Spin decoherence and manipulation in quantum dots : the role of the spin-orbit interaction

Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques, the spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes. We reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins. Chapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies. Chapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble

Cluster States From Heisenberg Interaction

We show that a special type of entangled states, cluster states, can be created with Heisenberg interactions and local rotations in 2d steps where d is the dimension of the lattice. We find that, by tuning the coupling strengths, anisotropic exchange interactions can also be employed to create cluster states. Finally, we propose electron spins in quantum dots as a possible realization of a one-way quantum computer based on cluster states

Spin Decay in a Quantum Dot Coupled to a Quantum Point Contact

We consider a mechanism of spin decay for an electron spin in a quantum dot due to coupling to a nearby quantum point contact (QPC) with and without an applied bias voltage. The coupling of spin to charge is induced by the spin-orbit interaction in the presence of a magnetic field. We perform a microscopic calculation of the effective Hamiltonian coupling constants to obtain the QPC-induced spin relaxation and decoherence rates in a realistic system. This rate is shown to be proportional to the shot noise of the QPC in the regime of large bias voltage and scales as $a^{-6}$ where $a$ is the distance between the quantum dot and the QPC. We find that, for some specific orientations of the setup with respect to the crystallographic axes, the QPC-induced spin relaxation and decoherence rates vanish, while the charge sensitivity of the QPC is not changed. This result can be used in experiments to minimize QPC-induced spin decay in read-out schemes.Comment: 10 pages, 2 figures, 2 table

Two-spin relaxation of P-dimers in Silicon

We study two-electron singlet-triplet relaxation of donor-bound electrons in Silicon. Hyperfine interaction of the electrons with the phosphorus (P) nuclei, in combination with the electron-phonon interaction, lead to relaxation of the triplet states. Within the Heitler-London and effective mass approximations, we calculate the triplet relaxation rates in the presence of an applied magnetic field. This relaxation mechanism affects the resonance peaks in current Electron Spin Resonance (ESR) experiments on P-dimers. Moreover, the estimated time scales for the spin decay put an upper bound on the gate pulses needed to perform fault-tolerant two-qubit operations in donor-spin-based quantum computers (QCs).Comment: 3 figures, 1 tabl

Some Studies on Mass Spectrometry of Organic Compounds

The present thesis contains five chapters: 1. The historical development of mass spectrometry and the theory of various designs of instrumentation are discussed. 2. This chapter records the synthesis of a series of alcohols, acids, and iodides (C5-C7) enriched with 13C at C-1. The mass spectra of these nine compounds have been obtained and compared for the more abundant ions with those of the normal mass spectra obtained from the unenriched molecules. The characteristic fragmentation pathways of these compounds were clarified. The importance of beta-cleavages to the other bonds are emphasised. No evidence was obtained to support the rupture of a 13C-12C bond prior to beta-cleavage, although this bond is weaker than the C-C bond. 3. Chapter three reports the synthesis and interpretation of the mass spectra of some heterocyclic compounds with special emphasis on rearrangement processes. Some comments upon the McLafferty rearrangement are reported. Attempts were made, without success, to replace sulphur firstly by selenium and then by tellurium in the synthesis of thioamides. 4. The fourth chapter discusses a computer matching technique for the identification of organic compounds. Programmes have been developed to compare the unknown spectrum with the library file without using the molecular weight of the compound. A successful result was obtained after each search. 5. In this chapter the analysis of unknown mixtures by mass spectrometry is described. The use of high resolution mass spectrometry clarified the occurrence of certain synthetic reactions in the source of mass spectrometer. In this investigation the composition of fifteen extra compounds and also ten protonated ions, induced by electron impact of a four component mixture, are reported. From the results obtained it is concluded that the analysis of mixtures by mass spectrometry may not always be an efficient technique, particularly when the mixture contains sulphur compounds