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HL: Fachverband Halbleiterphysik

HL 1: Tutorial: Coherent Control

HL 1.1: Tutorium

Sonntag, 10. März 2013, 16:00–16:35, H2

Optimal Control Theory — •E.K.U. Gross — Max Planck Institute of Microstructure Physics, Halle (Saale), Germany

An overview of quantum optimal control theory will be given. Usually in quantum mechanics we prescribe an external field, say a laser or a magnetic field, and then solve the time-dependent Schroedinger equation to calculate from the wave function the observables of interest. Optimal control deals with an inverse problem: One first defines a goal that the laser pulse should achieve, the so-called "control target", and then one calculates, with certain algorithms, an optimally shaped laser field that achieves the prescribed goal. Examples of control targets are (i) to switch the chirality of the current in a quantum ring [1], (ii) to keep electrons localized in a given region of space [2], (iii) to minimize or maximize ionization of a molecule with the total fluence of the laser kept fixed [3], or (iv) to drag a wave packet along a given path through a nanostructure. We shall describe in detail how a given goal can be formulated in terms of a target functional which is to be maximized by the optimized pulse. Together with the underlying equation of motion, i.e. the time-dependent Schroedinger equation or the time-dependent Kohn-Sham equation [4], this maximization leads to a set of variational equations whose numerical solution yields the desired optimal pulses. [1] E. Rasanen, A. Castro, J. Werschnik, A. Rubio, E.K.U. Gross, PRL 98, 157404 (2007). [2] E. Rasanen, A. Castro, J. Werschnik, A. Rubio, E.K.U. Gross, PRB 77, 085324 (2008). [3] A. Castro, E. Rasanen, A. Rubio, E.K.U. Gross, EPL 87, 53001 (2009). [4] A. Castro, J. Werschnik, E.K.U. Gross, PRL 109, 153603 (2012).