Spin decoherence of electrons and holes in semiconductor quantum dots

The computer industry has seen an immense development in the last decades.
Personal computers have become available for everybody living in industrialized
countries with rapidly increasing performance in terms of speed and storage capacities.
However, the performance of nowadays' computers is fundamentally limited by the
laws of classical physics: a classical bit can only take on either of the two distinct
values `0' or `1'.
In contrast, a quantum computer could, in principle, make direct use
of quantum phenomena, such as state superpositions
-- a quantum bit can be in both states `0' and `1' simultaneously --,
to perform complex computational tasks much faster than any classical computer.
The idea of building computers that work according to the laws of quantum physics
has opened various fields of research, one of which is the search for the best
physical system to use as a quantum bit (qubit). One important criterion for determining
the optimal qubit system is the lifetime of state superpositions.
Typically, once initialized, such superpositions are destroyed on remarkably short
timescales due to interactions with the environment -- a process which is referred to
as decoherence --, posing the question which physical qubit candidate system might show a high-enough robustness against the
influence of the `outside world' to allow for viable quantum computation.
In this thesis, we will consider three particular realizations of one specific and
very promising type of qubit candidate system:
an electron (or hole) confined to a quantum dot -- a nanoscale structure
within a (typically semiconducting) material --, where the spin states `down'
and `up' of our electron (or hole) encode the logical states `0' and `1'.
Our task will be to study the decay of spin-state superpositions in such quantum-dot
systems. The main objective of this thesis is to understand the most important physical
processes that lead to spin decoherence and to show ways to suppress this undesirable effect.
It turns out that at low temperatures, the main source of decoherence
is the coupling of the electron (hole) to the surrounding nuclear spins.
This thesis is divided into three logical parts, corresponding to the three qubit candidate
systems under consideration. First we will study electron-spin qubits in III-V semiconductor
quantum dots, where the electron spin interacts with the nuclear spins of the semiconducting
host material
via the isotropic Fermi contact hyperfine interaction. Second we consider quantum-dot-confined
heavy holes and the decoherence of their (pseudo-)spin states due to anisotropic interactions with the
nuclear spins. Third and last, we study electron-spin qubits made from carbon-nanotube and
graphene quantum dots. Quantum dots made of carbon have the advantage of a low abundance
of spin-carrying nuclear isotopes, therefore reducing decoherence effects significantly.
For each of the systems under consideration, we will carry out analytical calculations on
the nuclear-spin interactions and the spin dynamics of the qubit. Although one main goal of
this thesis is to show ways to extend spin decoherence times, we will also focus on physically more
fundamental questions. Not only the timescale of the decay is relevant for
the system's applicability as a qubit, but also the form of the decay which can vary
significantly from system to system. For example, the decay of spin-state superpositions
can follow an exponential, super-exponential or power-law decay, and can even pass through
various stages. This is not only of academic interest, but also important for practical
purposes, such as the implementation of quantum error-correction schemes in a potential
quantum computer.