# Alumni Dissertations

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### THEORY OF BCS-BEC CROSSOVER IN ULTRACOLD ATOMIC GASES

Author:Yasemin GurcanYear of Dissertation:2012Program:PhysicsAdvisor:SULTAN CATTOAbstract:In ultracold atomic fermions, the sign and the magnitude of pairing interactions can be controlled by using the magnetically-tuned Feshbach resonances to achieve a continuos transition between Cooper pairs of dilute fermi gas to BEC of diatomic molecules, which is known as the "BCS-BEC crossover". At present, although several models have been proposed, there is still no exact analytical solution of the many-body problem of BCS-BEC crossover region. The standard BCS mean field theory of superconductivity was used [1-3] to describe the whole crossover resulting a useful approximation. In our studies, we investigated solvable models for the best variational analytical solution for BCS-BEC crossover at T= 0.

### Photonic Structures Based on Hybrid Nanocomposites

Author:Saima HusainiYear of Dissertation:2011Program:PhysicsAdvisor:Vinod MenonAbstract:In this thesis, photonic structures embedded with two types of nanomaterials, (i) quantum dots and (ii) metal nanoparticles are studied. Both of these exhibit optical and electronic properties different from their bulk counterpart due to their nanoscale physical structure. By integrating these nanomaterials into photonic structures, in which the electromagnetic field can be confined and controlled via modification of geometry and composition, we can enhance their linear and nonlinear optical properties to realize functional photonic structures. Before embedding quantum dots into photonic structures, we study the effect of various host matrices and fabrication techniques on the optical properties of the colloidal quantum dots. The two host matrices of interest are SU8 and PMMA. It is shown that the emission properties of the quantum dots are significantly altered in these host matrices (especially SU8) and this is attributed to a high rate of nonradiative quenching of the dots. Furthermore, the effects of fabrication techniques on the optical properties of quantum dots are also investigated. Finally a microdisk resonator embedded with quantum dots is fabricated using soft lithography and luminescence from the quantum dots in the disk is observed. We investigate the absorption and effective index properties of silver nanocomposite films. It is shown that by varying the fill factor of the metal nanoparticles and fabrication parameters such as heating time, we can manipulate the optical properties of the metal nanocomposite. Optimizing these parameters, a silver nanocomposite film with a 7% fill factor is prepared. A one-dimensional photonic crystal consisting of alternating layers of the silver nanocomposite and a polymer (Polymethyl methacrylate) is fabricated using spin coating and its linear and nonlinear optical properties are investigated. Using reflectivity measurements we demonstrate that the one-dimensional silver-nanocomposite-dielectric photonic crystal exhibits a 200% enhancement of the reflection band which is attributed to the interplay between the plasmon resonance of the silver nanoparticles and the Bloch modes of the photonic crystal. Nonlinear optical studies on this one-dimensional silver-nanocomposite-dielectric structure using z-scan measurements are conducted. These measurements indicate a three-fold enhancement in the nonlinear absorption coefficient when compared to a single film of comparable metal composite thickness.

### Quantum Physics of Molecular Magnets

Author:Reem JaafarYear of Dissertation:2010Program:PhysicsAdvisor:Eugene ChudnovskyAbstract:In this thesis we focus on various aspects of quantum physics in molecular magnets, in particular, in Mn

