Guennaddi K. Paramonov, O. Kuehn, Andre D. Bandrauk

• Quantum dynamics of H-2(+) excited by two-cycle laser pulses with laser carrier frequencies corresponding to the wavelengths lambda(1) = 800 and 200 nm (corresponding to the periods tau(1) = 2.667 and 0.667 fs, respectively) and being linearly polarized along the molecular axis have been studied by the numerical solution of the non-Born-Oppenheimer time-dependent Schrodinger equation within a three-dimensional (3D) model, including the internuclear distance R and electron coordinates z and rho. The amplitudes of the pulses have been chosen such that the energies of H-2(+) after the ends of the laser pulses, < E > approximate to-0.515 au, were close to the dissociation threshold of H-2(+). It is found that there exists a certain characteristic oscillation frequency omega(osc) = 0.2278 au (corresponding to the period tau(osc) = 0.667 fs and the wavelength lambda(osc) = 200 nm) that plays the role of a "carrier" frequency of temporally shaped oscillations of the expectation values <-partial derivative V/partial derivative z) emergingQuantum dynamics of H-2(+) excited by two-cycle laser pulses with laser carrier frequencies corresponding to the wavelengths lambda(1) = 800 and 200 nm (corresponding to the periods tau(1) = 2.667 and 0.667 fs, respectively) and being linearly polarized along the molecular axis have been studied by the numerical solution of the non-Born-Oppenheimer time-dependent Schrodinger equation within a three-dimensional (3D) model, including the internuclear distance R and electron coordinates z and rho. The amplitudes of the pulses have been chosen such that the energies of H-2(+) after the ends of the laser pulses, < E > approximate to-0.515 au, were close to the dissociation threshold of H-2(+). It is found that there exists a certain characteristic oscillation frequency omega(osc) = 0.2278 au (corresponding to the period tau(osc) = 0.667 fs and the wavelength lambda(osc) = 200 nm) that plays the role of a "carrier" frequency of temporally shaped oscillations of the expectation values <-partial derivative V/partial derivative z) emerging after the ends of the laser pulses, both at lambda(1) = 800 nm and at lambda(1) = 200 nm. Moreover, at lambda(1) = 200 nm, the expectation value < z > also demonstrates temporally shaped oscillations after the end of the laser pulse. In contrast, at lambda(1) = 800 nm, the characteristic oscillation frequency omega(osc) = 0.2278 au appears as the frequency of small-amplitude oscillations of the slowly varying expectation value < z > which makes, after the end of the pulse, an excursion with an amplitude of about 4.5 au along the z axis and returns back to < z > approximate to 0 afterward. It is found that the period of the temporally shaped post-field oscillations of <-partial derivative V/partial derivative z > and < z >, estimated as tau(shp) approximate to 30 fs, correlates with the nuclear motion. It is also shown that vibrational excitation of H-2(+) is accompanied by the formation of "hot" and "cold" vibrational ensembles along the R degree of freedom. Power spectra related to the electron motion in H-2(+) calculated for both the laser-driven z and optically passive rho degrees of freedom in the acceleration form proved to be very interesting. In particular, both odd and even harmonics can be observed.…