#### Date of Award

January 2021

#### Document Type

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Physics & Astrophysics

#### First Advisor

Yen L. Loh

#### Abstract

In theory, a quantum computer can do everything a classical computer can do, and more. This is possible because of the principal difference between their respective fundamental units of computation. Classical computers use bits that can take on values of 0 or 1, but quantum computers use quantum bits, called qubits, that can take on values of 0, 1, or any combination of 0 and 1 by exploiting the rules of quantum mechanics. However, this quantum nature is extremely fragile and therefore it is imperative that qubits are protected from their environment. Conversely, qubits cannot be so isolated that their manipulation, necessary for any basic computation, becomes impossible. One approach to realizing these qubits is by using single-molecule magnets (SMMs).

Recent experiments were able to achieve electrical control of a TbPc2 SMM nuclear spin qubit via the hyperfine Stark effect (HSE). TbPc2 consists of a terbium (III) ion sandwiched between two phthalocyanine molecules, referred to as the organic ligands. The nuclear spin qubits are well isolated from the environment, but this also makes them more difficult to manipulate since their manipulation is only achieved by using the electron spins as mediators.

The purpose of this project is two-fold and ongoing. First, we aim to understand the hyperfine Stark effect in TbPc2 from first principles. We do this by building up a theoretical quantum mechanical framework from single-electron atoms and then generalizing the results to many-electron atoms, as shown in chapters 1 through 3. In chapter 3, we assume the ligands give rise to easy-axis anisotropy and thus we glean an order-of-magnitude estimate of the splittings. By computing the hyperfine splittings in both the LS coupling and jj coupling schemes, we calculate a range of values which agrees with experiments.

The second aim of this project is to investigate whether the HSE can be enhanced by modifying the organic ligand structures to allow for easier qubit manipulation. In chapter 4 we present a path toward this goal, starting with the procurement of TbPc2's electrostatic charge distribution with density functional theory. From there, we sketch out what it would take to calculate the hyperfine splittings, and how the organic ligand structures may be altered to enhance the HSE.

#### Recommended Citation

Fehr, David, "Modulation Of The Hyperfine Coupling In A TbPc2 Single-Molecule Magnet With Electric Fields" (2021). *Theses and Dissertations*. 3924.

https://commons.und.edu/theses/3924