Eliminating ground-state dipole moments in quantum optics via canonical transformation

Abstract

By means of a canonical transformation it is shown how it is possible to recast the equations for molecular nonlinear optics to completely eliminate ground-state static dipole coupling terms. Such dipoles can certainly play a highly important role in nonlinear optical response - but equations derived by standard methods, in which these dipoles emerge only as special cases of transition moments, prove unnecessarily complex. It has been shown that the elimination of ground-state static dipoles in favor of dipole shifts results in a considerable simplification in form of the nonlinear optical susceptibilities. In a fully quantum theoretical treatment the validity of such a procedure has previously been verified using an expedient algorithm, whose defense was afforded only by a highly intricate proof. In this paper it is shown how a canonical transformation method entirely circumvents such an approach; it also affords new insights into the formulation of quantum field interactions.