Ultracold atoms confined in an optical lattice have been utilized as a powerful platform to
study versatile many-body physics both experimentally and theoretically. A recent research
focus has been the novel phenomena that would emerge with long-range interactions,
which become especially important for atomic clocks where ultrahigh precision can amplify
these effects. We develop theoretical models treating the two-level atoms as oscillators and
study the synchronization of phases among a large ensemble of atoms coupled by dipole …