_{12}-acetate. This thesis is divided into three parts. In the first part, we present a review on molecular magnets. Since Mn_{12}-acetate has a large spin (equal to 10), the theory of tunneling of a large spin is discussed as well as the early experiments that were performed two decades ago and which has shown spin tunneling, in particular, the ones that were performed on &gamma -Fe_{2}-O_{3}- and on antiferromagnetic ferritin. Then, the first experiments that presented evidence on spin tunneling in Mn_{12}--acetate are outlined in detail. Magnetic hysteresis curves are shown and Landau-Zener effect in molecular magnets is discussed. Quantum classical crossover between thermally assisted and pure quantum tunneling regimes is described. Finally, magnetic avalanches are introduced: they are another feature of the magnetization curve in Mn_{12}-Acetate where there is a sudden reversal in the magnetization. We exploit the first two experiments performed to elucidate the nature of magnetic avalanches in Mn_{12}--acetate and the theory developed as a result of these experiments. In the second part of this thesis, we focus on three of my publications on quantum magneto-mechanical effects. First, a recent experiment on Einstein-de Haas effect in a NiFe film deposited on a microcantilever is discussed. The cantilever was placed inside a coil that generated an ac magnetic field. Oscillation of the cantilever was measured by a fiber-optic interferometer positioned above the tip of the cantilever. When the frequency of the ac field matched the resonance frequency of the cantilever the amplitude of the oscillations was about 3 nm. The data were analyzed within a model that replaced the mechanical torque due to change in the magnetization with the effect of the periodic force acting on the fictitious point mass at the free end of the cantilever so this model did not account for the microscopic dynamics of the Einstein-de Haas effect. This motivated us to develop a more rigorous theoretical framework for the description of the dynamics of the Einstein-de Haas effect that we applied to the problem of the magnetic cantilever. We then study the quantum dynamics of a magnetic molecule deposited on a microcantilever. Amplitude and frequencies of the coupled magneto-mechanical oscillations have been computed. We show that oscillations of the spin and the cantilever occur independently at frequencies &Delta/&hbar and &omega_{n}respectively, unless these two frequencies come very close to each other. The results show that the splitting &delta has no free parameters and that for a given resonance, &Delta=&hbar&omega_{n}the relative splitting &delta depends only on the position of the molecule on the cantilever. We then show that existing experimental techniques permit observation of the driven coupled oscillations of the spin and the cantilever, as well as of the splitting of the mechanical modes of the cantilever caused by spin tunneling. Finally, the dynamics of a magnetic molecule bridged between two conducting leads is investigated. We start by reviewing various experiments performed when there is a weak coupling between the molecule and the leads and when there is a strong coupling which results in the Kondo effect. Experimental efforts were mainly motivated to measure the electronic current through a single molecule. We study the dynamics of the total angular momentum that couples spin tunneling to the mechanical rotations. We show that the Landau-Zener spin transition produced by the time-dependent magnetic field generates a unique pattern of mechanical oscillations that can be detected by measuring the electronic tunneling current through the molecule. In the last and final part, we present our numerical work to describe quantum magnetic deflagration in Mn_{12}-acetate. This part is related to magnetic deflagration as discussed in part I of this thesis. The focus is on the quantum features of magnetic deflagration which are exhibited by the maxima in the speed of deflagration front as a function of the applied magnetic field. We review recent work on the effect of the dipolar field in forming self-organized fronts of spin tunneling, and present our enhanced computational work on the calculation of the relaxation rate. Previously, spin relaxation rates were calculated using a simple Arrhenius exponent. In this thesis we calculate the relaxation rate as a function of both the external field and temperature using the density matrix formalism and use them to study the effect of the transverse field on the front speed of deflagration.### Solid State NMR Studies of Energy Conversion and Storage Materials

Author:Sohan Roshel De Silva Jankuru HennadigeYear of Dissertation:2011Program:PhysicsAdvisor:Steve GreenbaumAbstract:NMR (Nuclear magnetic resonance) spectroscopy is utilized to study energy conversion and storage materials. Different types of NMR techniques including Magic Angle Spinning, Cross-polarization and relaxation measurement experiments were employed. Four different projects are discussed in this dissertation. First, three types of CF

_{x}battery materials were investigated. Electrochemical studies have demonstrated different electrochemical performances by one type, delivering superior performance over the other two.13 C and19 F MAS NMR techniques are employed to identify the atomic/molecular structural factors that might account for differences in electrochemical performance among different types. Next as the second project, layered polymer dielectrics were investigated by NMR. Previous studies have shown that thin film capacitors are improved by using alternate layers of two polymers with complementary properties: one with a high breakdown strength and one with high dielectric constant as opposed to monolithic layers.13 C to1 H cross-polarization techniques were used to investigate any inter-layer properties that may cause the increase in the dielectric strength. The third project was to study two types of thermoelectric materials. These samples were made of heavily doped phosphorous and boron in silicon by two different methods: ball-milled and annealed. These samples were investigated by NMR to determine the degree of disorder and obtain insight into the doping efficiency. The last ongoing project is on a lithium-ion battery system. The nature of passivating layers or the solid electrolyte interphase (SEI) formed on the electrodes surface is important because of the direct correlation between the SEI and the battery life time/durability. Multinuclear (7 Li,19 F,31 P) techniques are employed to identify the composition of the SEI formation of both positive and negative electrodes.### STATISTICAL MECHANICS OF JAMMED PACKINGS OF SPHERES

