  Considering a system of ultracold atoms in an optical lattice, we propose a
simple and robust implementation of a quantum simulator for the homogeneous t-J
model with a well-controlled fraction of holes x. The proposed experiment can
provide valuable insight into the physics of cuprate superconductors. A similar
scheme applied to bosons, moreover, allows one to investigate experimentally
the subtle role of inhomogeneity when a system passes from one quantum phase to
another.
