<p dir="ltr">Ultrafast optics is an important field of study for chemistry and physics, providing new information on the dynamics of matter and electrons. In this thesis I describe my work on ultrafast laser systems. The two main systems discussed are a high harmonic generated extreme ultraviolet system and a terahertz spectroscopy system. The first half describes the importance and background of both as well as how these systems are set up. The second half describes my work in designing and implanting these systems, and my work in constructing components for the operation of both.</p>

<p> Excitons represent the electronic excited state of organic semiconductor and many low-dimensional inorganic semiconductors. In solar energy conversion systems, exciton transport affects how fast the charges reach the electrodes thus governs the performance of photovoltaic cells. In optoelectronic applications such as semiconductor lasers and light-emitting diodes, exciton radiative rate determines the efficiency of luminescence in competition to various nonradiative processes. Therefore, understanding how exciton migrates over space as well as its decay dynamics are vital for the design of highly efficient optoelectronic devices. To interrogate these photophysical processes requires experimental tools with simultaneous high temporal and spatial resolution. In this thesis, I introduce two transient imaging systems (photoluminescence imaging with 300 ps time resolution, and transient absorption microscopy with 200 fs time) that are innovative tools to directly probe excited state dynamics and transport in sub-μm domains. The techniques were applied to a type of promising semiconductor, perovskites, including surface-passivated hybrid perovskite and 2D layered perovskites to explore the fundamental mechanisms that affect exciton transport. The fundamental understanding of excitons shed light on the underlying physics such as exciton delocalization, exciton-exciton interaction, and how these properties affected by the static and dynamic disorders of the material. We further demonstrated a novel twisted superlattice using ultrathin perovskites that confines excitons due to increased density of state from the moiré flat bands. In addition, excitons can be accelerated by strongly interacts photons, forming polariton quasiparticles that possess small effective mass. This is demonstrated by coupling 2D layered perovskites to a plasmonic array. We further showcase the formation of bulk polaritons without an external optical cavity in a self-assembled organic aggregate. Experimental investigation into these intriguing phenomena provide an approach to study fundamental processes such as many-body interaction and quantum coherence. </p>

The vacuum of quantum field theory is not empty space but filled with quantum vacuum fluctuations, which give rise to many intriguing effects. The first part of this Thesis addresses cosmic inflation, where the quantum fluctuations of the inflaton field freeze and get amplified in the expanding universe. Afterwards, we turn our attention towards Bose-Einstein condensates, a laboratory system. Since most of our calculations are performed using a mean-field expansion, we will study the accuracy of a finite-range interaction potential onto such an expansion. Exploiting the universality of quantum fluctuations, several aspects of cosmic inflation will be identified in ballistically expanding Bose-Einstein condensates. The effective action technique for calculating the quantum backreaction will be scrutinized. Finally, we consider dynamic quantum phase transitions in the last part of this Thesis. To this end two specific scenarios will be investigated: firstly, the structure formation during the superfluid to Mott-insulator transition in the Bose-Hubbard model; and secondly, the formation of spin domains as a two-dimensional spin-one Bose gas is quenched from the (polar) paramagnetic to the (planar) ferromagnetic phase. During this quench, the symmetry of the ground state is spontaneously broken and vortices (topological defects) form.

The vacuum of quantum field theory is not empty space but filled with quantum vacuum fluctuations, which give rise to many intriguing effects. The first part of this Thesis addresses cosmic inflation, where the quantum fluctuations of the inflaton field freeze and get amplified in the expanding universe. Afterwards, we turn our attention towards Bose-Einstein condensates, a laboratory system. Since most of our calculations are performed using a mean-field expansion, we will study the accuracy of a finite-range interaction potential onto such an expansion. Exploiting the universality of quantum fluctuations, several aspects of cosmic inflation will be identified in ballistically expanding Bose-Einstein condensates. The effective action technique for calculating the quantum backreaction will be scrutinized. Finally, we consider dynamic quantum phase transitions in the last part of this Thesis. To this end two specific scenarios will be investigated: firstly, the structure formation during the superfluid to Mott-insulator transition in the Bose-Hubbard model; and secondly, the formation of spin domains as a two-dimensional spin-one Bose gas is quenched from the (polar) paramagnetic to the (planar) ferromagnetic phase. During this quench, the symmetry of the ground state is spontaneously broken and vortices (topological defects) form.

