Quantum Dots: Coulomb Blockade, Mesoscopic Fluctuations, and Qubit Decoherence

TL;DR

This thesis provides analytic models for conductance and Coulomb blockade effects in quantum dots, and evaluates the feasibility and decoherence mechanisms of quantum dot qubits, highlighting the impact of mesoscopic fluctuations and phonon interactions.

Contribution

It introduces analytic expressions for conductance and Coulomb blockade corrections, and assesses error sources and decoherence in quantum dot qubits using realistic models.

Findings

Analytic expressions for conductance in single electron transistors.

Quantitative analysis of Coulomb blockade peak spacing corrections.

Phonon decoherence rates are weaker than previously thought.

Abstract

In this thesis I find an analytic expression for the conductance of a single electron transistor in the regime when temperature, level spacing, and charging energy of an island are all of the same order. I also study the correction to the spacing between Coulomb blockade peaks due to finite dot-lead tunnel couplings. I find analytic expressions for both correction to the spacing averaged over mesoscopic fluctuations and the rms of the correction fluctuations. In the second part of the thesis I discuss the feasibility of quantum dot based spin- and charge-qubits. Firstly, I study the effect of mesoscopic fluctuations on the magnitude of errors that can occur in exchange operations on quantum dot spin-qubits. Mid-size double quantum dots, with an odd number of electrons in the range of a few tens in each dot, are investigated through the constant interaction model using realistic parameters. It is found that the number of independent parameters per dot that one should tune depends on the configuration and ranges from one to four. Then, I study decoherence of a quantum dot charge qubit due to coupling to piezoelectric acoustic phonons in the Born-Markov approximation. After including appropriate form factors, I find that phonon decoherence rates are one to two orders of magnitude weaker than was previously predicted. My results suggest that mechanisms other than phonon decoherence play a more significant role in current experimental setups.