Collective resonances in $χ^{(3)}$; a QED study

Abstract: We calculate the third order susceptibility $\chi^{(3)}$ of a pair of 2 level atoms which interact via the exchange of photons. QED corrections to second order in coupling to vacuum field modes yield collective two photon absorption resonances which can be observed in transmission spectroscopy of shaped broadband pulses. While some collective effects can be obtained by introducing an effective interatomic coupling using a quantum master equation, the predicted signals contain clear features that are missed by that level of theory and require a full diagrammatic QED treatment.