In femtosecond degenerate four-wave mixing experiments in sodium vapor, quantum beats are observed at the wavelength of the third harmonic when the fundamental beams are three-photon resonant. The period of beating, which corresponds to fine structure energy-level splitting, does not change with the atomic number density, buffer gas pressure, or laser intensity. Surprisingly, the third-harmonic signal is observed only at negative time delays for the transient grating pulse sequence. We relate this to the well-known interference effect between excitation pathways involving the fundamental and the third-harmonic fields, which leaves atoms virtually unexcited and prevents formation of population grating.
We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and \ensuremath{\Vert}\ensuremath{\Delta}
krL\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}
kr is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when \ensuremath{\Vert}\ensuremath{\Delta}
krb\ensuremath{\Vert}\ensuremath{\gg}1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.
The effect of temporal coherent control on the two-photon resonant third-harmonic generation in the continuum of ionization of an atomic system is experimentally investigated by means of a pair of partially incoherent, identical laser pulses. The evidence of quantum interference in the third-harmonic generation, as a function of delay between pulses, is reported. The transition from a resonant to a nonresonant case is also shown. The results agree with the predictions of a recently published theoretical model showing that the onset of quantum interference appears to be related to the coherence time of the laser radiation that is much shorter than the pulse duration.