Electron spins in dots and rings: coherence, read out, and transport

The spin of the electron leads to many effects in solid state physics. These effects provide the base for spintronics and promise many applications. One prominent proposal is to use individual electron spins as carriers of quantum information, as qubits, to build a quantum computer. Conversely, these effects can be used to assess the quantum mechanical properties of the spin using the well developed technologies of solid state physics. In this thesis, we consider semiconducting and metallic nanostructures and identify setups where new spin effects can be found. The main part of the thesis is focussed on quantum dots. These dots are small structures in which one can confine a single electron via its charge. Then, the spin of this electron can be addressed in a controlled way. One can apply an oscillating magnetic field which results in electron spin resonance (ESR) and drives the spin dynamics of the dot. We propose to assess the spin state of the dot by coupling to leads and driving an electrical current through the dot. This setup probes the quantum mechanical features of the single spin. In particular, the coherent Rabi oscillations and the decoherence time of the spin can be observed via the current through the dot. Furthermore, we describe how the electron spin on a dot can be assessed without requiring contact to leads. The combination of ESR and laser excitation with polarized light enables us to define schemes where the spin coherence and Rabi oscillations can be measured optically. In the absence of ESR, we consider the fluctuations (noise) of the dot current. Noise provides information on quantum effects which do not appear in the d.c. current itself. We study the asymmetric noise of dots in the quantum limit of high noise frequencies ω, where non-Markovian effects have to be taken into account. A further question is how to measure the state of a spin on a quantum dot, i.e., to detect if it is “up” or “down.” We propose several schemes for such a read out, including measuring the current through the dot coupled to spin-polarized leads and implementations based on a double dot which electrostatically in
uences the current through a nearby quantum
point contact. We also analyze the read-out statistics of an arbitrary two level
system (qubit), taking into account possible imperfections of the measurement
apparatus. De�ning a measurement e�ciency allows us to characterize
a reliable n-shot read out. In the last part of this thesis, we consider electron
spins in rings. In electron currents through mesoscopic rings one observes
that each electron moves as a superposition simultaneously through the upper
and lower arm of the ring and then interferes with itself. Additional
interference e�ects can occur when the spins of the electrons evolve adiabatically
and acquires a Berry phase, due to an inhomogeneous magnetic �eld or
spin-orbit interaction. We study di�usive rings and determine the required
�eld strength for the Berry phase to emerge and show that this phase leads to
a suppression of the Aharonov-Bohm oscillations at certain magic angles of
the magnetic �eld. Finally, for all setups proposed in this thesis, we discuss
the experimental requirements and show that they can be satis�ed under
realistic conditions.