  We demonstrate that it is possible to prepare a lattice gas of ultracold
atoms with a desired non-classical spin-correlation function using atom-light
interaction of the kind routinely employed in quantum spin polarization
spectroscopy. Our method is based on quantum non-demolition (QND) measurement
and feedback, and allows in particular to create on demand exponentially or
algebraically decaying correlations, as well as a certain degree of
multi-partite entanglement.
