Exploiting time-independent Hamiltonian structure as controls for manipulating quantum dynamics

Abstract

The opportunities offered by utilizing time-independent Hamiltonian structure as controls are explored for manipulating quantum dynamics. Two scenarios are investigated using different manifestations of Hamiltonian structure to illustrate the generality of the concept. In scenario 1, optimally shaped electrostatic potentials are generated to flexibly control electron scattering in a two-dimensional subsurface plane of a semiconductor. A simulation is performed showing the utility of optimally setting the individual voltages applied to a multi-pixel surface gate array in order to produce a spatially inhomogeneous potential within the subsurface scattering plane. The coherent constructive and destructive electron wave interferences are manipulated by optimally adjusting the potential shapes to alter the scattering patterns. In scenario II, molecular vibrational wave packets are controlled by means of optimally selecting the Hamiltonian structure in cooperation with an applied field. As an illustration of the concept, a collection (i.e., a level set) of dipole functions is identified where each member serves with the same applied electric field to produce the desired final transition probability. The level set algorithm additionally found Hamiltonian structure controls exhibiting desirable physical properties. The prospects of utilizing the applied field and Hamiltonian structure simultaneously as controls is also explored. The control scenarios I and TI indicate the gains offered by algorithmically guided molecular or material discovery for manipulating quantum dynamics phenomenon. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4743954]