# Alumni Dissertations and Theses

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### Quantum State Discrimination and Quantum Cloning: Optimization and Implementation

Author:Andi ShehuYear of Dissertation:2015Program:PhysicsAdvisor:János BergouAbstract:Abstract. Recently the problem of optimal state discrimination with a Fixed Rate of Inconclusive Outcomes (FRIO strategy) has been solved for two pure quantum states and a few other highly symmetric cases. An optical implementation to FRIO for pure states is provided. The physical implementation can be carried out with the use of a six-port interferometer constructed with optical fibers beam splitters, phase shifters and mirrors. The input states are composed of qubits which are realized as photons in the dual-rail representation. The non-unitary measurements are carried out at the output for the presence or absence of a photon. The setup optimally interpolates between minimum error and unambiguous state discrimination. We also extend the FRIO strategy to two mixed states, whose eigenvectors in their spectral representation form a Jordan basis. We derive the minimum error rate P_{E} for a fixed inconclusive rate Q and, in particular, the optimal distribution of the total Q over the Jordan subspaces. As Q is varied between the two limits, 0

### Measuring the transmission matrix for microwave radiation propagating through random waveguides: fundamentals and applications

Author:Zhou ShiYear of Dissertation:2014Program:PhysicsAdvisor:Azriel GenackAbstract:This thesis describes the measurement and analysis of the transmission matrix (TM) for microwave radiation propagating through multichannel random waveguides in the crossover to Anderson localization. Eigenvalues of the transmission matrix and the associated eigenchannels are obtained via a singular value decomposition of the TM. The sum of the transmission eigenvalues yields the transmittance

T , which is the classical analog of the dimensionless conductanceg . The dimensionless conductanceg is the electronic conductance in units of the quantum conductance,G/(e^2/h) . For diffusive wavesg >1, approximatelyg transmission eigenchannels contribute appreciably to the transmittanceT . In contrast, for localized waves withg <1,T is dominated by the highest transmission eigenvalue, &tau&_{1}. For localized waves, the inverse of the localization lengths of different eigenchannels are found to be equally spaced. Measurement of the TM allows us to explore the statistics of the transmittanceT . A one-sided log-normal distribution ofT is found for a random ensemble withyour g =0.37 and explained using an intuitive Coulomb gas model for the transmission eigenvalues. Single parameter scaling (SPS) predicted for one dimension random system is approached in multichannel systems onceT is dominated by a single transmission eigenchannel. In addition to the statistics of the TM for ensembles of random samples, we investigated the statistics of a single TM. The statistics within a large single TM are found to depend upon a single parameter, the eigenchannel participation number,M . The variance of the total transmission normalized by its averaging in the TM is equal toM -1 . We found universal fluctuation ofM , reminiscent of the well known universal conductance fluctuations for diffusive waves. We demonstrate focusing of steady state and pulse transmission through a random medium via phase conjugation of the TM. The contrast between the focus and the background is determined byM and the size of the transmission matrixN . The spatio-temporal profile of focused radiation in the diffusive limit is shown to be the square of the field-field correlation function in space and time. We determine the density of states (DOS) of a disordered medium from the dynamics of transmission eigenchannels and from the quasi-normal modes of the medium for localized samples. The intensity profile of each eigenchannel within the random media is closely linked to the dynamics of transmission eigenchannels and an analytical expression for intensity profile of each of the eigenchannel based on numerical simulation was provided.### Self-consistent calculations of optical properties of type I and type II quantum heterostructures