In this thesis, we study the kinetic disordering of systems interacting with an agent or a walker. Our studies divide naturally into two classes: for the first, the dynamics of the walker conserves the total magnetization of the system, for the second, it does not. These distinct dynamics are investigated in part I and II respectively. In part I, we investigate the disordering of an initially phase-segregated binary alloy due to a highly mobile vacancy which exchanges with the alloy atoms. This dynamics clearly conserves the total magnetization. We distinguish three versions of dynamic rules for the vacancy motion, namely a pure random walk , an "active" and a biased walk. For the random walk case, we review and reproduce earlier work by Z. Toroczkai et. al., [9] which will serve as our base-line. To test the robustness of these findings and to make our model more accessible to experimental studies, we investigated the effects of finite temperatures ("active walks") as well as external fields (biased walks). To monitor the disordering process, we define a suitable disorder parameter, namely the number of broken bonds, which we study as a function of time, system size and vacancy number. Using Monte Carlo simulations and a coarse-grained field theory, we observe that the disordering process exhibits three well separated temporal regimes. We show that the later stages exhibit dynamic scaling, characterized by a set of exponents and scaling functions. For the random and the biased case, these exponents and scaling functions are computed analytically in excellent agreement with the simulation results. The exponents are remarkably universal. We conclude this part with some comments on the early stage, the interfacial roughness and other related features. In part II, we introduce a model of binary data corruption induced by a Brownian agent or random walker. Here, the magnetization is not conserved, being related to the density of corrupted bits ρ. Using both continuum theory and computer simulations, we study the average density of corrupted bits, and the associated density-density correlation function, as well as several other related quantities. In the second half, we extend our investigations in three main directions which allow us to make closer contact with real binary systems. These are i) a detailed analysis of two dimensions, ii) the case of competing agents, and iii) the cases of asymmetric and quenched random couplings. Our analytic results are in good agreement with simulation results. The remarkable finding of this study is the robustness of the phenomenological model which provides us with the tool, continuum theory, to understand the nature of such a simple model. / Ph. D.

Icicles are a ubiquitous and picturesque feature of cold winter weather. Their familiar form emerges from a subtle interplay between the solidification dynamics of ice and the gravity-driven flow of the thin water film flowing over their evolving surface. The latent heat released by freezing is advected by the water film and ultimately carried away by the surrounding sub-zero air, which is also flowing. Like many processes far from equilibrium, icicle growth can exhibit nonlinear pattern formation. While scaling theory predicts that icicles converge to `platonic', self-similar shapes, natural icicles often exhibit regular ripple patterns about their circumference, which are due to a morphological instability. This thesis presents a comprehensive experimental study of icicles that sheds new light on the dynamics of their growth and the origin of their form. A table-top apparatus was designed and built for the controlled growth of icicles, under different conditions of temperature, water supply rate, ambient air motion, and water purity. Image analysis and Fourier methods were used to examine their morphology. Contrary to theoretical expectations, ripples do not appear on icicles made from pure water. Instead, ripples grow and travel on icicles made from salt solutions, even at very low concentrations. The addition of non-ionic surfactant or dissolved gases does not produce ripples, unless ionic impurities are also present. The ripple wavelength is independent of time and growth conditions. The ripple amplification rate and traveling velocity vary weakly with the ionic concentration, as do the tip and radial growth speeds of the icicle. While the tip and radial growth also depend on the ambient temperature and input mass flux, the ripple dynamics is not correlated with extrinsic conditions. If the ambient temperature or input mass flux is sufficiently low, the tip growth only advances for a short period of time before it ceases. After cessation, the shape of the icicle deviates increasingly from self-similarity. The most self-similar icicles are made from pure water with the surrounding air gently stirred, whereas icicles made from impure water in still air tend to grow multiple tips.

