Coherence domains in matter interacting with radiation

The coupling of the electromagnetic field to matter polarization (dipole interaction) is examined in order to assess the possibility of setting up a coherent state as envisaged by Preparata and coworkers [G. Preparata, QED Coherence in Matter, World Scientific, 1995, and references therein]. It is found that coherence domains may set up in matter, their phases being arranged in a periodic lattice, as a consequence of, basically, a two-level interaction, which leads to a long-range ordered state, governed by a macroscopic occupation of both the photon state and the two levels. The non-linear equations of motion are solved for the new, non-perturbative ground-state, which is energetically favourable, provided the coupling strength exceeds a critical value. The elementary excitations with respect to this ground-state are derived, their energy being non-trivially affected by interaction. The “thermodynamics” of the coherent phase is computed and the super-radiant phase transition is re-derived in this context. Except for the general suggestion of coherence, the present results differ appreciably from Preparata's, loc cit.