Author:Vladimir ShuvayevYear of Dissertation:2009Program:PhysicsAdvisor:Lev DeychAbstract:In this Thesis the self-consistent computational methods are applied to the study of the optical properties of semiconductor nanostructures with one- and two-dimensional quantum confinements. At first, the self-consistent Schrodinger-Poisson system of equations is applied to the cylindrical core-shell structure with type~II band alignment without direct Coulomb interaction between carriers. The electron and hole states and confining potential are obtained from a numerical solution of this system. The photoluminescence kinetics is theoretically analyzed, with the nanostructure size dispersion taken into account. The results are applied to the radiative recombination in the system of ZnTe/ZnSe stacked quantum dots. A good agreement with both continuous wave and time-resolved experimental observations is found. It is shown that size distribution results in the photoluminescence decay that has essentially non-exponential behavior even at the tail of the decay where the carrier lifetime is almost the same due to slowly changing overlap of the electron and hole wavefunctions. Also, a model situation applicable to colloidal core-shell nanowires is investigated and discussed. With respect to the excitons in type I quantum wells, a new computationally efficient and flexible approach of calculating the characteristics of excitons, based on a self-consistent variational treatment of the electron-hole Coulomb interaction, is developed. In this approach, a system of self-consistent equations describing the motion of an electron-hole pair is derived. The motion in the growth direction of the quantum well is separated from the in-plane motion, but each of them occurs in modified potentials found self-consistently. This approach is applied to a shallow quantum well with the delta-potential profile, for which analytical expressions for the exciton binding energy and the ground state eigenfunctions are obtained, and to the quantum well with the square potential profile with several different well and barrier materials. The numerical results yield lower exciton binding energies in comparison to standard variational calculations, while the iterative scheme used to calculate the energies and respective wavefunctions is stable, rapidly convergent and requires reduced computational effort. Thus, the method can be an important computational tool in computing exciton characteristics in quantum wells exceeding currently existing approaches in accuracy and efficiency. The method can also be naturally generalized for quantum wires and dots.

### Control of Light-Matter Interaction via Dispersion Engineering

Author:Harish Natarajan Swaha KrishnamoorthyYear of Dissertation:2014Program:PhysicsAdvisor:Vinod MenonAbstract:This thesis describes the design, fabrication and characterization of certain nanostructures to engineer light-matter interaction. These materials have peculiar dispersion properties owing to their structural design, which is exploited to control spontaneous emission properties of emitters such as quantum dots and dye molecules. We will discuss two classes of materials based on the size of their unit cell compared to the wavelength of the electromagnetic radiation they interact with. The first class are hyperbolic metamaterials (HMM) composed of alternate layers of a metal and a dielectric of thicknesses much smaller than the wave- length. Using a HMM composed of silver and titanium dioxide, we demonstrate the optical equivalent of the well-known Lifshitz transition in electronic systems. Then we describe the development of a tunable HMM whose optical properties can be tuned. The tunability is achieved by exploiting the insulator to metal phase transition in vanadium dioxide. We then discuss the second class of materials - photonic crystals, in which the size scale of the unit cell is of the order of the wavelength of electromagnetic radiation they interact with. Due to strong scattering in such systems, bandgaps open up in certain directions, which we use to modify the spontaneous emission of a fluorescent dye.

### Fuzzy Field Theory as a Random Matrix Model

Author:Juraj TekelYear of Dissertation:2013Program:PhysicsAdvisor:V Parameswaran NairAbstract:This dissertation considers the theory of scalar fields on fuzzy spaces from the point of view of random matrices. First we define random matrix ensembles, which are natural description of such theory. These ensembles are new and the novel feature is a presence of kinetic term in the probability measure, which couples the random matrix to a set of external matrices and thus breaks the original symmetry. Considering the case of a free field ensemble, which is generalization of a Gaussian matrix ensemble, we develop a technique to compute expectation values of the observables of the theory based on explicit Wick contractions and we write down recursion rules for these. We show that the eigenvalue distribution of the random matrix follows the Wigner semicircle distribution with a rescaled radius. We also compute distributions of the matrix Laplacian of the random matrix given by the new term and demonstrate that the eigenvalues of these two matrices are correlated. We demonstrate the robustness of the method by computing expectation values and distributions for more complicated observables. We then consider the ensemble corresponding to an interacting field theory, with a quartic interaction. We use the same method to compute the distribution of the eigenvalues and show that the presence of the kinetic terms rescales the distribution given by the original theory, which is a polynomially deformed Wigner semicircle. We compute the eigenvalue distribution of the matrix Laplacian and the joint distribution up to second order in the correlation and we show that the correlation between the two changes from the free field case. Finally, as an application of these results, we compute the phase diagram of the fuzzy scalar field theory, we find multiscaling which stabilizes this diagram in the limit of large matrices and compare it with the results obtained numerically and by considering the kinetic part as a perturbation.

