Symmetry approach to reveal hidden coherent structures in quantum optics. General outlook and examples

Abstract

A general invariant-algebraic approach to reveal hidden coherent structures (closed complexes and configurations of states) is developed in quantum-optical models due to symmetry of their HamiltonianH. This approach is based on using the mathematical concept of dual algebraic pairs, incorporating action of both invariance groups and dynamic-symmetry algebras. Its general features are demonstrated on some recent examples: (i)G-invariant biphotons and related invariant treatment of unpolarized light and (ii) quasispin clusters and optical atoms in nonlinear models of quantum optics. The first example leads to a positive solution (within the framework of composite field theory) of the old problem put in polarization optics by Fresnel—the existence of elementary waves of unpolarized light. The second example yields a new mathematical technique for analyzing a wide class of nonlinear problems in quantum optics and laser physics that, in turn, enables one to reveal new coherent effects and phenomena in the process of time evolution of the models under study.