Lamb and ac Stark shifts in cavity quantum electrodynamics*

Abstract A quantum system consisting of a single-mode microcavity and a two-level quantum dot or atom placed inside this microcavity, the interaction of monoenergetic photons in the microcavity with the electron in the two-level quantum dot or atom being the allowed electrical dipole transition between two energy levels, is a basic element of prospective devices for quantum information processing. Its time evolution is governed by cavity quantum electrodynamics (CQED). The photon–electron coupling induces the shifts of energy levels of the electron in the two-level quantum dot or atom. If there is no photon in the microcavity, then the shift of electron energy levels is induced by the radiative corrections and it is called the Lamb shift. The presence of photons in the microcavity induces another type of electron energy level shift—the ac Stark shift. In this paper, we present the exact derivation of the formulae for the Lamb and ac Stark shifts of electron energy levels in the two-level quantum dot or atom placed inside a single-mode microcavity.