Physics

With wide applications ranging from quantum communication and metrology to biomedicine, single photon sources in solid-state hosts have become a major area of study. Here, we focus on three applications: nanothermometry, optically detected magnetic resonance (ODMR), and second order autocorrelation. We present novel statistical and machine learning (ML) approaches to extract information from experimental and simulated data and benchmark these methods against traditional inference-based statistical approaches. We found that compared to traditional inference-based methods ML algorithms can: i) predict temperatures at the nanoscale with greater accuracy and with less calibration points than traditional fitting methods; ii) identify the resonance peaks in ODMR spectra with factors ~1.3x and ~4.7x better accuracy and resolution and achieved equal or better performance with ~5x less data; and iii) have the potential to parse second order autocorrelation data more efficiently. ML algorithms are thus powerful tools for quantum sensing techniques.

Author Keywords: colour centers, machine learning, nanosensing, nanothermometry, optically detected magnetic resonance, second order autocorrelation

We study a one-dimensional Fermi-Hubbard model with disorder in charge and spin degrees of freedom. We calculate the time dependence of the entanglement entropy. While previous research on disordered interacting systems has typically focused on systems with either charge or spin, our model enables us to explore the interplay between charge and spin in shaping the behavior of entanglement. We use a method that identifies optimally local charge- and spin-specific integrals of motion. We ask how the locality level of these integrals of motion influences the capacity of low-order terms in the l-bit Hamiltonian to capture the entanglement entropy. Our results show that increasing the locality level improves the accuracy of low-order terms in capturing entanglement entropy dynamics. With equally strong charge and spin disorder, the behavior of the entanglement entropy closely resembles that observed in single-degree-of-freedom systems, and the l-bit Hamiltonian truncated at second order accurately captures this behavior.

Author Keywords: Entanglement Entropy, Fermi-Hubbard Model, Hungarian Algorithm, l-bit Hamiltonian, Local Integrals of Motion, Many-Body Localization

Microwave resonances in isolated water-based spheres, dimers, and trimers are explored using simulations conducted with COMSOL Multiphysics. The study centers on morphology-dependent resonances (MDRs) and hotspot characteristics in cm-sized objects at microwave frequencies. Monomers subjected to microwave radiation exhibit four distinct resonant modes at specific sizes characterized by electric and magnetic field distributions which correspond to magnetic-dipolar, electric-dipolar, magnetic quadrupolar, and electric quadrupolar resonances, respectively. Dimer configurations reveal intriguing hotspot features, with axial hotspots emerging as a key resonant characteristic. The three fundamental dimer orientations dictate unique resonant behaviors, highlighting the sensitivity of hotspot intensity to orientation changes, but smooth and consistent trends during transitions between them. Investigations into trimer structures, as a more intricate geometry formed by interconnected dimers, reveal the subtle interactions of spheres in a trimer structure. Trimer hotspots largely reflect the sum of isolated dimer hotspot contributions, showcasing the energy conservation with no evidence of a newly formed hotpot. Our results, while arising as a consequence of the particularly high index of refraction of water at GHz frequencies, are generalizable to other length scales (such as nano-photonics), were materials with sufficiently high refractive index and transparency to be found.

Author Keywords: COMSOL simulations, Electromagnetic physics, Microwave frequencies, Morphology-dependent resonance, water-based objects

In electron-doped ferroelectrics, the free electrons can become concentrated along the domain walls which act like a conducting surface. We consider the impact of free electrons occupying the t2g orbitals on the domain walls of an electron-doped perovskite ferroelectric. We build an analytical model based on Landau-Ginzburg-Devonshire theory, and a trio of tight-binding Hamiltonians for free electrons. We self-consistently solve for the polarization, potential, and electron density using a finite-difference approximation. We find that the ferroelectric is effectively charge neutral. The free electrons are attracted to the positively-charged domain wall, leaving it with a small residual charge. As the electron density increases, the domain walls tilt to form zig-zag domain walls. Orbital selectivity of the t2g orbitals depends on the relative orientations of the orbital plane and the domain wall. This property influences the rate at which the domain wall tilts as a function of the electron density.

