Large pressure-dependent cooperative shifts in multicolor odd-photon resonant atomic excitation

We show that when three-photon excitation of a dipole-allowed transition is mediated by two laser beams at angular frequencies ${\mathrm{\omega }}_{\mathit{L}1}$ and ${\mathrm{\omega }}_{\mathit{L}2}$ that are crossed at an angle θ, large cooperative pressure-dependent shifts occur in the line shape for resonant excitation. When excitation of the state is by a 2${\mathrm{\omega }}_{\mathit{L}1}$±${\mathrm{\omega }}_{\mathit{L}2}$ process and either θ≪1 or ${\mathrm{\omega }}_{\mathit{L}1}$≫${\mathrm{\omega }}_{\mathit{L}2}$, the cooperative shift is large compared with the pressure-induced width of the line. For the 2${\mathrm{\omega }}_{\mathit{L}1}$+${\mathrm{\omega }}_{\mathit{L}2}$ case the shift is toward higher excitation energy, while for 2${\mathrm{\omega }}_{\mathit{L}1}$-${\mathrm{\omega }}_{\mathit{L}2}$ the shift is to lower excitation energies. In cases where the resonance can be reached by more than one pathway, differing only in the directions of propagation of the photons involved in the excitation, multiple peaks are predicted in the excitation line shape.