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On the role of the electron-electron interaction in two-dimensional quantum dots and rings
Stockholm University, Faculty of Science, Department of Physics. (Atomic Physics)
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Many-Body Perturbation Theory is put to test as a method for reliable calculations of the electron-electron interaction in two-dimensional quantum dots. We show that second order correlation gives qualitative agreement with experiments on a level which was not found within the Hartree-Fock description. For weaker confinements, the second order correction is shown to be insufficient and higher order contributions must be taken into account. We demonstrate that all order Many-Body Perturbation Theory in the form of the Coupled Cluster Singles and Doubles method yields very reliable results for confinements close to those estimated from experimental data. The possibility to use very large basis sets is shown to be a major advantage compared to Full Configuration Interaction approaches, especially for more than five confined electrons.

Also, the possibility to utilize two-electron correlation in combination with tailor made potentials to achieve useful properties is explored. In the case of a two-dimensional quantum dot molecule we vary the interdot distance, and in the case of a two-dimensional quantum ring we vary the ring radius, in order to alter the spectra. In the latter case we demonstrate that correlation in combination with electromagnetic pulses can be used for the realization of quantum logical gates.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University , 2010. , 99 p.
Keyword [en]
quantum dot, quantum ring, quantum dot molecule, electronic structure, two-dimensional, many-body physics, many-body perturbation theory, coupled cluster, coupled cluster singles and doubles, quantum logical gates, quantum computing, quantum control, quantum control algorithm
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:su:diva-38862ISBN: 978-91-7447-086-4 (print)OAI: oai:DiVA.org:su-38862DiVA: diva2:317059
Public defence
2010-06-02, FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Note
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Manuscript.Available from: 2010-05-11 Created: 2010-05-02 Last updated: 2010-05-03Bibliographically approved
List of papers
1. Many-body perturbation theory calculations on circular quantum dots
Open this publication in new window or tab >>Many-body perturbation theory calculations on circular quantum dots
2007 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 76, no 4, 045314- p.Article in journal (Refereed) Published
Abstract [en]

The possibility to use perturbation theory to systematically improve calculations on circular quantum dots is investigated. A few different starting points, including Hartree-Fock, are tested and the importance of correlation is discussed. Quantum dots with up to 12 electrons are treated and the effects of an external magnetic field are examined. The sums over excited states are carried out with a complete finite radial basis set obtained through the use of B splines. The calculated addition energy spectra are compared with experiments and the implications for the filling sequence of the third shell are discussed in detail.

Identifiers
urn:nbn:se:su:diva-12393 (URN)10.1103/PhysRevB.76.045314 (DOI)000248540000067 ()
Available from: 2008-01-15 Created: 2008-01-15 Last updated: 2017-12-13Bibliographically approved
2. Structure of lateral two-electron quantum dot molecules in electromagnetic fields
Open this publication in new window or tab >>Structure of lateral two-electron quantum dot molecules in electromagnetic fields
Show others...
2007 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 76, no 3, 035303- p.Article in journal (Refereed) Published
Abstract [en]

The energy levels of laterally coupled parabolic double quantum dots are calculated for varying interdot distances. Electron-electron interaction is shown to dominate the spectra: In the diatomic molecule limit of large interdot separation, the two nearly degenerate singlet and triplet ground states are followed by a narrow band of four singlet and four triplet states. The energy spacing between the ground state and the first band of excited states scales directly with the confinement strength of the quantum wells. Similar level separation and band structure are found when the double dot is exposed to a perpendicular magnetic field. Conversely, an electric field parallel to the interdot direction results in a strong level mixing and a narrow transition from a localized state to a covalent diatomic molecular state.