Icicles are a ubiquitous and picturesque feature of cold winter weather. Their familiar form emerges from a subtle interplay between the solidification dynamics of ice and the gravity-driven flow of the thin water film flowing over their evolving surface. The latent heat released by freezing is advected by the water film and ultimately carried away by the surrounding sub-zero air, which is also flowing. Like many processes far from equilibrium, icicle growth can exhibit nonlinear pattern formation. While scaling theory predicts that icicles converge to `platonic', self-similar shapes, natural icicles often exhibit regular ripple patterns about their circumference, which are due to a morphological instability. This thesis presents a comprehensive experimental study of icicles that sheds new light on the dynamics of their growth and the origin of their form. A table-top apparatus was designed and built for the controlled growth of icicles, under different conditions of temperature, water supply rate, ambient air motion, and water purity. Image analysis and Fourier methods were used to examine their morphology. Contrary to theoretical expectations, ripples do not appear on icicles made from pure water. Instead, ripples grow and travel on icicles made from salt solutions, even at very low concentrations. The addition of non-ionic surfactant or dissolved gases does not produce ripples, unless ionic impurities are also present. The ripple wavelength is independent of time and growth conditions. The ripple amplification rate and traveling velocity vary weakly with the ionic concentration, as do the tip and radial growth speeds of the icicle. While the tip and radial growth also depend on the ambient temperature and input mass flux, the ripple dynamics is not correlated with extrinsic conditions. If the ambient temperature or input mass flux is sufficiently low, the tip growth only advances for a short period of time before it ceases. After cessation, the shape of the icicle deviates increasingly from self-similarity. The most self-similar icicles are made from pure water with the surrounding air gently stirred, whereas icicles made from impure water in still air tend to grow multiple tips.

<p>Supersaturating drug delivery systems are an attractive solubility enabling formulation strategy for poorly soluble drugs due to their potential to significantly enhance solubility and hence, bioavailability. Compendial dissolution testing is commonly used a surrogate for assessing the bioavailability of enabling formulations. However, it increasingly fails to accurately predict <i>in vivo</i> performance due its closed-compartment characteristics and the lack of absorptive sink conditions. <i>In vivo</i>, drug is continually removed due to absorption across the gastrointestinal membrane, which impacts the luminal concentration profile, which in turn affects the dissolution kinetics of any undissolved material, as well as crystallization kinetics from supersaturated solutions. Thus, it is critical to develop an improved methodology that better mimics <i>in vivo</i> conditions. An enhanced approach integrates dissolution and absorption measurements. However, currently-used two-compartment absorptive apparatuses, employing a flat-sheet membrane are limited, in particular by the small membrane surface area that restricts the mass transfer, resulting in unrealistic experimental timeframes. This greatly impacts the suitability of such systems as a formulation development tool. The goal of this research is two-fold. First, to develop and test a high surface area, flow-through, absorptive dissolution testing apparatus, designed to provide <i>in vivo</i> relevant information about formulation performance in biologically relevant time frames. Second, to use this apparatus to obtain mechanistic insight into physical phenomenon occurring during formulation dissolution. Herein, the design and construction of a coupled dissolution-absorption apparatus using a hollow fiber membrane module to simulate the absorption process is described. The hollow fiber membrane offers a large membrane surface area, improving the mass transfer rates significantly. Following the development of a robust apparatus, its application as a formulation development tool was evaluated in subsequent studies. The dissolution-absorption studies were carried out for supersaturated solutions generated via anti-solvent addition, pH-shift and by dissolution of amorphous formulations. The research demonstrates the potential of the apparatus to capture subtle differences between formulations, providing insight into the role of physical processes such as supersaturation, crystallization kinetics and liquid-liquid phase separation on the absorption kinetics. The study also explores dissolution-absorption performance of amorphous solid dispersions (ASDs) and the influence of resultant solution phase behavior on the absorption profile. Residual crystalline content in ASDs is a great concern from a physical stability and dissolution performance perspective as it can promote secondary nucleation or seed crystal growth. Therefore, the