Interaction of a two level atom with many photons

Abstract

The interaction of a two level atom with many photons in a continuum of modes is investigated on the base of a Weisskopf-Wigner theory of infinite order. Special emphasis is given to the problem whether a given “uncertainty” in the number of incident photons has observable effects upon the atom. This refers in particular to the special uncertainty related to the Poisson distribution of photons in a fully coherent state. It is shown that, if at all, the photon number uncertainty can only shift the atomic levels. These shifts are of the order of magnitude of the 2S _1/2−2P _1/2 level separation by Lambschifts. In an approximation in which these level shifts are omitted the photon number uncertainty has no effects upon the atom: The atom interacts simultaneously withall n-photon components of the incident beam, but inindependent interaction processes taking place in orthogonal Hilbert-spaces. Arguments are given to justify the mentioned approximation, a variant of the usual rotating wave approximation. This approximation reduces the Weisskopf-Wigner theory of infinite order to an infinite set of Weisskopf-Wigner theories of finite, lowest order. The latter govern the independent processes mentioned.