Identifiers
urn:nbn:se:su:diva-12392 (URN)10.1103/PhysRevB.76.035303 (DOI)000248500800078 ()
Available from: 2008-01-15 Created: 2008-01-15 Last updated: 2017-12-13Bibliographically approved
3. Fundamental gates for a strongly correlated two-electron quantum ring
Open this publication in new window or tab >>Fundamental gates for a strongly correlated two-electron quantum ring
2010 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 81, no 3, 033303- p.Article in journal (Refereed) Published
Abstract [en]

We demonstrate that conditional as well as unconditional basic operations which are necessary for universal quantum gates can be performed with almost 100% fidelity within a strongly interacting two-electron quantum ring. Both sets of operations are based on a quantum control algorithm that optimizes a driving electromagnetic pulse for a given quantum gate. The demonstrated transitions occur on a time scale much shorter than typical decoherence times of the system.

Place, publisher, year, edition, pages
American Physical Society, 2010
Keyword
Quantum logical gates, quantum computing, electronic structure, electromagnetic pulses, quantum ring, low-dimensional, two-dimensional
National Category
Condensed Matter Physics Other Physics Topics
Research subject
Physics
Identifiers
urn:nbn:se:su:diva-38860 (URN)10.1103/PhysRevB.81.033303 (DOI)000274002300011 ()
Available from: 2010-05-02 Created: 2010-05-02 Last updated: 2017-12-12Bibliographically approved
4. Controlled operations in a strongly correlated two-electron quantum ring
Open this publication in new window or tab >>Controlled operations in a strongly correlated two-electron quantum ring
2009 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 79, no 11, 115318- p.Article in journal (Refereed) Published
Abstract [en]

We have analyzed the electronic spectrum and wave-function characteristics of a strongly correlated two-electron quantum ring with model parameters close to those observed in experiments. The analysis is based on an exact diagonalization of the Hamiltonian in a large B-spline basis. We propose a qubit pair for storing quantum information, where one component is stored in the total electron spin and one multivalued “quMbit” is represented by the total angular momentum. In this scheme the controlled-NOT quantum gate is demonstrated with near 100% fidelity for a realistic far-infrared electromagnetic pulse.

Place, publisher, year, edition, pages
American Physical Society, 2009
Keyword
Quantum Rings, Quantum Dots, Electron structure, Electron correlation, Configuration Interaction, Quantum Computing, quantum gates, CNOT, Controlled operations, angular momentum, electron spin, quantum entanglement, strongly correlated electron systems, wave functions
National Category
Atom and Molecular Physics and Optics Other Physics Topics Condensed Matter Physics Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:su:diva-32133 (URN)10.1103/PhysRevB.79.115318 (DOI)000264768900100 ()
Available from: 2010-01-25 Created: 2009-12-04 Last updated: 2017-12-12Bibliographically approved
5. Performance of the coupled cluster singles and doubles method on two-dimensional quantum dots
Open this publication in new window or tab >>Performance of the coupled cluster singles and doubles method on two-dimensional quantum dots
(English)Manuscript (preprint) (Other academic)
Abstract [en]

An implementation of the coupled-cluster single- and double excitations (CCSD) method on two-dimensional quantum dots is presented. Advantages and limitations are studied through comparison with other high accuracy approaches for two to eight confined electrons. The possibility to effectively use a very large basis set is found to be an important advantage compared to full configuration interaction implementations. For the two to eight electron ground states, with a confinement strength close to what is used in experiments, the error in the energy introduced by truncating triple excitations and beyond is shown to be on the same level or less than the differences in energy given by two different Quantum Monte Carlo methods. Convergence of the iterative solution of the coupled cluster equations is, for some cases, found for surprisingly weak confinement strengths even when starting from a non-interacting basis. The limit where the missing triple and higher excitations become relevant is investigated through comparison with full Configuration Interaction results.

Keyword
electronic structure, electron correlation methods, coupled cluster, coupled cluster singles and doubles, quantum dot, two-dimensional, many-body physics, many-body perturbation theory
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:su:diva-38861 (URN)
Available from: 2010-05-02 Created: 2010-05-02 Last updated: 2010-05-03Bibliographically approved

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