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 2ωL1±{}ωL2. 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 {}{Δ}k{} at the angular frequency 2ωL1±{}ωL2 and (or) the absorption coefficient {β} at the same frequency should be very large, so that with unfocused focused beams {}{Δ}k{}L>5[(Δₛ⁽ᵐᵃˣ⁾{τ}]1/2, where L is the thickness of gas penetrated before the shift is measured, Δₛ⁽ᵐᵃˣ⁾ is the maximum ac Stark shift at very low pressure, and {τ} is the pulse length of the lasers.At positions and concentrations such that 1{}{Δ}k{}L{≤}2[(Δₛ⁽ᵐᵃˣ⁾{τ})]1/2 the ac Stark shift is present but the two-photon excitation is suppressed due to a destructive interference between excitation by two photons from the first laser and by two-photon excitation between a four-wave-mixing photon and a photon from the second laser.