Stability of polarizable materials against superradiant phase transition

TL;DR

This paper investigates the stability of the normal ground state in polarizable materials against superradiant phase transition, showing that certain dipole interactions do not induce such a transition under specific conditions.

Contribution

It clarifies the conditions under which superradiant phase transition is prevented in polarizable materials, especially regarding the role of dipole-dipole interactions and field coupling.

Findings

Longitudinal dipole-dipole interaction does not enable superradiant transition when fields are decoupled.

Elimination of dipole interactions in the electric-dipole gauge is limited to non-overlapping dipoles.

Normal ground state remains stable in inhomogeneous systems if homogeneous case is stable.

Abstract

The possibility of the superradiant phase transition in polarizable materials described by the minimal-coupling Hamiltonian with the longitudinal dipole-dipole interaction is examined. We try to reduce the Hamiltonian into the Dicke one in homogeneous and infinite case, and discuss the stability of normal ground state by the formalism of Green function in spatially inhomogeneous case. The presence of the longitudinal dipole-dipole interaction does not enable the superradiant phase transition, if the transverse and longitudinal fields are decoupled. Although the full dipole-dipole interaction can be eliminated in the electric-dipole gauge in the absence of overlap between individual atomic dipoles, we cannot reduce the Hamiltonian to the Dicke one, because the elimination is justified only if all the transverse and longitudinal fields remain. Even if the transverse and longitudinal fields are mixed in spatially inhomogeneous systems, the normal ground state is still stable if the system does not show the superradiant phase transition in the homogeneous case.