Laser phase effect on asymmetric harmonic distribution in H₂⁺

The laser phase effect on the spatial distribution of the molecular high-order harmonic generation (MHHG) spectrum from H₂⁺ is theoretically investigated through solving the Non-Bohn-Oppenheimer (NBO) time-dependent Schrödinger equation (TDSE). The results are shown as follows. (i) The generated harmonics from the two nuclei each present an asymmetric distribution. Particularly, when the laser phases are chosen from 0.0π to 0.6π and from 1.7π to 2.0π, the contribution from the negative-H plays a main role in harmonic generation. When the laser phases are chosen from 0.7π to 1.6π, the contribution from the positive-H to the harmonic generation is remarkably enhanced and becomes greater than that from the negative-H. The electron localization, the time-frequency analyses of the harmonic spectrum and the time-dependent wave function are shown to explain the asymmetric harmonic distribution in H₂⁺, which provides us with a method to control the electron motion in molecules. (ii) As the pulse duration increases, the asymmetric distributions of the MHHG in two H nuclei decrease. (iii) Isotope investigation shows that the asymmetric harmonic distribution can be reduced by introducing the heavy nucleus (i.e., D₂⁺).