Interactions, initial states, and low-dimensional semiconductors
2006 (English)Doctoral thesis, monograph (Other academic)
This thesis is concerned with different aspects of quantum mechanical interactions. The first part of the thesis focuses on their effects in low-dimensional semiconductors; the second part on one of their applications: quantum algorithms, which utilize superpositions created from quantum mechanical interactions. Bridging the gap between these two slightly different areas is a method for implementing quantum gates using interactions in low-dimensional semiconductors.
We address the issue of dimensionality by studying the local density of states in a quantum point contact (QPC). This is important since many results regarding electron transport through the QPC rely on as assumption of one-dimensionality. We show that in order for this assumption to be valid, certain conditions regarding the shape of the potential have to be fulfilled (Paper I).
We also study electron transport in quantum wires and QPCs, with emphasis on electron-electron interaction effects, using Density Functional Theory (DFT). In Paper II we provide an explanation of the experimentally observed 0.7 analogues in quantum wires in strong magnetic fields. We show that their origin is intimately linked with the exchange-correlation energy, and is thus as spin polarization phenomenon. In Paper III we analyze the conductance properties of QPCs and claim that spontaneous spin polarization is the driving mechanism behind the 0.7 anomaly in long QPCs. We also investigate the validity of the "Reilly model", and extend the study to nonzero temperature.
Furthermore, we investigate the trapping of spin-polarized electrons in edge states around a pair of antidots (Paper IV). This study supports a proposal for using the trapped electrons to realize quantum gates – the building blocks of a quantum computer. The main advantage of our proposal is that the edge states have a very long lifetime, which will reduce problems with decoherence.
Papers V and VI, finally, are concerned with quantum algorithms for initial state preparation. In Paper V a method is devised for preparing initial states for quantum eigenvalue calculation; it is based on a scheme for extending the size of a quantum register through duplication of its quantum bits (qubits). The central result in Paper VI is an algorithm for preparing initial states for quantum simulation. The state to be prepared is chosen as an eigenstate, with eigenvalu 0, of some quantum system, on which eigenvalue calculation is performed using the method in Paper V.
Place, publisher, year, edition, pages
Institutionen för fysik, kemi och biologi , 2006. , 101 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 994
Q!uantum mechanical interactions, quantum point contact (QPC), quantum wires, exchange-correlation energy, Reilly model, quantum algorithms
IdentifiersURN: urn:nbn:se:liu:diva-7537ISBN: 91-85457-91-4OAI: oai:DiVA.org:liu-7537DiVA: diva2:22544
2006-02-08, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Reimann-Wacker, Stephanie M., Docent