High harmonic spectroscopy of electron localization in the hydrogen molecular ion

Interaction of a laser pulse with a centrally symmetric medium, such as an isotropic gas of atoms, leads to the generation of harmonic emission which contains exclusively odd harmonics of the incident field. This result is the consequence of both the central symmetry of the medium and the temporal symmetry of the oscillating electric field, E(t+π/ωl)=−E(t), where ωl is the laser frequency. In the case of oriented heteronuclear molecules, the spatial symmetry no longer holds and both odd and even harmonics become allowed. Here we show, by solving the time-dependent Schrödinger equation for H2+, D2+, and T2+, that even-order harmonic generation is also possible for sufficiently long infrared (IR) laser pulses in homonuclear molecules. The appearance of even harmonics is a signature of the coupled electron-nuclear dynamics and reflects field-induced electron localization initiated by the strong laser field, which breaks the spatial symmetry in the system. The analysis of even harmonics generated by pulses of different durations might therefore provide information on correlated electron-nuclear dynamics and charge migration in more complex un-oriented molecular ensembles. (paper)