Silicon Silicon Germanium Quantum Dot Spin Qubits

Quantum computing in nanoscale silicon heterostructures has received much attention, both from the scientific community and private industry, largely due to compatibility with highly-developed silicon-based device fabrication and design present in essentially all aspects of modern life. Breakthroughs in quantum control and coupled qubit systems in silicon in the last five years have accelerated scientific research in this area, with gate-defined quantum dots at the forefront of this effort. As techniques for quantum control become more sophisticated, subtle details of the silicon band structure are now of vital importance for the ultimate success of silicon quantum computing. Chief among these band features are the valley states, regions of the conduction band that form the ground state and a nearly degenerate excited state in quantum dot heterostructures. These valley states and their effects on electron dynamics can lead to quantum information loss and qubit decoherence, and so detailed characterization of the valleys is of great importance. In this work, I first describe a spectroscopic technique utilizing fast voltage pulses on one or two gates in a double quantum dot device to precisely measure the relevant valley state energies in both quantum dots as well as the coupling between valley states and electron orbital states. With this information, the valley states are leveraged to form a novel qubit basis with innate protection against decoherence from charge noise. Sub-nanosecond operations on this "valley qubit" are used to demonstrate complete quantum control. Finally, using real-time read-out of energy-selective tunneling in a single quantum dot, pure valley state coherence in the form of intervalley relaxation is directly probed. This relaxation is subsequently linked to spin-valley electron dynamics and the observance of a valley-dependent tunneling process is discussed theoretically using tight-binding formalism.

Si/SiGe quantum dots (QDs) are promising candidates for spin-based quantum bits (qubits) as a result of the reduced spin-orbit coupling as well as the Si isotopes with zero nuclear spin. Meanwhile qubit readout is a challenge related to semiconductor-based quantum computation. A superconducting single-electron transistor (SET), when operating in the radio-frequency (rf) regime, has a combination of high charge sensitivity and low back-action and can potentially become an ideal charge sensor for the QDs. This thesis describes the development of superconducting SET charge sensors for Si/SiGe QDs. Using rf-SETs we have detected real-time electron tunneling events on the order of 10 microseconds in a single QD and mapped out the stability diagram of a double QD, showing spin blockade and bias triangles due to excited-state transitions. In addition Kondo effects that are significantly different from the standard spin 1/2 model have been observed and investigated in both perpendicular and in-plane magnetic fields, indicating the interplay between the spin and valley degrees of freedom in Si.

This thesis discusses the effects of confinement strength on two-electron states in an electrostatically defined quantum dot (QD) in a Si/SiGe quantum well at zero magnetic field, focusing on geometries appropriate for qubits. We account for electron-electron (e-e) interactions via full-configuration interaction calculations as well as the nontrivial interplay between the conduction band valleys of silicon, and disorder at the Si/SiGe interface via tight-binding approach. We show that the experimental signatures of strong e-e interactions in these devices can be subtle. While the suppression of the singlet-triplet (ST) splitting in two-electron quantum dots formed in direct band gap materials is a clear indication of e-e interactions, in silicon devices this effect can be masked by the additional valley degree of freedom of the conduction band electrons, if the Si/SiGe interface is flat. Interfacial-disorder-induced valley-orbit coupling, on the other hand, can induce this suppression. To study these phenomena, we explore the effects of different interface profiles on the ST splitting. The presence of the valley degree of freedom in silicon quantum dots enables the existence of excited two-electron states whose excitation energy is less sensitive to e-e interactions than their counterparts based on orbital excitations. We show that, by virtue of this difference in the sensitivity to e-e interactions, the confinement strength can be used to change the valley vs. orbital character of the first-excited state, with the former yielding excitation energies that are more resilient to charge noise. We further discuss the role of e-e interactions in two recent experiments demonstrating (1) the use of valley-orbit states to probe Si/SiGe interface, and (2) a spectroscopically-dense set of low-lying energy levels.

The project goals are to fabricate qubits in quantum dots in Si/SiGe modulation-doped heterostructures, to characterize and understand those structures, and to develop the technology necessary for a Si/SiGe quantum dot quantum computer. The physical qubit in our approach is the spin of an electron confined in a top-gated silicon quantum dot in a Si/SiGe modulation-doped heterostructure. Operations on such a qubit may be performed by controlling the voltages on gates in-between neighboring quantum dots. A quantum computer and qubits in silicon offer potential advantages, both fundamental and practical. Electron spins in silicon quantum dots are expected to have long coherence times. Silicon has an isotope, Si, which has zero nuclear spin and thus no nuclear magnetic moment. As a result, electron spins in silicon have longer coherence times than they would in the presence of a fluctuating nuclear spin background. From a practical perspective, modern classical computers are made in silicon, and one hopes that this will lead to synergy in the future with a silicon quantum computer. This QCCM includes both theory and experiment focusing on (i) the development of qubits in the form of electron spins in silicon quantum dots, (ii) the measurement and manipulation of those qubits, and (iii) the science essential for understanding the properties of such qubits.

Electrically-gated quantum dots in semiconductors is an excellent architecture on which to make qubits for quantum information processing. Silicon is attractive because of the potential for excellent manipulability, scalability, and for integration with classical electronics. This thesis describes several aspects of the theoretical issues related to quantum dot qubits in silicon. It may be broadly divided into three parts -- (1) the hybrid qubit and quantum gates, (2) decoherence and (3) charge transport. In the first part, we present a novel architecture for a double quantum dot spin qubit, which we term the hybrid qubit, and demonstrate that implementing this qubit in silicon is feasible. Next, we consider both AC and DC quantum gating protocols and compare the optimal fidelities for these protocols that can be achieved for both the hybrid qubit and the more traditional singlet-triplet qubit. In the second part, we present evidence that silicon offers superior coherence properties by analyzing experimental data from which charge dephasing and spin relaxation times are extracted. We show that the internal degrees of freedom of the hybrid qubit enhance charge coherence, and demonstrate tunable spin loading of a quantum dot. In the last part, we explain three key features of spin-dependent transport -- spin blockade, lifetime-enhanced transport and spin-flip cotunneling. We explain how these features arise in the conventional two-electron as well as the unconventional three-electron regimes, using a theoretical model that captures the key characteristics observed in the data.

Ongoing developments in nanofabrication technology and the availability of novel materials have led to the emergence and evolution of new topics for mesoscopic research, including scanning-tunnelling microscopic studies of few-atom metallic clusters, discrete energy level spectroscopy, the prediction of Kondo-type physics in the transport properties of quantum dots, time dependent effects, and the properties of interacting systems, e.g. of Luttinger liquids. The overall understanding of each of these areas is still incomplete; nevertheless, with the foundations laid by studies in the more traditional systems there is no doubt that these new areas will advance mesoscopic electron transport to a new phenomenological level, both experimentally and theoretically. Mesoscopic Electron Transport highlights selected areas in the field, provides a comprehensive review of such systems, and also serves as an introduction to the new and developing areas of mesoscopic electron transport.