  We make a systematic study of high-order harmonic generation (HHG) in a
He$^+$-like model ion when the initial states are prepared as a coherent
superposition of the ground state and an excited state. It is found that,
according to the degree of the ionization of the excited state, the laser
intensity can be divided into three regimes in which HHG spectra exhibit
different characteristics. The pulse-duration dependence of the HHG spectra in
these regimes is studied. We also demonstrate evident advantages of using
coherent superposition state to obtain high conversion efficiency. The
conversion efficiency can be increased further if ultrashort laser pulses are
employed.
