Nuclear Spin Phenomena in Optically Active Semiconductor Quantum Dots

The motivating background for this thesis lies in the recent development in the coherent optical control of electron spin states in semiconductor quantum dots. One possible and attractive application for these achievements is a physical implementation of a quantum computer based on spin qubits (quantum bit) in quantum dots. However, one of the obstacles in building such quantum computer is decoherence caused by the interaction of the electron spins with nuclear spins of the host material. In this thesis we theoretically investigate the effects caused by the hyperfine interaction in optically active semiconductor quantum dots. In Chapter 2 we assume optically induced rotations of single electron spins in semiconductor quantum dots. The optical control of the electron spin states is considered to be conducted by means of Raman type optical transitions between electron spin states. We investigate the influence of nuclear spins on the performance of the single-qubit gates by incorporating the additional effect of the Overhauser field into the electron spin dynamics. To calculate the errors caused by the hyperfine interaction, we determine average fidelities of rotations around characteristic axes in the Bloch sphere in the presence of nuclear spins analytically with perturbation theory up to second order in the Overhauser field. By applying numerical averaging over the nuclear field distribution we find the average fidelity to the arbitrary orders of the hyperfine interaction.