Author Keywords: Charged Domain Wall, Domain Wall, Ferroelectric, Landau-Ginzburg, Perovskite, Strontium Titanate

Microwave resonances in isolated water-based spheres, dimers, and trimers are explored using simulations conducted with COMSOL Multiphysics. The study centers on morphology-dependent resonances (MDRs) and hotspot characteristics in cm-sized objects at microwave frequencies. Monomers subjected to microwave radiation exhibit four distinct resonant modes at specific sizes characterized by electric and magnetic field distributions which correspond to magnetic-dipolar, electric-dipolar, magnetic quadrupolar, and electric quadrupolar resonances, respectively. Dimer configurations reveal intriguing hotspot features, with axial hotspots emerging as a key resonant characteristic. The three fundamental dimer orientations dictate unique resonant behaviors, highlighting the sensitivity of hotspot intensity to orientation changes, but smooth and consistent trends during transitions between them. Investigations into trimer structures, as a more intricate geometry formed by interconnected dimers, reveal the subtle interactions of spheres in a trimer structure. Trimer hotspots largely reflect the sum of isolated dimer hotspot contributions, showcasing the energy conservation with no evidence of a newly formed hotpot. Our results, while arising as a consequence of the particularly high index of refraction of water at GHz frequencies, are generalizable to other length scales (such as nano-photonics), were materials with sufficiently high refractive index and transparency to be found.

Author Keywords: COMSOL simulations, Electromagnetic physics, Microwave frequencies, Morphology-dependent resonance, water-based objects

In electron-doped ferroelectrics, the free electrons can become concentrated along the domain walls which act like a conducting surface. We consider the impact of free electrons occupying the t2g orbitals on the domain walls of an electron-doped perovskite ferroelectric. We build an analytical model based on Landau-Ginzburg-Devonshire theory, and a trio of tight-binding Hamiltonians for free electrons. We self-consistently solve for the polarization, potential, and electron density using a finite-difference approximation. We find that the ferroelectric is effectively charge neutral. The free electrons are attracted to the positively-charged domain wall, leaving it with a small residual charge. As the electron density increases, the domain walls tilt to form zig-zag domain walls. Orbital selectivity of the t2g orbitals depends on the relative orientations of the orbital plane and the domain wall. This property influences the rate at which the domain wall tilts as a function of the electron density.

Author Keywords: Charged Domain Wall, Domain Wall, Ferroelectric, Landau-Ginzburg, Perovskite, Strontium Titanate

The replacement of petroleum with renewable feedstock for energy and materials has become a priority because of concerns over the environment and finite nature of petroleum. The structures of the available natural biomass feedstocks fall short in delivering key functionality required in materials such as lubricants and phase change energy storage materials (PCMs). The approach taken in this thesis was to combine select functional groups with vegetable oil derivatives to create novel PCMs and lubricantswhich deliver desired functionality. One series of diester PCMs were prepared with terephthalic acid and fatty alcohols to address known shortcomings of esters. The second class of PCMs are sulfones prepared from oxidation of fatty sulfides to improve thermal energy storage. Overall, the new PCMs presented narrow phase change temperature ranges, high transition temperature (between 67 to 110℃), high transition enthalpy (210 to 266J/g), minimal supercooling and congruent phase transitions unaffected by cooling rates. They also demonstrated higher thermal degradation stability with onset of degradation from 290 to 310℃. The series of lubricants studied consists of sulfide and sulfonyl functional groups attached to the unsaturation sites of oleyl oleate as pendant groups to improve the thermal and flow properties. The new lubricants present subzero crystallization temperatures, very low crystallization enthalpy and dynamic viscosity as high as 180mPas.

