Entanglement and spin-squeezing in a network of distant optical lattice clocks

We propose an approach for collective enhancement of precision for remotely located optical lattice clocks and a way of generation of the Einstein-Podolsky-Rosen state of remote clocks. Close to Heisenberg scaling of the clock precision with the number of clocks M can be achieved even for an optical channel connecting clocks with substantial losses. This scenario utilizes a collective quantum nondemolition measurement on clocks with parallel Bloch vectors for enhanced measurement precision. We provide an optimal network solution for distant clocks as well as for clocks positioned in close proximity of each other. In the second scenario, we employ collective dissipation to drive two clocks with oppositely oriented Bloch vectors into a steady state entanglement. The corresponding EPR entanglement provides enhanced time sharing beyond the projection noise limit between the two quantum synchronized clocks protected from eavesdropping, as well as allows better characterization of systematic effects.