Nuclear Spin Phenomena in Optically Active Semiconductor Quantum Dots

Abstract

The motivating background for this thesis lies in the recent development inthe coherent optical control of electron spin states in semiconductor quan-tum dots. One possible and attractive application for these achievements is aphysical implementation of a quantum computer based on spin qubits (quan-tum bit) in quantum dots. However, one of the obstacles in building suchquantum computer is decoherence caused by the interaction of the electronspins with nuclear spins of the host material. In this thesis we theoreticallyinvestigate the effects caused by the hyperfine interaction in optically activesemiconductor quantum dots.In Chapter 2 we assume optically induced rotations of single electron spins insemiconductor quantum dots. The optical control of the electron spin statesis considered to be conducted by means of Raman type optical transitionsbetween electron spin states. We investigate the influence of nuclear spinson the performance of the single-qubit gates by incorporating the additionaleffect of the Overhauser field into the electron spin dynamics. To calculatethe errors caused by the hyperfine interaction, we determine average fidelitiesof rotations around characteristic axes in the Bloch sphere in the presenceof nuclear spins analytically with perturbation theory up to second order inthe Overhauser field. By applying numerical averaging over the nuclear fielddistribution we find the average fidelity to the arbitrary orders of the hyper-fine interaction.In Chapter 3 we investigate the dynamics of spin qubits interacting by meansof an optical cavity. The qubits are represented by a single electron spin eachconfined to a quantum dot. Knowing that electron spins in III-V semiconduc-tor quantum dots are affected by the decoherence due to the hyperfine inter-action with nuclear spins, we find that the interaction between two qubits isconsequently influenced by the Overhauser field. Assuming an unpolariziednuclear ensemble, we investigate the fidelities for two-qubit gates dependingon the Overhauser field. We include the hyperfine interaction perturbativelyto second order in our analytical results, and to arbitrary precision numerically.Quantum dots can be used not only as physical systems for qubits, but alsoas sources for entangled photons. In chapter 4 we consider an emission ofentangled photons by spontaneous decay of the biexciton state to the groundstate. Due to electron-hole exchange interaction, the intermediate excitonicstates have a finite fine structure splitting. The electron spins of the excitonsalso interact via hyperfine interaction with the nuclear spins. We study thetemporal and fine structure splitting dependance of the coherence measuresconsidering the effect of the nuclear magnetic field. We find that the hyperfine interaction contributes considerably to the reduction of the photoncoherence.One of the possibilities to minimize the decoherence effects of the hyperfineinteraction is to polarize the nuclear spins to 100%. However, up to date itwas not possible to reach such degree of the nuclear polarization in experi-ments. In a recent experiment by Chekhovich et al. it was shown that highnuclear spin polarization can be achieved in self-assembled quantum dots byexploiting an optically forbidden transition between a heavy hole and a trionstate. A fully polarized state in this case was predicted by a classical rateequation, but could not be obtained experimentally. Therefore we theoret-ically investigate this problem with the help of a quantum master equationin Chapter 5, and we show that a fully polarized state cannot be achieveddue to formation of a nuclear dark state. Moreover, we demonstrate thatthe maximal degree of polarization depends on the form of the electron wavefunction inside of the quantum dot.