Theoretical approaches to laser spectroscopy in the presence of gravitational fields

Abstract

We present a general framework in which non-linear optical phenomena for an ensemble of accelerated atoms can be studied. We show the equivalence of various approaches through frame transformations. This equivalence is understood within the context of a covariant formalism which is briefly sketched. The choice of the frame, in which the atoms are not accelerated but where the light spectrum and the atomic source term are correspondingly modified, leads to the simplest calculation. It enables one to use the usual density matrix diagrams and associated rules. Explicit examples are given in the case of a sinusoidal gravitational wave. Finally a brief discussion of the signal-to-noise ratio of the sidebands induced by gravitational waves on saturation resonances is outlined Presentation d'un cadre theorique general pour l'etude des processus d'optique non lineaire, relatifs a un ensemble d'atomes acceleres. Demonstration de l'equivalence de differentes approches grâce a des changements de systeme de reference, en particulier dans le cas d'un formalisme covariant. Simplification des calculs par le choix du systeme de reference ou les atomes ne sont pas acceleres mais ou le contenu spectral de la lumiere et le terme de pompage atomique sont modifies en consequence. Calculs explicites dans le cas d'une onde de gravitation sinusoidale. Discussion du rapport signal/bruit des raies laterales induites par les ondes de gravitation sur les resonances de saturation