Hyperfine interaction and spin decoherence in quantum dots

Hyperfine interaction is a typical example of a topic in physics, that, due to technological advances, experiences a revival. Originally, hyperfine interaction was studied in atomic physics. In atoms, the interaction between the magnetic moments of the electrons and the nucleus leads to the hyperfine structure. The name hyperfine is historically due to the fact that the energy level splittings in atoms due to spin-orbit interaction were discovered first, and referred to as the atomic fine structure. The further splitting of these levels was then named hyperfine structure and the interaction that gives rise to it hyperfine interaction. In recent years, with the rise of nanotechnology, new structures have been created, one of them being so-called quantum dots. Quantum dots are also called artificial atoms, since, like atoms, they confine electrons to tiny (nanometer-size) regions. As for atoms, there is also hyperfine interaction in quantum dots: the spin of an electron confined to a quantum dot interacts with the lattice nuclei. In contrast to atoms, which have properties that are “given” by nature, the properties of quantum dots can be designed and thus allow to not only study new phenomena, but also open the way for new applications. Quantum computing is one of these applications where quantum dots could play an important role. The basic building block for a quantum computer is a quantum bit (qubit). Like a classical bit a qubit is an ideal two-level system. However, a qubit is a quantum mechanical two-level system instead of a classical one. There are several requirements a quantum-mechanical twolevel system has to fulfill to be a good qubit. The requirement central in this thesis is that the two states of the qubit and their superpositions should be long lived. More precisely it is crucial that coherent superpositions of the two states remain coherent for a long time compared to the manipulation time, i.e., that decoherence (the loss of coherence) is sufficiently slow. One promising candidate for the physical implementation of a qubit is the spin of an electron confined in a quantum dot. In an applied magnetic field the spin component along the field direction forms a natural two-level system. Research in the last few years, parts of which are being presented in this thesis, has shown that the main source of decoherence for spins in quantum dots is the hyperfine interaction with the surrounding nuclei in the host material. Since the wave function of an electron confined to a quantum dot extends over many
sites of the underlying cristal lattice, the electron spin also interacts with many
nuclei, in sharp contrast to an electron spin in an atom, which only interacts
with a single nucleus.
In this thesis we address several aspects of hyperfine interaction and decoherence
in quantum dots. First, we analyze some aspects of the decoherence
that arises from the hyperfine interaction. In the case of driven single-spin
oscillations we show that hyperfine interaction leads to a universal phase shift
and a power-law decay. Both of these effects have been confirmed experimentally.
We also find a universal phase shift and a power-law decay for the case
of two electron spins in a double quantum dot in the subspace with total spin
zero along the quantization axis. The appearance of the these effects both
in single and in double quantum dots is a consequence of the non-Markovian
nature of the nuclear spin bath.
Since the main effect of hyperfine-induced decoherence can be attributed to
the uncertainty in the Overhauser field, the effective magnetic field generated
by the nuclei at the position of the electron, one strategy to reduce decoherence
is to prepare the nuclei in a state with a narrow Overhauser field distribution,
i.e., to narrow the nuclear spin state. We propose a method to measure the
Overhauser field using the dynamics of the electron spins as a probe. More
specifically, we propose to narrow the nuclear spin state by monitoring Rabi
oscillations in a double quantum dot.
Hyperfine interaction not only leads to decoherence of the electron spin
state, it also provides a mechanism for interaction between the nuclei in the
quantum dot. We study the dynamics of the Overhauser field under the mutual
interaction between nuclear spins that is mediated by the electron via the
hyperfine interaction. At high magnetic fields we find an incomplete decay of
the Overhauser field. We further show that the decay of the Overhauser field
can be suppressed by measuring the Overhauser field, a clear manifestation of
the quantum Zeno effect.