  We present a study of the possibility to significantly enhance the efficiency
of high-order harmonic generation (HHG) using few-cycle optical waveforms
obtained by superposing two laser pulses of different color delayed optimally
relative to each other. Special attention is paid to the dynamics of the
depopulation of atomic states, which, one the one hand, promotes electrons to
the continuum to take part in the high-energy photon emission, but, on the
other hand, depletes the nonlinear medium. The use of the waveforms proposed
here gives extra flexibility to control both the bound-state depopulation and
the electron acceleration in the continuum. We demonstrate that the approach
proposed here allows to increase by up to order of magnitude the efficiency of
optical frequency conversion into sub-keV or few-keV photon energy ranges. High
efficiency of HHG in optimal conditions is explained by the peculiarities of
the photoelectron dynamics, which are in this case characterized by a
combination of high-probability ejection of the electron responsible for the
highest-order harmonic production and its subsequent strong acceleration
accompanied by a relatively low probability of the bound-state depletion during
the time interval between ionization and recollision.
