Perturbative development, molecular photonics

To describe the shifts and intensities of the m-photon assisted collisional resonances with the microwave field Pillet et al. developed a picture based on dressed molecular states,3 and we follow that development here. As in the previous chapter, we break the Hamiltonian into an unperturbed Hamiltonian H(h and a perturbation V. The difference from our previous treatment of resonant collisions is that now H0 describes the isolated, noninteracting, atoms in both static and microwave fields. Each of the two atoms is described by a dressed atomic state, and we construct the dressed molecular state as a direct product of the two atomic states. The dipole-dipole interaction Vis still given by Eq. (14.12), and using it we can calculate the transition probabilities and cross sections for the radiatively assisted collisions. 

The procedures for many-body perturbation calculations (MBPT) for atomic and molecular systems are nowadays very well developed, and the dominating electrostatic as well as magnetic perturbations can be taken to essentially all orders of perturbation theory (see, for instance, [1]). Less pronounced, but in many cases still quite significant, are the quantum electrodynamical (QED) perturbations—retardation, virtual pairs, electron self-energy, vacuum polarization and vertex correction. Sophisticated procedures for their evaluation have also been developed, but for practical reasons such calculations are prohibitive beyond second order (two-photon exchange). Pure QED effects beyond that level can be expected to be very small, but the combination of QED and electrostatic perturbations (electron correlation) can be significant. However, none of the previously existing methods for MBPT or QED calculations is suited for this type of calculation. 

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