Spins in quantum dots : hyperfine interaction, transport, and coherent control

This thesis deals with several topics related to spin dynamics and transport of
electrons in quantum dots. We begin with an introduction in Chapter 1, where
we review several important aspects of quantum dots and the microscopic Hamiltonians
governing the dynamics of electron spins in the presence of hyperfine
interaction with nuclei in the surrounding lattice. Chapter 2 provides an exact
solution for single-electron-spin dynamics due to the hyperfine interaction for
the special case of uniform coupling constants, and analyzes the range of validity
of a common semiclassical approximation. Chapter 3 includes a detailed
analysis of the non-Markovian (memory-dependent) dynamics for a localized
electron spin in the presence of the contact hyperfine interaction with a bath of
nuclear spins, including the effects of non-uniform hyperfine coupling constants.
Chapter 4 describes the hyperfine-induced dynamics of two-electron spin states
in terms of a singlet-triplet correlator. Chapter 5 completes our analysis of twoelectron
spin state decay with a description of all possible correlation functions,
exchange-induced Rabi oscillations, and “spin-state narrowing” of the nuclear
spin system, which could extend the lifetime of electron spin states if implemented.
Chapter 6 describes an experiment on transport through a carbonnanotube
double quantum dot, from which information about the strong tunnel
coupling can be obtained. In Chapter 7 we describe a method that could be
used to perform high-fidelity coherent single-spin rotations by pulsing only the
exchange interaction in the presence of fixed static magnetic fields.
Each chapter is based on a separate published or submitted work, with the
relevant reference given following each chapter title.