Quantum control theory for coupled 2-electron dynamics in quantum dots

We investigate optimal control strategies for state to state transitions in a model of a quantum dot molecule containing two active strongly interacting electrons. The Schrodinger equation is solved nonperturbatively in conjunction with several quantum control strategies. This results in optimized electric pulses in the THz regime which can populate combinations of states with very short transition times. The speedup compared to intuitively constructed pulses is an order of magnitude. We furthermore make use of optimized pulse control in the simulation of an experimental preparation of the molecular quantum dot system. It is shown that exclusive population of certain excited states leads to a complete suppression of spin dephasing, as was indicated in Nepstad et al. [Phys. Rev. B 77, 125315 (2008)].Comment: 24 pages, 9 figure

The circumstellar envelope of the C-rich post-AGB star HD 56126

We present a detailed study of the circumstellar envelope of the post-asymptotic giant branch ``21 micron object'' HD 56126. We build a detailed dust radiative transfer model of the circumstellar envelope in order to derive the dust composition and mass, and the mass-loss history of the star. To model the emission of the dust we use amorphous carbon, hydrogenated amorphous carbon, magnesium sulfide and titanium carbide. We present a detailed parametrisation of the optical properties of hydrogenated amorphous carbon as a function of H/C content. The mid-infrared imaging and spectroscopy is best reproduced by a single dust shell from 1.2 to 2.6 arcsec radius around the central star. This shell originates from a short period during which the mass-loss rate exceeded 10^(-4) M_sun/yr. We find that the strength of the ``21'' micron feature poses a problem for the TiC identification. The low abundance of Ti requires very high absorption cross-sections in the ultraviolet and visible wavelength range to explain the strength of the feature. Other nano-crystalline metal carbides should be considered as well. We find that hydrogenated amorphous carbon in radiative equilibrium with the local radiation field does not reach a high enough temperature to explain the strength of the 3.3-3.4 and 6-9 micron hydrocarbon features relative to the 11-17 micron hydrocarbon features. We propose that the carriers of these hydrocarbon features are not in radiative equilibrium but are transiently heated to high temperature. We find that 2 per cent of the dust mass is required to explain the strength of the ``30'' micron feature, which fits well within the measured atmospheric abundance of Mg and S. This further strengthens the MgS identification of the ``30'' micron feature.Comment: 20 Pages, 10 Figures, accepted for publication in Astronomy and Astrophysic

Investigation of Optimal Control Problems Governed by a Time-Dependent Kohn-Sham Model

A viable way to develop optimal control strategies for multi-particle quantum systems is to consider the framework of time-dependent density functional theory (TDDFT), where low-dimensional nonlinear Schrödinger models are developed to compute the electronic density of related high-dimensional linear Schrödinger equations. Among these models, the Kohn-Sham TDDFT system allows to accommodate control mechanisms in the same potentials that appear in the original multi-dimensional Schrödinger equations, thus allowing a physical interpretation and a laboratory implementation. The purpose of this paper is the mathematical analysis of optimal control problems governed by the time-dependent Kohn-Sham (TDKS) equations including a control potential that has the purpose to drive the evolution of the electron density to perform given tasks. For the resulting optimal control problems, existence of optimal solutions is proved and their characterization as solutions of TDKS optimality systems is investigated