Nonadiabatic effects in the molecular high-order harmonic generation from two-center molecular ions

The nonadiabatic effects in the molecular high-order harmonic generation (MHHG) from H-2 + and its isotope have been theoretically investigated beyond the Born-Oppenheimer approximations. It is found that (i) due to the asymmetric contributions of the harmonic emission on the rising and the falling parts of the laser field, the frequency red-shifts in the MHHG can be found. As the initial vibrational state or the pulse intensity increases, the red-shifts of the harmonics are decreased and even the blue-shifts of the harmonics can be found in the higher pulse intensity with the higher vibrational state. With the increase of the pulse duration, the frequency red-shifts and the blue-shifts in the MHHG are decreased and enhanced, respectively. The shifts of the harmonics from the heavy nuclei are decreased compared with those from the light nuclei. (ii) Due to the coupling of the electron-nuclear dynamics, the non-odd harmonics can be produced at the larger internuclear distance. With the increase of the initial vibrational state or the pulse duration, the generations of the non-odd harmonics can be enhanced. As the pulse intensity increases, the intensities of the non-odd harmonics are first increased and then decreased at the much larger pulse intensity. Due to the slower nuclear motion, the generations of the non-odd harmonics are decreased as the nuclear mass increases. (iii) With the increase of the alignment angle of the molecule ions, the nonadiabatic effects in MHHG (including the shifts of the harmonics and the generations of the non-odd harmonics) are decreased.