  We propose a method to obtain a regular arrangement of two-level atoms in a
three-dimensional optical lattice with unit filling, where all the atoms share
internal state coherence and metrologically useful quantum correlations. Such a
spin-squeezed atomic crystal is obtained by adiabatically raising an optical
lattice in an interacting two-component Bose-Einstein condensate. The scheme
could be directly implemented on a microwave transition with state-of-the art
techniques and used in optical-lattice atomic clocks with bosonic atoms to
strongly suppress the collisional shift and benefit from the spins quantum
correlations at the same time.
