Quantum optical control of spins and excitons in semiconductor quantum dots

In this dissertation we present a theory of quantum optical control of spins and excitons in semiconductor quantum dots. Energy structure and optical selection rules of multi-excitons in a semiconductor quantum dot are constructed from a microscopic model. The effect of the electron-hole exchange interaction is discussed. Nonlinear coherent optical effects in a single quantum dot are investigated. A general theory is developed to calculate non-perturbatively the cross-polarized and the co-polarized pump-probe spectra as a function of laser intensity. Aulter-Towners configuration is proposed to be the best scenario to observe the onset of Rabi splitting. This is the prerequisite for performing the Rabi rotation in the multi-exciton space. A theory of fast quantum optical control of exciton dynamics in quantum dots is investigated. The concept of the optimal control is proposed. Pulse design using the average Hamiltonian method and the numerical method is explored. It is shown that by using the shaped-pulses the operation time can be reduced by an order of magnitude. Natural gates instead of the conventional universal quantum gates are used to reduce the number of quantum gates needed for any quantum algorithm. Pulse sequences for the Deutsch-Jozsa algorithm and the quantum Fourier transform are designed explicitly to illustrate the concept of optimal control. Quantum trajectories method is used to simulate the dynamics of the quantum computer including the decoherence process. It is shown that the quantum algorithm can be finished within the decoherence time of the system with high fidelity. To explore the control of single electron spin in quantum dots, adiabatic Raman transition via single Λ system is extended to perform arbitrary spin rotations in a single charged quantum dot. Adiabatic condition is discussed. Extension to other Λ system is explored. To couple and control the spins localized in neighboring quantum dots, a theory of optical RKKY interaction is developed. This indirect interaction is mediated by the photoexcited delocalized electron-hole pairs or excitons. The general formula and the numerical value of the effective exchange constant are presented. Application to quantum computation is discussed.