Analysis and control of electron motion
Pr. E. K. U. GROSS
Max-Planck Institute for Microstructure Physics
Halle, Allemagne
Mardi, 15 novembre 2011,
14h00 Bibliothèque 4e étage,
tour 12 - 13, site Jussieu
Modern density functional theory is based on the surprising fact that knowledge of the density alone is sufficient to calculate all physical observables of a quantum many-body system. In this lecture, the time-dependent generalization of density functional theory (TDDFT) will be employed to visualize, analyse and, ultimately, control electronic motion on the femto-second time scale.
After an overview of the basic concepts of timedependent density functional theory, the calculation of optical spectra, especially excitonic effects, will be described.
After that, some phenomena beyond the linear-response regime will be investigated: 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, can be addressed. We demonstrate that Coulomb blockade corresponds, in the time-domain, to a periodic charging and discharging of the quantum dot. With modern pulse-shaping facilities, the control of electronic motion is becoming more and more realistic. Questions like "By which laser pulse can one make an electronic wave packet follow a given trajectory in real space or a given path in Hilbert space?" will be addressed.
Quantum optimal control theory will be presented as a method to compute such laser pulses that are optimized to achieve a given goal.
As examples we will calculate the laser pulse needed to break a chosen preselected bond in a molecule, and we will study how the chirality of the electronic current in a quantum ring can be controlled.
Finally, the coupling between electronic and nuclear motion will be addressed. 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. This decomposition leads to a rigorous definition of time-depend-ent 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.