Theory of the effect of odd-photon destructive interference on optical shifts in resonantly enhanced multiphoton excitation and ionization

We present a theory for two- and three-photon excitation, optical shifting, and four-wave mixing when a first laser is tuned onto, or near, a two-photon resonance and a second much more intense laser is tuned near or on resonance between the two-photon resonance and a second excited state. When the second excited state has a dipole-allowed transition back to the ground state and the concentration is sufficiently high, a destructive interference is produced between three-photon coupling of the ground state and the second excited state and one-photon coupling between the same states by the internally generated four-wave mixing field. This interference leads to several striking effects. For instance, as the onset of the interference occurs, the optical shifts in the two-photon resonance excitation line shape become smaller in copropagating geometry so that the line shapes for multiphoton ionization enhanced by the two-photon resonance eventually become unaffected by the second laser. In the same range of concentrations the four-wave mixing field evolves to a concentration-independent intensity. With counterpropagating laser beams the line shape exhibits normal optical shifts like those observed for both copropagating and counterpropagating laser beams at very low concentrations. The theoretical work presented here extends our earlier works by including the effect of laser bandwidth and by removing the restriction of having the second laser be tuned far from three-photon resonance. In this way we have now included, as a special case, the effect of both laser bandwidth and interference on laser-induced transparency. Unlike other effects related to odd-photon destructive interference, the effect of a broad bandwidth is to bring about the predicted effects at much lower concentrations. Studies in rubidium show good agreement between theory and experiment for both ionization line shapes and four-wave mixing intensity as a function of concentration.