Author:Yuliang JinYear of Dissertation:2012Program:PhysicsAdvisor:Hernan MakseAbstract:The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. There are presently numerous experiments showing that randomly packing spheres of equal size into a container consistently results in a static configuration with a density of 0.64. The ubiquity of random close packing (RCP) rather than the equilibrium crystalline array at 0.74 begs a new statistical framework. Here we introduce a general volume ensemble statistical approach for jammed packings of spheres. This approach provides a thermodynamic definition of RCP: RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the ``freezing point'' in a first-order phase transition between ordered and disordered packing phases. We generalize the theory to jammed packings of high dimensional and different size spheres. The asymptotic high-dimensional scaling of the RCP density is consistent with that of other approaches, such as replica theory and density functional theory. The theory predicts the density of random close packing and random loose packing (RLP) of polydisperse systems for a given distribution of sphere size. The present mean-field approach may help to treat packing problems of non-spherical particles, and could serve as a starting point to understand the higher-order correlations present in jammed packings.

### NMR Studies of Ionic Liquids and Polymer Membrane Electrolytes for Batteries and Fuel Cells

Author:SUFIA KHATUNYear of Dissertation:2012Program:PhysicsAdvisor:Steve GreenbaumAbstract:In this thesis, NMR (Nuclear Magnetic Resonance) spectroscopic techniques are used to study ionic liquids (ILs) and polymer membranes for advanced Li-ion batteries and fuel cells. Besides structural measurements, dynamics and motional properties were also measured using pulsed field gradient spin echo and relaxation experiments. Five projects are described in this thesis. The first two projects involve

1 H,19 F,7 Li and13 C NMR transport studies of two different ILs. The third project is a study of Nafion ionomer aggregations where diffusion and viscosity measurements are made. The fourth project involves the structural study of lithium triflate:PEO_{3}polymer membranes via7 Li static NMR. The fifth and final project described in the thesis involves27 Al NMR studies of a chloroaluminate (AlCl_{3}) IL and the assessment of the tetrahedral Al species content.### PHASE LOCKING IN FIBER LASER ARRAYS

Author:FANTING KONGYear of Dissertation:2010Program:PhysicsAdvisor:Ying-Chih ChenAbstract:This dissertation reports a series of studies on phase locking in two-element laser arrays, with an emphasis on fiber laser arrays, and an application of Q-switched microchip laser to high-resolution photoacoustic imaging. Phase locking is achieved by coupling the lasing elements to a common Fourier-transform resonator, in which the lasing elements and the output mirror are positioned in the focal planes of a converging lens so that the far-field profiles of the laser elements are projected to the output mirror through Fourier transformation. Since the far-field profiles generally have simpler and more symmetric structures, the relative phase of the lasing elements can be selected by placing a simple spatial filter on the output mirror. We have studied phase locking in fiber lasers operating in the continuous-wave mode and in stimulated-Brillouin-scattering (SBS) Q-switched mode, and in Q-switched microchip laser arrays formed in a single crystal. These systems represent vastly different parameters which can affect the development of phase locking. We have found that the continuous-wave fiber lasers can always be phase locked and the relative phase remains stable despite random phase fluctuations in individual fibers. This is attributed to the combination of broad bandwidths of the fiber gain media and small frequency spacing of the longitudinal mode which allows resonance frequencies of the composite resonator of the laser array to be found under all circumstances. In short-pulse laser arrays, phase locking can be realized only when the fiber lengths are nearly equal in the SBS Q-switched fiber lasers, or the frequency mismatch is less than the bandwidth of the laser pulse in the microchip laser array. In the latter case, the boundary of phase-locked and unlocked states is characterized by partial coherence in the combined laser beam due to the pulses from the individual elements not perfectly overlapping in time. Photoacoustic images are constructed based on the ultrasound signals generated when a tissue undergoes thermal expansion after laser pulses are absorbed by chromophores in the tissue. The use of focused laser pulse and high-frequency ultrasound has led to much higher image resolution than obtainable with conventional pulse-echo ultrasound. The ability to identify chemical compositions in tissues based on their distinct wavelength-dependent optical absorption also leads to new capabilities in diagnostic imaging.

