A master thesis from Aalborg University
Electrostatic and Electrodynamical Manipulation of Electrons on Cryogenic Substrates for Quantum Computing Applications
Author(s)
Term
4. term (FYS10)
Education
Publication year
2025
Submitted on
2025-05-30
Pages
114 pages
Abstract
The purpose of this thesis was to study aspects of the out-of-plane qubit control induced by external electric fields using quantum mechanical perturbation theory in both the time-dependent and time-independent cases for the electron-on-Helium qubit platform. By limiting ourselves to simpler models, we are able to apply both analytical and numerical approaches, which show the viability and ease of which qubits may be electrically controlled on this platform. We initially derive an expression for the image-charge induced Coulomb potential binding the electron using classical electrostatics. The energies and eigenstates of the electron are then found by solving the time-independent Schrödinger equation under the given potential. The corresponding dipole matrix elements and oscillator strengths are subsequently found. The model is then generalized in the form a Kratzer potential using a quantum defect parameter. The generalized energies, eigenstates, dipole matrix elements and oscillator strengths are then determined. The system is then perturbed by a static electric field and time-independent perturbation theory is used to find energy and eigenstate corrections with both the basis expansion method and Dalgarno-Lewis approach. The first few energy corrections and polarizabilities are subsequently found for a general . The perturbative energy expansion is regularized using a hypergeometric approximant and its accuracy is verified with a numerical complex-scaled Sturmian expansion scheme. The model is compared with experimental results. A new harmonic field is then introduced as the perturbation and time-dependent perturbation theory is used to determine the eigenstate corrections with both the basis expansion method and a Sturmian expansion. The dynamic linear polarizability for Kratzer potential is found in closed form and plotted. The closed form Pockels polarizability for the Coulomb potential is shown.
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