  We demonstrate and study the enhancement of intermediate-field two-photon
absorption by shaped femtosecond pulses having spectral phases of antisymmetric
nature. The intermediate-field regime corresponds to pulse intensities, where
the two-photon absorption is coherently induced by the weak-field nonresonant
two-photon transitions as well as by additional resonance-mediated four-photon
transitions. It is a regime of significant excitation yields, exceeding the
weak-field yields by two orders of magnitudes, reaching about 10-20% population
transfer. The considered antisymmetric nature is with respect to one-half of
the (initial-to-final) two-photon transition frequency. The corresponding pulse
spectrum is detuned from this frequency (the detuning direction is according to
the system). We study in detail the coherent interference mechanism leading to
the observed enhancement using forth-order frequency-domain perturbative
analysis. We also show that, even though the maximal enhancement is achieved
with phase patterns of perfect antisymmetry, at high enough intermediate-field
intensities absorption enhancement beyond the transform-limited level is still
achievable even with patterns having some degree of deviation from perfect
antisymmetry. The degree of tolerance to deviations from perfect antisymmetry
increases as the pulse intensity increases. The theoretical and experimental
model system of the study is atomic sodium. These findings are of particular
importance for coherent control scenarios that simultaneously involve multiple
excitation channels.
