Data shows that coherent optical interactions can control both the electronic and nuclear spin states in single and coupled quantum dots to. Measurements report on various quantum parameters associated with these states and their interaction.
Single electron spin in a semiconductor quantum dot (QD) and single photon wavepacket propagating in an optical waveguide are investigated as carriers of quantum bit (qubit) for information processing. Cavity quantum electrodynamics of the coupled system composed of charged QD, microcavity and waveguide provides a quantum interface for the interplay of stationary spin qubits and flying photon qubits via cavity assisted optical control. This interface forms the basis for a wide range of essential functions of a quantum network, including transferring, swapping, and entangling qubits at distributed quantum nodes as well as a deterministic source and an efficient detector of a single photon wavepacket with arbitrarily specified shape. The cavity assisted optical process also made possible ultrafast initialization and QND readout of the spin qubit in QD. In addition, the strong optical nonlinearity of dot-cavity-waveguide coupled system enables phase gate and entanglement operation for flying single photon qubits in waveguides. The coherence of the electron spin is the wellspring of these quantum applications being investigated. At low temperature and strong magnetic field, the dominant cause of electron spin decoherence is the coupling with the interacting lattice nuclear spins. We present a quantum solution to the coupled dynamics of the electron with the nuclear spin bath. The decoherence is treated in terms of quantum entanglement of the electron with the nuclear pair-flip excitations driven by the various nuclear interactions. A novel nuclear interaction, mediated by virtue spin-flips of the single electron, plays an important role in single spin free-induction decay (FID). The spin echo not only refocuses the dephasing by inhomogeneous broadening in ensemble dynamics but also eliminates the decoherence by electron-mediated nuclear interaction. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The quantum theory of decoherence also leads to a method of coherence recovery of the electron by disentanglement, realized through maneuvering the nuclear bath evolution by control of the electron spin-flip. The studies form the basis to outline the construction of a solid-state quantum network for scalable and distributed processing of quantum information
Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of the nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip–flops, as elementary excitations in the mesoscopic bath, can be mapped into the precession of non-interacting pseudo-spins. Such mapping provides a geometrical picture for understanding the decoherence and for devising control schemes. A close examination of nuclear bath dynamics reveals a wealth of phenomena and new possibilities of controlling the electron spin decoherence. For example, when the electron spin is flipped by a π-pulse at τ, its coherence will partially recover at as a consequence of quantum disentanglement from the mesoscopic bath. In contrast to the re-focusing of inhomogeneously broadened phases by conventional spin-echoes, the disentanglement is realized through shepherding quantum evolution of the bath state via control of the quantum object. A concatenated construction of pulse sequences can eliminate the decoherence with arbitrary accuracy, with the nuclear–nuclear spin interaction strength acting as the controlling small parameter.
The motivating background for this thesis lies in the recent development in the coherent optical control of electron spin states in semiconductor quan- tum dots. One possible and attractive application for these achievements is a physical implementation of a quantum computer based on spin qubits (quan- tum 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 hyper- fine interaction. In Chapter 3 we investigate the dynamics of spin qubits interacting by means of an optical cavity. The qubits are represented by a single electron spin each confined 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 is consequently influenced by the Overhauser field. Assuming an unpolarizied nuclear ensemble, we investigate the fidelities for two-qubit gates depending on the Overhauser field. We include the hyperfine interaction perturbatively to second order in our analytical results, and to arbitrary precision numeri cally. Quantum dots can be used not only as physical systems for qubits, but also as sources for entangled photons. In chapter 4 we consider an emission of entangled photons by spontaneous decay of the biexciton state to the ground state. Due to electron-hole exchange interaction, the intermediate excitonic states have a finite fine structure splitting. The electron spins of the excitons also interact via hyperfine interaction with the nuclear spins. We study the temporal and fine structure splitting dependance of the coherence measures considering the effect of the nuclear magnetic field. We find that the hy perfine interaction contributes considerably to the reduction of the photon coherence. One of the possibilities to minimize the decoherence effects of the hyperfine interaction is to polarize the nuclear spins to 100%. However, up to date it was 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 high nuclear spin polarization can be achieved in self-assembled quantum dots by exploiting an optically forbidden transition between a heavy hole and a trion state. A fully polarized state in this case was predicted by a classical rate equation, but could not be obtained experimentally. Therefore we theoret- ically investigate this problem with the help of a quantum master equation in Chapter 5, and we show that a fully polarized state cannot be achieved due to formation of a nuclear dark state. Moreover, we demonstrate that the maximal degree of polarization depends on the form of the electron wave function inside of the quantum dot.