Shaped Post-Field Electronic Oscillations in H2+ Excited by Two-Cycle Laser Pulses: Three-Dimensional Non-Born-Oppenheimer Simulations.

Quantum dynamics of H2+ excited by two-cycle laser pulses with laser carrier frequencies corresponding to the wavelengths λl = 800 and 200 nm (corresponding to the periods τl = 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 Schrödinger equation within a three-dimensional (3D) model, including the internuclear distance R and electron coordinates z and ρ. The amplitudes of the pulses have been chosen such that the energies of H2+ after the ends of the laser pulses, {E} ≈; -0.515 au, were close to the dissociation threshold of H2+. It is found that there exists a certain characteristic oscillation frequency ωosc = 0.2278 au (corresponding to the period τosc = 0.667 fs and the wavelength λosc = 200 nm) that plays the role of a "carrier" frequency of temporally shaped oscillations of the expectation values {-∂;V/∂;z} emerging after the ends of the laser pulses, both at λl = 800 nm and at λl = 200 nm. Moreover, at λl = 200 nm, the expectation value {z} also demonstrates temporally shaped oscillations after the end of the laser pulse. In contrast, at λ= 800 nm, the characteristic oscillation frequency ωosc = 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} ≈; 0 afterward. It is found that the period of the temporally shaped post-field oscillations of {-∂;V/∂;z} and {z}, estimated as τshp ≈; 30 fs, correlates with the nuclear motion. It is also shown that vibrational excitation of H2+ 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 H2+ calculated for both the laser-driven z and optically passive ρ degrees of freedom in the acceleration form proved to be very interesting. In particular, both odd and even harmonics can be observed. [ABSTRACT FROM AUTHOR]