Atom in a coherent superposition state reveals an advantage in the enhancement conversion efficiency of high-order harmonic generation (HHG), which is meaningful in producing attosecond pulses. In this study, we expand to investigate a more complicated system, H\(_2^+\) molecule in the superposition of the ground and second excited states, exposed to an ultrashort intense laser pulse by numerically solving the time-dependent Schrödinger equation. Firstly, we examine the enhancement of HHG from this system. Then, we study the depletion effect on the cutoff energy of HHG spectra with the coherent superposition state. We found that these effects on the HHG from molecules are similar to those from atoms. Finally, we study the signature of the interesting effect, which is absent for atoms -- two-center interference effect in the HHG from H\(_2^+\) in the coherent superposition state. We recognize that the minimum positions in HHG from molecules in the superposition state, and in the pure ground state are the same. Especially, for weak laser intensity, in the HHG with the superposition state, the minimum due to the interference effect is apparent, while it is invisible in the HHG from pure ground state. As a result, in comparison with the ground-state molecule, the coherent molecule can be used as a more accurate tool to determine the internuclear distance of molecule.
Femtosecond X-rays Produced by Inverse Compton Scattering between a Low Emittance Electron Beam and an Intense Laser Light.