A2 Term, Renormalization of Matter-Photon Interaction and Coherent States in Matter-Photon Systems

Abstract

A non-relativistic quantum theory of matter-photon interaction is formulated, within the framework of the dipole approximation, by employing a canonical transformation to diago­ nalize the A' term plus the free photon Hamiltonian. The matter-photon interaction is there­ by expressed rigorously in a renormalized A·p form. Using this form for the Dicke model of two-level atoms interacting with a single-mode radiation field, we examine a possibility of the occurrence of stationary coherent states which could arise for a photon and atomic polarization as the ground state of the system, deducing a condition for such coherent states. The condition, expressed as an inequality which imposes a stable nontrivial Bloch angle of the uniform atomic polarization, is identical with that for the occurrence of a second order phase transition, and indicates that the non-existence of a second order phase transition pointed out by Rza2ewski et al. io; in fact a consequence of the present treatment of the A'­ term renormalization. However, a fulfillment of the condition is recovered, if exchange­ type atom-atom interaction is taken into account in the matter system. We also present a method to construct an effective Hamiltonian of atom-atom interaction which is equivalent to the above Dicke model in the thermodynamic limit.