risk of drug crystallization during dissolution of ASDs containing some residual crystals was assessed using absorptive dissolution measurements and compared to outcomes observed using closed-compartment dissolution testing. Mesoporous silica-based formulations are another type of amorphous formulations that are gaining increased interest due to higher physical stability and rapid release of the amorphous drug. However, their application may be limited by incomplete drug release resulting from the adsorption tendency of the drug onto the silica surface. Thus, the performance of mesoporous silica-based formulations was also evaluated in the absorptive dissolution testing apparatus to determine the impact of physiological conditions such as gastrointestinal pH and simultaneous membrane absorption on the adsorption kinetics during formulation dissolution. Overall, the aim of this research was to demonstrate the potential of the novel <i>in vitro</i> methodology and highlight the significance of a dynamic absorptive dissolution environment to enable better assessment of complex enabling formulations. <i>In vivo</i>, there are multiple physical processes occurring in the gastrointestinal lumen and the kinetics of these processes strongly depend on the absorption kinetics and <i>vice-a-versa</i>. Thus, using this novel tool, the interplay between solution phase behavior and the likely impacts on bioavailability of supersaturating drug delivery systems can be better elucidated. This approach and apparatus is anticipated to be of great utility to the pharmaceutical industry to make informed decisions with respect to formulation optimization.</p>

<p dir="ltr">Laser absorption spectroscopy (LAS) is a widely used technique to acquire path-integrated measurements of gas properties such as temperature and mole fraction. Although extremely useful, the application of LAS to study heterogeneous combustion environments can be challenging. For example, beam steering can be one such challenge that arises during measurements in heterogeneous combustion environments such as metallized propellant flames or measurements at high-pressure conditions. The ability to only obtain path integrated measurements has been a major challenge of conventional LAS techniques, especially in characterizing combustion environments with a non-uniform thermo-chemical distribution along the line of sight (LOS). Additionally, simultaneous measurements of multiple species using LAS with narrow-bandwidth lasers often necessitates employing multiple light sources. Aerospace applications, such as characterizing hypersonic flows may require ultrashort time resolution to study fast-evolving chemistry. Similarly, atmospheric entry most often requires measurements of atoms and molecules that absorb at wavelengths ranging from ultraviolet to mid-infrared. The availability of appropriate light sources for such measurements has been limited. In the past, several researchers have come up with diagnostic techniques to overcome the above-mentioned challenges to a certain extent. Most often, these solutions have been need-based while compromising on other diagnostic capabilities. Therefore, LAS diagnostics capable of acquiring broadband measurements with ultrafast time resolution and the ability to acquire measurements at wavelengths in ultraviolet through mid-infrared is required to study advanced combustion systems and for the development of advanced aerospace systems for future space missions. Ultrafast laser absorption spectroscopy is one such technique that provides broadband measurements, enabling simultaneous multi-species and high-pressure measurements. The light source utilized for ULAS provides the ultrafast time resolution necessary for resolving fast-occurring chemistry and more importantly the ability to acquire measurements at a wide range of wavelengths ranging from ultraviolet to far-infrared. The development and application of ULAS for characterizing propellant flames and hypersonic flows under non-equilibrium conditions by overcoming the above-mentioned challenges is presented here. </p><p>This work describes the development of a single-shot ultrafast laser absorption spectroscopy (ULAS) diagnostic for simultaneous measurements of temperature and concentrations of CO, NO, and H₂O in flames and aluminized fireballs of HMX (C₄H₈N₈O₈). Ultrashort (55 fs) pulses from a Ti:Sapphire oscillator emitting near 800 nm were amplified and converted into the mid-infrared through optical parametric amplification (OPA) at a repetition rate of 5 kHz. Ultimately, pulses with a spectral bandwidth of ≈600 cm^-1 centered near 4.9 µm were utilized in combination with a mid-infrared spectrograph to measure absorbance spectra of CO, NO, and H₂O across a 30 nm bandwidth with a spectral resolution of 0.3 nm. The gas temperature and species concentrations were determined by least-squares fitting simulated absorbance spectra to measured absorbance spectra. Measurements of temperature, CO, NO, and H₂O were acquired in an HMX flame burning in air at atmospheric pressure and the measurements agree well with previously published results. Measurements were also acquired in fireballs of HMX with and without 16.7 wt% H-5 micro-aluminum. Time histories of temperature and column densities are reported with a 1-σ precision of 0.4% for temperature and 0.3% (CO), 0.6% (NO), and 0.5% (H₂O), and 95% confidence intervals (C.I.) of 2.5% for temperature and 2.5% (CO), 11% (NO), and 7% (H₂O), thereby demonstrating the ability of ULAS to provide high-fidelity, multi-parameter measurements in harsh combustion environments. The results indicate that the addition of the micron-aluminum increases the fireball peak temperature by ≈100 K and leads to larger concentrations of CO. The addition of aluminum also increases the duration fireballs remain at elevated temperatures above 2000 K.