Effect of pressure-dependent quantum interference on the ac Stark shifting of two-photon resonances

We describe ac Stark shift production and measurement in a two-laser mode where a first laser is tuned through a two-photon resonance between the ground state and an excited state in order to record a line shape for the corresponding resonantly enhanced multiphoton ionization. A second laser is tuned to a fixed wavelength which is close to a resonance between the upper state in the two-photon transition and a third state which has dipole-allowed transitions back to the ground state. At low concentrations the second laser leads to very large ac Stark shifts in the two-photon excitation and in the related resonantly enhanced multiphoton ionization. However, at high concentrations a destructive interference occurs involving the three-photon coupling between the third state and the ground state and the one-photon coupling due to the four-wave-mixing field at frequency 2${\mathrm{\omega }}_{\mathit{L}1}$±${\mathrm{\omega }}_{\mathit{L}2}$. This interference leads to a pressure-dependent suppression of the amplitude for the third state. When this destructive interference occurs, the ac Stark shift due to the second laser undergoes a corresponding pressure-dependent suppression. The criteria for the pressure to be high enough to completely suppress the ac Stark shift is that the real part of phase mismatch ‖Δk‖ at the angular frequency 2${\mathrm{\omega }}_{\mathit{L}1}$±${\mathrm{\omega }}_{\mathit{L}2}$ and (or) the absorption coefficient β at the same frequency should be very large, so that with unfocused focused beams ‖Δk‖L>5[(${\mathrm{\Delta }}_{\mathit{s}}^{\mathrm{}\left(\max \right)\mathrm{}}$τ${]}^{1/2}$, where L is the thickness of gas penetrated before the shift is measured, ${\mathrm{\Delta }}_{\mathit{s}}^{\mathrm{}\left(\max \right)\mathrm{}}$ is the maximum ac Stark shift at very low pressure, and τ is the pulse length of the lasers.