Speaker
E. K. U. Gross
(MPI Halle)
Description
This lecture is about how electronic motion can be
monitored, analyzed and, ultimately, controlled, in real
time. In particular:
(i) A novel approach to describe electronic transport
through single molecules or atomic wires, sandwiched between
semi-infinite leads, will be presented. The basic idea is to
propagate the time-dependent Kohn Sham equations in time
upon ramping up a bias between the metallic leads. In this
way, genuinely time-dependent phenomena, not accessible in
the standard Landauer approach, can be addressed. For
example, employing an Anderson model, we demonstrate that
Coulomb blockade corresponds, in the time-domain, to a
periodic charging and discharging of the quantum dot [1].
(ii) With modern pulse-shaping facilities, the control of
electronic motion is becoming more and more realistic. By
combining quantum optimal control theory with TDDFT, we
calculate shaped laser pulses suitable to control, e.g., the
chirality of currents in quantum rings [2], the location of
electrons in double quantum dots, as well as the enhancement
of a single peak in the harmonic spectrum of atoms and
molecules.
(iii) In all practical TDDFT calculations, approximate
forms of the exchange-correlation potential need to be
employed. One of the most popular approximations, the
adiabatic local-density approximation (ALDA) will be
analyzed as to whether the main error comes from the
adiabaticity assumption, i.e. locality in time, or from the
LDA, i.e. locality in space. For an exactly solvable model
where the exact adiabatic approximation can be extracted, we
find the surprising fact, that the adiabaticity assumption
can be an excellent approximation even in highly intense
laser fields [3].
(iv) Finally, the coupling between electronic and nuclear
motion will be addressed. As a first step towards a full
ab-initio treatment of the coupled electron-nuclear motion
in time-dependent external fields, we deduce an exact
factorization of the complete wavefunction into a purely
nuclear part and a many-electron wavefunction which
parametrically depends on the nuclear configuration. We
derive formally exact equations of motion for the nuclear
and electronic wavefunctions [4]. These exact equations lead
to a rigorous definition of time-dependent potential energy
surfaces as well as time-dependent geometric phases. With
the simple example of the hydrogen molecular ion in a laser
field we demonstrate the significance of these concepts in
understanding the full electron-ion dynamics. In particular,
the time-dependent potential energy surfaces are shown to
represent a powerful tool to analyse and interpret different
(direct vs. tunneling) types of dissociation processes.
[1] S. Kurth, G. Stefanucci, E. Khosravi, C. Verdozzi,
E.K.U. Gross, Phys. Rev.Lett.104, 236801 (2010).
[2] E. Räsänen, A. Castro, J. Werschnik, A. Rubio, E.K.U.
Gross, Phys. Rev. Lett. 98,157404 (2007).
[3] M. Thiele, E.K.U. Gross and S. Kümmel, Phys. Rev. Lett.
100, 153004 (2008).
[4] A. Abedi, N.T. Maitra, E.K.U. Gross, Phys. Rev. Lett.
105, 123002 (2010).
