Adiabatic and diabatic responses of H2+ to an intense femtosecond laser pulse: Dynamics of the electronic and nuclear wave packet
Authors: Kawata Isao , Kono Hirohiko , Fujimura Yuichi 
Published: July 2002

We investigate the quantal dynamics of the electronic and nuclear wave packet of H2+ in strong femtosecond pulses (⩾1014 W/cm2). A highly accurate method which employs a generalized cylindrical coordinate system is developed to solve the time-dependent Schrödinger equation for a realistic three-dimensional (3D) model Hamiltonian of H2+. The nuclear motion is restricted to the polarization direction z of the laser electric field E(t). Two electronic coordinates z and ρ and the internuclear distance R are treated quantum mechanically without using the Born-Oppenheimer approximation. As the 3D packet pumped onto 1σu moves toward larger internuclear distances, the response to an intense laser field switches from the adiabatic one to the diabatic one; i.e., electron density transfers from a well associated with a nucleus to the other well every half optical cycle, following which interwell electron transfer is suppressed. As a result, the electron density is asymmetrically distributed between the two wells. Correlations between the electronic and nuclear motions extracted from the dynamics starting from 1σu can be clearly visualized on the time-dependent “effective” 2D surface obtained by fixing ρ in the total potential. The 2D potential has an ascending and descending valley along z=±R/2 which change places with each other every half cycle. In the adiabatic regime, the packet starting from 1σu stays in the ascending valley, which results in the slowdown of dissociative motion. In the diabatic regime, the dissociating packet localized in a valley gains almost no extra kinetic energy because it moves on the descending and ascending valleys alternately. Results of the 3D simulation are also analyzed by using the phase-adiabatic states |1〉 and |2〉 that are adiabatically connected with the two states 1σg and 1σu as E(t) changes. The states |1〉 and |2〉 are nearly localized in the descending and the ascending valley, respectively. In the intermediate regime, both |1〉 and |2〉 are populated because of nonadiabatic transitions. The interference between them can occur not only at adiabatic energy crossing points but also near a local maximum or minimum of E(t). The latter type of interference results in ultrafast interwell electron transfer within a half cycle. By projecting the wave packet onto |1〉 and |2〉, we obtain the populations of |1〉 and |2〉, P1 and P2, which undergo losses due to ionization. The two-state picture is validated by the fact that all the intermediates in other adiabatic states than |1〉 and |2〉 are eventually ionized. While E(t) is near a local maximum, P2 decreases but P1 is nearly constant. We prove from this type of reduction in P2 that ionization occurs mainly from the upper state |2〉 (the ascending well). Ionization is enhanced irrespective of the dissociative motion, whenever P2 is large and the barriers are low enough for the electron to tunnel from the ascending well. The effects of the packet’s width and speed on ionization are discussed.