Reconstruction of the electronic flux during adiabatic attosecond charge migration in HCCI+

Recently, it was shown that a well-designed laser pulse may prepare an oriented linear molecular ion in a specific superposition state of the electronic ground (g) and first excited (e) states, with different amplitudes and non-zero phases. The reconstruction of the initial state, with time resolution of 100 attoseconds (as), yields the subsequent charge migration that proceeds adiabatically, on the attosecond time scale (AACM). We develop the theory for the time evolutions of the axial density and the flux of the electrons, during AACM. The flux is obtained by simple scaling and time-shifting the results for the 'reference' scenario with equal amplitudes and zero phases. Application to the system HCCI+ confirms periodic AACM of a rather small number (0.663) of valence electrons, from the acetylenic moiety to the domain of the iodine, and back, with period = 1.85 fs. The underlying axial electronic flux is always unidirectional, with maximum absolute value at the border between the acetylenic moiety and the domain of the iodine, close to the local minimum of the axial density of the valence electrons and to its zero time derivative. The theoretical results imply new challenges for experiment, e.g. one should apply optimal control to steer AACM with maximum electronic flux, and one should investigate its initiation with time resolution below 100 as.