Dynamics and decoherence in two-electron quantum dots

Semiconductor quantum dots have been studied experimentally and theoretically for two decades. With the help of modern experimental techniques, it is possible to control the number of electrons in the dots at single-electron level, and one can apply different confinement potentials and vary the strength of the external magnetic field. These properties make quantum dots ideal for studies of quantum mechanical effects. The spin of the confined electron is a natural candidate for a quantum bit, as the z-component of spin can have two different values, up or down, making quantum dots suitable to be used as a building block of the quantum computer. The decoherence of the quantum states is a factor that has to be taken into account, and for this reason it is important to study the time-dependent phenomena in quantum dots. This Thesis studies the dynamics of two electrons confined in two dimensions in a double quantum dot or in a quantum ring. We study the decoherence of the two-electron states by calculating the dynamics of the two-electron system and compare the results with experimental data. We apply exact diagonalization methods for the numerical evolution of the dynamics. The Coulomb interaction of the two confined electrons is taken into account. For large electron numbers, the calculation of the dynamics with full exact diagonalization becomes too heavy, but for two electrons, the dynamics can still be calculated exactly with reasonable computing resources. This Thesis explains some decoherence measurements with numerical results. We study especially the hyperfine interaction of the nuclear spins of the surrounding material with the spins of the confined electrons and the effects of nuclear spin polarization. We propose novel control schemes that can be used to manipulate the two-electron states in quantum dots. Our results may prove to be useful for experimentalists in the development of quantum dot systems towards a realization of a semiconductor-based quantum computer.