Effect of Nuclear Motion on Molecular High Order Harmonic Pump Probe Spectroscopy

We study pump-probe schemes for the real time observation of. electronic. motion on attosecond time scale in the molecular ion H-2(+), and its heavier isotope T-2(+) while these molecules dissociate on femtosecond time scale by solving numerically the non-Born-Oppenheimer time-dependent Schrodinger equation. The UV pump laser pulse prepares a coherent superposition of the three lowest lying quantum states and the time delayed mid infrared, intense few-femtosecond probe pulse subsequently generates molecular high-order harmonics (MHOHG) from this coherent electron-nuclear wavepacket (CENWP). Varying the pump-probe time delay by.a few hundreds of attoseconds, the MHOHG signal intensity is shown to vary by orders of magnitude. Due to nuclear movement, the coherence of these two upper states and the ground state is lost after a few femtoseconds and the MHOHG intensity variations as function of pump-probe delay time are shown to be equal to the period of electron oscillation in the coherent superposition of the two upper dissociative quantum states. Although this electron oscillation period and hence the periodicity of the harmonic spectra are quite constant over a wide range of internuclear distances, a strong signature of nuclear motion is seen in the actual shapes and ways in which these spectra change as a function of pump-probe delay time, which is illustrated by comparison of the MHOHG spectra generated by the two isotopes H-2(+) and T-2(+). Two different regimes corresponding roughly to internuclear distance's R < 4(a0) and R > 4(a0) are identified. For R < 4(a0), the intensity of a whole range of frequencies in the plateau region is decreased by orders of magnitude when the delay time is changed by a few hundred attoseconds whereas in the cutoff region the Peaks in the MHOHG spectra are red-shifted with increasing pump-probe time delay. For R > 4(a0), on the other hand, the peaks both in the cutoff and plateau region, are red-shifted with increasing delay times with only slight variations in the peak intensities. A time-frequency analysis shows that in the case of a two-cycle probe pulse the sole contribution of One long and associated short trajectory correlates-With the attenuation of a whole range of frequencies. in the plateau region for R < 4(a0) whereas the observed red shift for R > 4(a0), even in the plateau region, correlates with a single electron return within one-half laser cycle.