Depolarization shift of the superradiant phase transition

We investigate the possibility of a Dicke-type superradiant phase transition of an atomic gas with an extended model which takes into account the short-range depolarizing interaction between atoms that approach each other as close as the atomic size scale, which interaction appears in a regularized electric-dipole picture of the QED of atoms. By using a mean-field model, we find that a critical density does indeed exist, though the atom-atom contact interaction shifts it to a higher value than that from the bare Dicke model.