### Interactions between a Bacterial Tyrosine Kinase and its Cognate Phosphatase- A Solution NMR Study

Author:Deniz TemelYear of Dissertation:2012Program:PhysicsAdvisor:Ranajeet GhoseAbstract:Bacterial tyrosine kinases (BY-kinases) play a central role in a variety of physiological processes in bacterial cells. Most notable among these processes is the formation of antiphagocytic capsule and biofilm for survival under environmental stress conditions. BY-kinases constitute a unique class of prokaryotic enzymes sharing no sequence or structural homology with their eukaryal counterparts. BY-kinases are regulated by eukaryotic-like protein tyrosine phosphatases and several tyrosine kinase/phosphatase pairs, which have been identified in both gram-positive and gram-negative bacterial species. The Escherichia coli (K12) BY-kinase Wzc is regulated by a cytosolic Low Molecular Weight Protein Tyrosine Phosphatase (LMW-PTP) Wzb through the autophosphorylation/dephosphorylation of five phosphorylatable tyrosine residues (termed the tyrosine cluster, YC) located in the C-terminal tail of the cytosolic catalytic domain of Wzc. The cycling between autophosphorylated form of Wzc and the Wzb-catalyzed dephosphorylated state, rather than the quantitative phosphorylation state of the YC, appears to play a central role in the synthesis and export of the exopolysaccharide, colanic acid. Despite biochemical evidence that Wzb dephosphorylates YC-phosphorylated Wzc, the nature of the interactions between these two enzymes and the detailed regulatory mechanism has not been elucidated. The aim of this research was to identify the structural, dynamic and mechanistic aspects of the regulation of Wzc by Wzb. We used state-of-the-art solution-state Nuclear Magnetic Resonance (NMR) techniques in order to illuminate the interaction between Wzc and Wzb. We have obtained near-complete resonance assignments of the catalytic domain of Wzc, the first for a BY-kinase. Utilizing these assignments and chemical shift titrations, we demonstrate that Wzb prevents oligomerization of Wzc by occluding its intramolecular interaction surface, that lies on the opposite face to that housing the Wzc catalytic site, thus facilitating the dephosphorylation of the exposed YC. The YC would be buried, and shielded from Wzb, in oligomeric Wzc. Similar chemical shift titrations on Wzb reveals that Wzc docks onto Wzb using a site proximal to the catalytic site of the latter. NMR spin-relaxation measurements confirm this hypothesis in addition to revealing interesting dynamics in the key regulatory elements in Wzc and Wzb.

### Magnetic Resonance Studies of Energy Storage Materials

Author:Rafael Vazquez ReinaYear of Dissertation:2013Program:PhysicsAdvisor:Steven GreenbaumAbstract:Abstract Magnetic Resonance Studies of Energy Storage Materials by Rafael Vázquez Reina Adviser: Professor Steven G. Greenbaum In today's society there is high demand to have access to energy for portable devices in different forms. Capacitors with high performance in small package to achieve high charge/discharge rates, and batteries with their ability to store electricity and make energy mobile are part of this demand. The types of internal dielectric material strongly affect the characteristics of a capacitor, and its applications. In a battery, the choice of the electrolyte plays an important role in the Solid Electrolyte Interphase (SEI) formation, and the cathode material for high output voltage. Electron Paramagnetic Resonance (EPR) and Nuclear Magnetic Resonance (NMR) spectroscopy are research techniques that exploit the magnetic properties of the electron and certain atomic nuclei to determine physical and chemical properties of the atoms or molecules in which they are contained. Both EPR and NMR spectroscopy technique can yield meaningful structural and dynamic information. Three different projects are discussed in this dissertation. First, High energy density capacitors where EPR measurements described herein provide an insight into structural and chemical differences in the dielectric material of a capacitor. Next, as the second project, Electrolyte solutions where an oxygen-17 NMR study has been employed to assess the degree of preferential solvation of Li+ ions in binary mixtures of EC (ethylene carbonate) and DMC (dimethyl carbonate) containing LiPF6 (lithium hexafluo- rophosphate) which may be ultimately related to the SEI formation mechanism. The third project was to study Bismuth fluoride as cathode material for rechargeable batteries. The objective was to study 19F and 7Li MAS NMR of some nanocomposite cathode materials as a conversion reaction occurring during lithiation and delithation of the BiF3/C nanocomposite.

