Self-consistent potential for a two-level atom in a standing-wave field

Abstract

It is shown that the effects of a standing electromagnetic wave of cosinusoidal form on a neutral two-level atom can be represented by an effective static potential, which is obtained by a local unitary transformation to dress the atom by the field. The form of the effective potential is obtained self-consistently by minimizing fluctuations of the atomic kinetic energy induced by the locality of the dressing transformation. Moreover this effective potential is shown to depend on the atom-field detuning and on the field intensity, and to exhibit discontinuities in some ranges of these parameters. The band structure which characterizes the eigenvalue spectrum of the dressed Hamiltonian is discussed in the spirit of the tight-binding approximation, and the fluctuations of the kinetic energy near resonance are shown to induce splitting of the bands; a physical interpretation of the atomic dynamics associated with these splittings is presented. Off resonance the fluctuations are shown to induce exchange of real photons and variations of the atomic kinetic energy. The results are compared with those of previous theories, leading to an improved understanding of the dynamics of a two-level atom in a standing-wave field.