</p><p dir="ltr">Next, the application of ULAS for dual-zone temperature and multi-species (CO, NO, H₂O, CO₂, HCl, and HF) measurements in solid-propellant flames is presented. ULAS measurements were acquired at three different central wavelengths (5.121 µm, 4.18 µm, and 3.044 µm) for simultaneous measurements of temperature and: 1) CO, NO, and H₂O, 2) CO₂ and HCl, and 3) HF and H₂O. Absorption measurements with a spectral resolution of 0.35 nm and bandwidth of 7 cm^-1, 18 cm^-1, and 35 cm^-1, respectively were acquired. In some cases, a dual-zone absorption spectroscopy model was implemented to accurately determine the gas temperature in the hot flame core and cold flame boundary layer via broadband absorption measurements of CO₂, thereby overcoming the impact of line-of-sight non-uniformities. Results illustrate that the hot-zone temperature of CO₂ agrees well with the equilibrium flame temperature and single-zone thermometry of CO, the latter of which is insensitive to the cold boundary layer due to the corresponding oxidation of CO to CO₂.</p><p dir="ltr">The initial development and implementation of an ultraviolet and broadband ultrafast-laser-absorption-imaging (UV-ULAI) diagnostic for one dimensional (1D) imaging of temperature and CN via its <i>B</i>²Σ⁺←<i>X</i>²Σ⁺absorption bands near 385 nm. The diagnostic was demonstrated by acquiring single-shot measurements of 1D temperature and CN profiles in HMX flames at a repetition rate of 25 Hz. Ultrashort pulses (55 fs) at 800 nm were generated using a Ti:Sapphire oscillator and then amplification and wavelength conversion to the ultraviolet was carried out utilizing an optical parametric amplifier and frequency doubling crystals. The broadband pulses were spectrally resolved using a 1200 l/mm grating and imaged on an EMCCD camera to obtain CN absorbance spectra with a resolution of ≈0.065 nm and a bandwidth of ≈4 nm (i.e. 260 cm^-1). Simulated absorbance spectra of CN were fit to the measured absorbance spectra using non-linear curve fitting to determine the gas properties. The spatial evolution of gas temperature and CN concentration near the burning surface of an HMX flame was measured with a spatial resolution of ≈10 µm. 1D profiles of temperature and CN concentration were obtained with a 1-σ spatial precision of 49.3 K and 4 ppm. This work demonstrates the ability of UV-ULAI to acquire high-precision, spatially resolved absorption measurements with unprecedented temporal and spatial resolution. Further, this work lays the foundation for ultraviolet imaging of numerous atomic and molecular species with ultrafast time resolution.</p><p dir="ltr">Ultraviolet ULAS was applied to characterize the temporal evolution of non-Boltzmann CN (<i>X</i>²Σ⁺) formed behind strong shock waves in N₂-CH₄ mixtures at conditions relevant to entry into Titan's atmosphere. An ultrafast (femtosecond) light source was utilized to produce 55 fs pulses near 385 nm at a repetition rate of 5 kHz and a spectrometer with a 2400 lines/mm grating was utilized to spectrally resolve the pulses after passing through the Purdue High-Pressure Shock Tube. This enabled broadband single-shot absorption measurements of CN to be acquired with a spectral resolution and bandwidth of ≈0.02 nm and ≈6 nm (≈402 cm^-1 at these wavelengths), respectively. A line-by-line absorption spectroscopy model for the <i>B</i>²Σ⁺←<i>X</i>²Σ⁺ system of CN was developed and utilized to determine six internal temperatures (two vibrational temperatures, four rotational) of CN from the (0,0), (1,1), (2,2) and (3,3) absorption bands. Measurements were acquired behind reflected shock waves in 5.65% CH₄ and 94.35% N₂ with an initial pressure of 1.56 mbar and incident shock speed of ≈2.1 km/s. For this test condition, the chemically and vibrationally frozen temperature of the mixture behind the reflected shock was 5000 K and the pressure was 0.6 atm. The high repeatability of the shock-tube experiments (0.3% variation in shock speed across tests) enabled multi-shock time histories of CN mole fraction and six internal temperatures to be acquired with a single-shot time resolution of less than 1 ns. The measurements revealed that CN <i>X</i>²Σ⁺ is non-Boltzmann rotationally and vibrationally for greater than 200 µs, thereby strongly suggesting that chemical reactions are responsible for the non-Boltzmann population distributions. </p><p><br></p>