Dissociative ionization of the H₂ molecule under a strong elliptically polarized laser field: carrier-envelope phase and orientation effect

Abstract

A coupled electron–nuclear dynamical study is performed to investigate the sub-cycle dissociation and ionization of the H2 molecule in a strong 750 nm 4.5 fs elliptically polarized laser pulse.

Strong Laser Field-Driven Coupled Electron–Nuclear Dynamics: Quantum vs Classical Description

“…In our present case, since the nuclei are restricted to move only along the polarization vector of the strong laser electric field, exclusion of molecular rotations seems to be a reasonably good assumption at first place. ,, This is consistent with the fact that the molecular rotation time scale ( T rot ∼ 1/ B e ∼ 10 4 , with B e being the rotational constant of the H 2 + molecule) is much larger than the time scales for the occurrence of ionization and dissociation processes initiated due to laser pulses with intensities above ∼10 13 W/cm 2 , more so for ultrashort laser pulses, where the interaction between molecule and the electric field can be regarded as “sudden” in comparison to rotation of the system. , Although incorporation of rotational–vibrational coupling phenomena originated due to the light-induced conical intersections effect , can have strong impact on the dissociation dynamics of H 2 + , we have excluded the molecular rotations, while the nuclei are free to move along the polarization direction of the laser electric field, and electrons move in three dimensions with conservation of cylindrical symmetry. On the other hand, within the present classical model, since the rotational motion is not restricted, the nonadiabatic effects can be captured as discussed in our previous study . However, to observe notable nonadiabatic effects, a longer pulse comparable to the rotational period of the molecule is needed .…”

“…For the first step, an ensemble of ∼10 5 molecules is formed by applying a similar sampling procedure. 42,56 In the second step, the prepared ensemble of for all the particles by using the adaptive fifth-order Runge− Kutta method, where Z is the nuclear charge and the laser electric field is given by E(t). The ensemble of trajectories evolved for a sufficiently long time after the pulse.…”

“…We have employed a quasi-classical method based on Heisenberg’s model potential, which is quite well tested − and has already been implemented in some of our previous studies on HD + and H 2 molecules. , Presently, we apply this model to a H 2 + molecular ion, which is a three-particle system consisting of two nuclei and one electron. The quasi-classical model is based on the Hamiltonian formulation of the classical mechanics, where the most crucial step is to define a total molecular Hamiltonian.…”

“…On the other hand, within the present classical model, since the rotational motion is not restricted, the nonadiabatic effects can be captured as discussed in our previous study. 56 However, to observe notable nonadiabatic effects, a longer pulse comparable to the rotational period of the molecule is needed. 81 Since, in the present study, the duration of the applied laser pulse is 4.5 fs, which is much smaller than the rotational period of the H 2 + molecule, the effect of rotational−vibrational coupling is expected to be negligible even if the molecular rotations are included (classically).…”

“…On a different note, Roudnev and Esry, in their theoretical study, proposed that CEP effects arise because of the superposition of electronic states with different parities, which, in turn, indicates that the CEP dependence is a quantum mechanical phenomenon. Understanding of such CEP-dependent coupled dynamics needs a fully quantum mechanical treatment , and requires the observation of both electronic and nuclear wave packet dynamics, simultaneously. − Indeed, during the interaction of a strong laser field, the dissociation and ionization phenomena occur concurrently , by following different pathways, where several control schemes were proposed to control as well as explain the electron localization phenomena. ,,, Due to this nonseparability of coupled electronic and nuclear degrees of freedom, − the solution of the time-dependent Schrödinger equation (TDSE) becomes extremely expensive, even for a one-electron system, for example, H 2 + , which requires propagation of both electronic and nuclear wave packets altogether. ,− To overcome the huge computational cost in quantum dynamics, alternate and computationally less-expensive methods based on classical mechanics had also been proposed in recent years, which have been able to successfully interpret several strong field experiments for atoms and molecules. ,− In the recent past, quasi-classical trajectory-based models − were employed to study the molecular double-ionization phenomena of molecules under the influence of intense laser fields, and also, some semiclassical theoretical methods , were used for studying electron collision–recollision dynamics and generation of higher order harmonics. Apart from the advantage in computational efficiency, trajectory-based classical models provide relatively easy interpretation of the observable by the back analysis of individual trajectories.…”