Furthermore, they also presented high onset of degradation (up to 322℃) and oxidation (up to 298℃). The PCMs and lubricants of the present thesis demonstrate that select functional groups can be used with common structural elements of vegetable oil such as fatty acids, ester groups and unsaturation sites to make a variety of molecular structures capable of delivering desired properties

Author Keywords: Crystal Structure, Lubricant, Phase Change Material, Renewable, Structure-Property Relationships, Vegetable Oil

The appearance of a two-dimensional electron gas (2DEG) in oxide interfaces between strontium titanate (STO) and other materials has become a major area of study. The behaviour of the 2DEG in STO is not well understood in part because the dielectric properties of STO are not well characterized. The differential susceptibility has a major impact on the electric fields within strontium titanate, and therefore to understand the 2DEG a better understanding of the susceptibility is needed. An expression for the soft mode phonon frequency of bulk strontium titanate is derived and used to model the susceptibility as a function of spatially homogeneous electric field, temperature and wavevector. This model is used to discuss the effect of spatially inhomogeneous electric fields and the local vs. nonlocal nature of the susceptibility. The critical exponents and the free energy are determined and discussed.

Author Keywords: critical exponents, differential susceptibility, quantum paraelectric, strontium titanate

This thesis is divided into two parts, each of which supports constructing and using a lithium magneto-optical trap for cold collision studies:

Part I

One outgoing channel of interest from cold collisions is the production of ion pairs. We describe an effective method for calculating bound-to-continuum cross-sections for charged binary systems by examining transitions to states above the binding energy that become bound when the system is placed within an infinite spherical well. This approach is verified for ionization of a hydrogen atom, and is then applied to the heavy Rydberg system Li+...I-.

Part II

A wavemeter previously built in the lab is redesigned for increased reliability and ease of use by replacing the optical hardware with a rocker system, which can be aligned in mere minutes rather than half a day as was previously the case. The new wavemeter has been tested through saturated absorption spectroscopy of lithium.

Author Keywords: cross-section, dissociation, lithium, magneto-optical trap, Michelson, wavemeter

The present thesis explores the cold flow properties of biodiesel and the effect of vegetable oil derived compounds on the crystallization path as well as the mechanisms at play at different stages and length scales. Model systems including triacylglycerol (TAG) oils and their derivatives, and a polymer were tested with biodiesel. The goal was to acquire the fundamental knowledge that would help design cold flow improver (CFI) additives that would address effectively and simultaneously the flow problems of biodiesel, particularly the cloud point (CP) and pour point (PP). The compounds were revealed to be fundamentally vegetable oil crystallization modifiers (VOCM) and the polymer was confirmed to be a pour point depressant (PPD).

The results obtained with the VOCMs indicate that two cis-unsaturated moieties combined with a trans-/saturated fatty acid is a critical structural architecture for depressing the crystallization onset by a mechanism wherein while the straight chain promotes a first packing with the linear saturated FAMEs, the kinked moieties prevent further crystallization. The study of model binary systems made of a VOCM and a saturated FAME with DSC, XRD and PLM provided a complete phase diagram including the thermal transformation lines, crystal structure and microstructure that impact the phase composition along the different crystallization stages, and elicited the competing effects of molecular mass, chain length mismatch and isomerism. The liquid-solid boundary is discussed in light of a simple thermodynamic model based on the Hildebrand equation and pair interactions.

In order to test for synergies, the PP and CP of a biodiesel (Soy1500) supplemented with several VOCM and PLMA binary cocktails were measured using a specially designed method inspired by ASTM standards. The results were impressive, the combination of additives depressed CP and PP better than any single additive. The PLM and DSC results suggest that the cocktail additives are most effective when the right molecular structure and optimal concentration are provided. The cocktail mixture achieves then tiny crystals that are prevented from aggregating for an extended temperature range. The results of the study can be directly used for the design of functional and economical CFI from vegetable oils and their derivatives.

Author Keywords: Biodiesel, Microstructure, Polymorphism, Pour point depressants, Triacylglycerol, Vegetable Oil Based Crystal Modifier