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Intermediate-field two-photon absorption enhancement by shaped femtosecond pulses with spectral phases of antisymmetric nature

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.