Progress of Theoretical Physics

Nonlinear Excitations in a Matter-Photon System

Sachio Takeno

Published Dec 1, 1975• 1 citation

Abstract

A quantum theory of nonlinear excitations in a matter-photon system is developed by generalizing the conventional two-level-atom model of a matter in several directions, on the assumption that the overlapping of atomic wave functions on different atomic sites is negligible.The model matter Hamiltonian is shown to be expressible in a generalized form' of the Heisenberg model Hamiltonian with anisotropic long-range exchange interactions with spin operators replaced by quasi-Pauli operators.From approxirpate formal solutions of a set of nonlinear equations satisfied by the quasi-Pauli operators ~nd photon operators, brief discussion is given on nonlinear Frenkel excitons and nonlinear exciton-photon coupled modes.An attempt is made to formulate a theory of higher-order nonlinear physical properties of the matter-photon system by including interactions of magnetic as •well as electric dipoles of atoms with photons.A brief discussion is also given on the coherence properties. of the matter-photon system which are characterized by the simultaneo~s existence of •a photon coherent state and an atomic-polarization coherent state.*> Throughout this paper, we will often use a simplified .notation l, rather than l 1, whenever appropriate, to avoid the use of complicated symbols.Also, the complex conjugate of a quantity• A is denoted by A*.

DOI: 10.1143/ptp.54.1616

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