### An experimental investigation into the mechanisms of bacterial evolution

Author:Zhenmao WanYear of Dissertation:2014Program:PhysicsAdvisor:Mark HilleryAbstract:This thesis studies the two fundamental mechanisms of bacterial evolution — horizontal gene transfer and spontaneous mutation, in the bacterium

Escherichia coli through novel experimental assays and mathematical simulations. First, I will develop a growth assay utilizing the quantitative polymerase chain reaction (qPCR) to provide real-time enumeration of genetic marker abundance within bacterial populations. Second, I will focus on horizontal gene transfer inE. coli occurring through a process called conjugation. By fitting the qPCR data to a resource limited, logistic growth model, I will obtain estimated values of several key parameters governing the dynamics of DNA transfer through conjugation under two different conditions: i) in the absence of selection; ii) in the presence of negative selection pressure — bacteriophage infection. Last, I will investigate spontaneous mutation through qPCR assay of competition between wild-type and mutator phenotypeE. coli . Mutator phenotype has an elevated mutation rate due to defects in DNA proofreading and repairing system. By introducing antibiotic selective pressure, I will examine the fixation probability of mutators competing with wild-type in novel environment. I also will utilize simulations to study the impact of three parameters on the fixation probability.### POTENTIAL ENERGY LANDSCAPE OF PARTICULATE MATTER

Author:Kun WangYear of Dissertation:2012Program:PhysicsAdvisor:Hernan MakseAbstract:The application of concepts from equilibrium statistical mechanics to out of equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials. These systems are considered "complex" since equilibrium statistics is insufficient in its attempt to describe the system dynamics. An appealing approach for understanding these complex systems is to study the properties of the system's "potential energy landscape" (PEL), described by the 3N-coordinates of all particles in the multi-dimensional configuration space, or landscape, of the potential energy of the system (N is the number of particles). For dissipative jammed systems- granular materials or droplets- a key concept introduced by S. Edwards in 1989 is to replace the energy ensemble describing conservative systems by the volume ensemble. However, this approach is no able to describe the jamming critical point (J-point) for deformable particles like emulsions, whose geometric configurations are influenced by the applied external stress. Therefore, the volume ensemble requires augmentation by the ensemble of stresses. Just as volume fluctuations in the Edwards ensemble can be described by compactivity, the stress fluctuations give rise to an angoricity, another analogue of temperature in equilibrium systems. In this Thesis, we test the combined volume-stress ensemble for granular matter by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble as a test of ergodicity. Agreement between both methods suggests the idea of "thermalization" at a given angoricity and compactivity. These intensive variables elucidate the thermodynamic order of the jamming phase transition by showing the absence of critical fluctuations above jamming in static observables like pressure and volume. Our results demonstrate the possibility of calculating important observables such as the entropy, volume, pressure, coordination number and the distribution of interparticle forces to fully characterize the scaling laws near the jamming transition from a statistical mechanics point of view. We also study the energy-landscape network. We find the stable basins and the first order saddles connecting them, and identify them with the network nodes and links, respectively. We analyze the network properties and model the system's evolution.

### QUASI-NORMAL MODES IN RANDOM MEDIA

Author:Jing WangYear of Dissertation:2012Program:PhysicsAdvisor:Azriel GenackAbstract:This thesis is an experimental study of microwave transmission through quasi-one-dimensional random samples via quasi-normal modes. We have analyzed spectra of localized microwave transmitted through quasi-one-dimensional random samples to obtain the central frequency, linewidth and field speckle pattern of the modes for an ensemble of samples at three lengths. We find strong correlation between modal field speckle patterns. This leads to destructive interference between modes which explain strong suppression of steady state transmission and of pulsed transmission at early times. At longer times, the rate of decay of transmission slows down because of the increasing prominence of long-lived modes. We have also studied the statistics of mode spacings and widths in localized samples. The distribution of mode spacings between adjacent modes is close to the Wigner surmise predicted for diffusive waves, which exhibit strong level repulsion. However, a deviation from Wigner distribution can be seen in the distribution of spacings beyond the nearest ones. A weakening in the rigidity of the modal spectrum is also observed as the sample length increases because of reduced level repulsion for more strongly localized waves. In contrast to residual diffusive behavior for level spacing statistics, the distribution of level widths are log-normal as predicted for localized waves. But the residual diffusive behavior can be seen from the smaller variance of the normalized mode width as compared to predictions for strongly localized waves. We also measured the steady state and dynamic fluctuations and correlation of localized microwave transmitted through random waveguides. We find the degree of intensity correlation first increases, and then decays with time delay, before increasing dramatically. The variation in the spatial correlation of intensity with time delay is due to the changing effective number of modes that contribute to transmission. A minimum in correlation is reached when the number of modes contributing appreciably to transmission peaks. At long times, the degree of intensity correlation and the variance of total transmission increase dramatically. This reflects the reduced role of short-lived overlapping states and the growing weight of long-lived spectrally isolated modes.