  We present a scheme for entangling the atoms of an optical lattice to reduce
the quantum projection noise of a clock measurement. The divalent clock atoms
are held in a lattice at a ``magic'' wavelength that does not perturb the clock
frequency -- to maintain clock accuracy -- while an open-shell J=1/2 ``head''
atom is coherently transported between lattice sites via the lattice
polarization. This polarization-dependent ``Archimedes' screw'' transport at
magic wavelength takes advantage of the vanishing vector polarizability of the
scalar, J=0, clock states of bosonic isotopes of divalent atoms. The on-site
interactions between the clock atoms and the head atom are used to engineer
entanglement and for clock readout.
