the atomic localization in the
incommensurate lattice. Here we carry out a systematic study of the quantum
adiabatic doping for a wide range of doping fractions from particle-doping to
hole-doping, including both commensurate and incommensurate cases. We find that
there is still a localization-like slowing-down problem at commensurate
fillings, and that it becomes less harmful in the hole-doped regime. With
interactions, the adiabatic preparation is found to be more efficient for that
interaction effect destabilizes localization. For both free and interacting
cases, we find the adiabatic doping has better performance in the hole-doped
regime than the particle-doped regime. We also study adiabatic doping starting
from the half-filling Mott insulator, which is found to be more efficient for
certain filling fractions.