### MODELING OF ULTRA-SHORT SOLITON PROPAGATION IN DETERMINISTIC AND STOCHASTIC NONLINEAR CUBIC MEDIA

Author:Levent KurtYear of Dissertation:2011Program:PhysicsAdvisor:Sultan CattoAbstract:We study the short pulse dynamics in the deterministic and stochastic environment in this thesis. The integrable short pulse equation is a modelling equation for ultra-short pulse propagation in the infrared range in the optical fibers. We investigate the numerical proof for the exact solitary solution of the short pulse equation. Moreover, we demonstate that the short pulse solitons approximate the solution of the Maxwell equation numerically. Our numerical experiments prove the particle-like behaviour of the short pulse solitons. Furthermore, we derive a short pulse equation in the higher order. A stochastic counterpart of the short pulse equation is also derived through the use of the multiple scale expansion method for more realistic situations where stochastic perturbations in the dispersion are present. We numerically show that the short pulse solitary waves persist even in the presence of the randomness. The numerical schemes developed demonstrate that the statistics of the coarse-graining noise of the short pulse equation over the slow scale, and the microscopic noise of the nonlinear wave equation over the fast scale, agree to fairly good accuracy.

### Aperture Array Photonic Metamaterials: Theoretical approaches, numerical techniques and a novel application

Author:Eli LanseyYear of Dissertation:2012Program:PhysicsAdvisor:David CrouseAbstract:Optical or photonic metamaterials that operate in the infrared and visible frequency regimes show tremendous promise for solving problems in renewable energy, infrared imaging, and telecommunications. However, many of the theoretical and simulation techniques used at lower frequencies are not applicable to this higher-frequency regime. Furthermore, technological and financial limitations of photonic metamaterial fabrication increases the importance of reliable theoretical models and computational techniques for predicting the optical response of photonic metamaterials. This thesis focuses on aperture array metamaterials. That is, a rectangular, circular, or other shaped cavity or hole embedded in, or penetrating through a metal film. The research in the first portion of this dissertation reflects our interest in developing a fundamental, theoretical understanding of the behavior of light's interaction with these aperture arrays, specifically regarding enhanced optical transmission. We develop an approximate boundary condition for metals at optical frequencies, and a comprehensive, analytical explanation of the physics underlying this effect. These theoretical analyses are augmented by computational techniques in the second portion of this thesis, used both for verification of the theoretical work, and solving more complicated structures. Finally, the last portion of this thesis discusses the results from designing, fabricating and characterizing a light-splitting metamaterial.

### Usefulness of Nuclear Magnetic Resonance in the Study of a Variety of Battery Systems and Materials

Author:Nicole LeiferYear of Dissertation:2009Program:PhysicsAdvisor:Steve GreenbaumAbstract:The usefulness of solid state Nuclear Magnetic Resonance (NMR) spectroscopy in the analysis of lithium ion batteries is presented. Some background information on lithium batteries is given, in addition to a summary of current research areas. A comprehensive review of the use of NMR and Electron Paramagnetic Resonance (EPR) in lithium batteries research thus far is also presented. The electrodes studied were the standard LiCoO2 cathode cycled against mesocarbon microbead (MCMB) anodes, as well as Li2Ag2V4O11 and CFx cathodes cycled against metallic lithium anodes in primary batteries. The focus of half of the work concerns the elucidation of the Solid Electrolyte Interphase (SEI), an irreversibly formed side-product found on the electrode surfaces, composed mainly from the electrolyte components; one study provides a deeper insight into the inorganic components of the SEI, while the other SEI study focuses on the organic components via 13C MAS NMR studies of cycled electrodes. The other half is comprised of two additional studies in which atomic and electronic rearrangement are monitored in the electrodes at different stages of the battery cycling process.