Entangling the lattice clock: Towards Heisenberg-limited timekeeping

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.