  Coherent control of femtosecond two-photon absorption in the
intermediate-field regime is analyzed in detail in the powerful frequency
domain using an extended 4th-order perturbative description. The corresponding
absorption is coherently induced by the weak-field non-resonant two-photon
transitions as well as by four-photon transitions involving three absorbed
photons and one emitted photons. The interferences between these two groups of
transitions lead to a difference between the intermediate-field and weak-field
absorption dynamics. The corresponding interference nature (constructive or
destructive) strongly depends on the detuning direction of the pulse spectrum
from half the two-photon transition frequency. The model system of the study is
atomic sodium, for which both experimental and theoretical results are
obtained. The detailed understanding obtained here serves as a basis for
coherent control with rationally-shaped femtosecond pulses in a regime of
sizable absorption yields.
