Time-dependent model calculations for a molecular hydrogen ion in a strong ultra-short laser pulse

Abstract

We have revisited the problem of a hydrogen molecular ion in the presence of a short intense laser field. Our approach for time-propagation the initial state subject to the Schrödinger equation is similar to that presented by Kulander et al. [1]. A common simplification to the full problem is the reduction to one dimension with two degrees of freedom, one for the nuclear separation (R) and one for the electronic motion along the internuclear (z) axis, with the electric field also along this axis. The goals of the present project are: 1) to apply our method, developed for e-H collisional excitation and ionization [2], to an explicitly time-dependent problem; 2) to check different time-propagation schemes; 3) to visualize the results; 4) to extract the physics by projection techniques; and 5) to try avoiding masking potentials that reduce the norm of the wavefunction.Going beyond the Born-Oppenheimer approximation, we solve the time-dependent Schrödinger equationby time-propagating the initial statewhere G 1σg R (z) is the electronic ground state for fixed R and F The screening parameters q n = 0.03 and q e = 1.0 are used to smooth out the Coulomb singularity. The term z f(t) E 0 sin(ωt) represents the effect of the electric field with amplitude E 0 and angular frequency ω. Finally, f (t) is a smooth turn-on/turn-off function for the field.We have used intensities of 1−2×10 18 W/m 2 , turn-on/turn-off times of 2−4 periods, and ontimes up to about 20 periods. We also follow the system for several periods after the pulse is over. Typical observables to calculate are < R(t) > and < z(t) >. However, < R(t) > has limited meaning since it includes vibration, dissociation, and Coulomb explosion; the same is true for < z(t) >. Looking at the complete nuclear and electronic distributions reveals significantly more information.We therefore created movies to watch for bond-stretching and bond-healing, vibrational excitation, dissociation (electron stays with one of the protons) and ionization (electron leaves the system and protons undergo "Coulomb explosion"). Links to these movies can be found at http://bartschat.drake.edu/. We are currently working on our projection techniques to find, for example, the probability of exciting a particular vibrational and/or electronic state.

Dissociative ionization ofH2+using intense femtosecond XUV laser pulses

“…In this work, we investigate dissociative ionization of H 2 + by direct numerical propagation of the time-dependent Schrödinger equation (TDSE) for a reduced-dimensionality model of H 2 + , treating both the electronic and nuclear degrees of freedom exactly within the limitations of the reduced dimensions. Such models have been studied extensively in the literature and reproduce experimental results at least qualitatively for lasers in the visible and infrared regimes [19][20][21]. Recently, the dynamic interference effect observed in a one-dimensional model of hydrogen was compared to the effect in the threedimensional case, and the one-dimensional model was shown to be adequate for the qualitative description of dynamic interference [17].…”

“…We consider a simplified model for H 2 + with reduced dimensionality that includes only the dimension that is aligned with a linearly polarized laser pulse [19][20][21]. Within this model, electronic and nuclear degrees of freedom are treated exactly.…”

Multiconfiguration time-dependent Hartree approach for electron-nuclear correlation in strong laser fields

“…In the present work, we apply the multiconfiguration theory for the first time to the case of coupled electronic and nuclear motion. We use a onedimensional (1D) model H 2 + system [26][27][28][29][30][31][32] to compare exact simulations to the MCTDH method with various numbers of configurations. For laser parameters that are typically used in present-day experiments, we find that a moderate number of single-particle functions is sufficient to provide accurate quantitative results for fragmentation probabilities and HHG spectra.…”

Intensity enhancement in the molecular ionization and dissociation dynamics in the presence of noise

“…q is the soft Coulomb potential and a, b (a00.03 and b01.0 [33] in this paper) represent the softening parameters to remove the Coulomb singularity [26,34], the use of which provides an efficient way to obtain realistic numerical results for multiphoton processes [26][27][28]35]. The most important feature of this potential is that at large z it falls off like the true Coulomb potential (a0 b00 is the true Coulomb potential), and it was proved previously that the physical characteristics of this model have allowed realistic investigations of the behavior of a H 2 + ion in a laser field [26,29].…”