Relation between collective Lamb shifts and the high-pressure odd-photon cancellation effect

Abstract

When three-photon atomic excitation is produced by two laser beams of angular frequencies ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}1}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}2}$, which are crossed at an angle \ensuremath{\theta}, large cooperative pressure-dependent shifts can be produced in the peak position of the excitation line shape. Such shifts occur when the transition between states is dipole allowed in both one and three photons. When \ensuremath{\theta} or ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}2}$/${\mathrm{\ensuremath{\omega}}}_{\mathit{L}1}$ is small, these shifts are very large compared to the pressure broadened width of the line. Our analysis shows that for small \ensuremath{\theta} or small ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}2}$/${\mathrm{\ensuremath{\omega}}}_{\mathit{L}1}$, where the shift is large, the excitation is suppressed near the unperturbed resonance due to a destructive interference between the three-photon excitation by the laser and one-photon excitation due to the four-wave-mixing field, whereas the shifted resonance appears at the position where the atoms interact through ``resonant'' four-wave-mixing photons that are phase matched with the laser field. By studying an experimental situation in xenon we show that the theoretical predictions are in precise agreement with experiment for several angles and a wide range of pressures.