We present a theory of two-photon resonance fluorescence of an atom or molecule in which the excitation by an external electromagnetic field as well as fluorescence emission is mediated by two-photon processes. The treatment is based on first dressing the atom or molecule by the external field and then evaluating perturbatively the effect of the interaction with the vacuum or fluorescent field and so resonance fluorescence can be considered as spontaneous emission from the dressed atom. The introduction of the combined system of atom and external field via dressed states leads to simpler calculations and more transparent physics. The fluorescence spectrum derived by us has similarities as well as differences with that of one-photon resonance fluorescence and earlier theoretical predictions for the two-photon case.
We examine squeezing properties of resonance fluorescence from two interacting atoms. Previous theoretical analyses of this model have predicted squeezing on one-photon resonance. Here we show that it is possible to obtain squeezing in two-atom resonance fluorescence through two-photon transitions induced by a cooperative atomic interaction. The squeezing occurs near a two-photon resonance and is not sensitive to the duration of the detection time in comparison with the decay time of the subradiant state. Moreover, squeezing near a two-photon resonance is completely independent of the direction of observation in respect to the atomic axis and can be significantly larger than that previously found on one-photon resonance.