Improving the learning and success of students in undergraduate science, technology, engineering, and mathematics (STEM) courses has become an increased focus of education researchers within the past decade. As part of these efforts, discipline-based education research (DBER) has emerged within STEM education as a way to address discipline-specific challenges for teaching and learning, by combining expert knowledge of the various STEM disciplines with knowledge about teaching and learning (Dolan et al., 2018; National Research Council, 2012). Particularly important to furthering DBER and improving STEM education are interdisciplinary studies that examine how the teaching and learning of specific concepts develop among and across various STEM disciplines... / Ph. D. / Dissertation proposal

Doping nonmagnetic materials is known as an effective way of investigating the properties of frustrated magnets. LiCuSbO4 is one of the simplest quasi-one dimensional spin-1/2 magnets which can be modelled with ferromagnetic(FM) nearest neighbour and antiferromagnetic (AFM) next nearest neighbour interactions. Here, doping with both non-magnetic ions, Zn, Mg, and magnetic ions, Co, is investigated. LiCu1-xMxSbO4 (M=Mg, Zn, Co 0≦x≦0.1) samples were synthesized by a ceramics process. At higher doping levels (x≧0.04), paramagnetic Curie features are observed below 4 K, however the broad peak characteristic of short range ordering at 6 K is retained. Isothermal magnetization indicates that the critical field found at 12 T in LiCuSbO4 was shifted by Zn and Mg doping. While the field is increased as the amount of Mg doping, it was increased as Zn doping in the range of 0≦x≦0.02 but decreased by x≧0.04. The trend in critical field is observed to follow that of the c lattice parameter for both Zn and Mg doping. On doping with Co2+ (S = 3/2), a low temperature Curie feature was observed from x=0.02. The value of the critical field increased on doping from (x=0) 12 T for 13.5 T (x=0.10). As for non-magnetic doping the trend in Hc has the same behaviour as the lattice parameter. The effect of doping on the pyrochlore spin ice A2B2O7 is also explored. The effect of oxygen vacancies induced by the aliovalent substitution on the B site on the crystal electric field was explored in the ceramic solid solutions. The effect of aliovalent doping on the pyrochlore A2Sn2(1-x)Sc2xO7-x (A=Ho and Dy 0≦x≦0.10) Tb2B2(1-x)Sc2xO7-x (B=Sn and Ti 0≦x≦0.05) were studied. While no dramatic changes of the saturation value of isothermal magnetization and heat capacities was observed in Dy2Sn2O7 by Sc doping in the range of 0≦x≦0.1, the saturation value of isothermal magnetization and magnetic entropy in Ho2Sn2O7 was clearly increased by Sc doping more than x=0.05, This difference could be from the difference of Kramer’s and non-Kramer’s spins between Dy and Ho, as while Dy is a Kramer’s ion and its ground state is protected, Ho is a non-Kramer’s ion and its ground state could be split. While Tb2Sn2O7 is known as quantum spin ice, Tb2Ti2O7 is known as spin liquid. A peak at 6 K of heat capacity, which is assigned as being due to a crystal electric field excitation to an excited doublet in Tb2Sn2O7 and Tb2Ti2O7 was observed in the Tb2Sn2(1-x)Sc2xO7-x sample. However in Tb2Ti2(1-x)Sc2xO7-x it was not observed. This indicates that the increased strain in the ceramic solid solution has a larger impact on the crystal electric field.

Probing nonequilibrium dynamics in a trapped, inhomogeneous atomic quantum gas can be a challenging task because coexisting mass transport and spreading of quantum correlations often make the problem intractable. By removing density inhomogeneity in an atomic quantum gas and employing local control of chemical potential as well as interaction parameters, it is possible to perform quasi-particle control, initiate and probe collective quantum dynamics without or with a controlled mass flow. We report our experimental results toward quasi-particle control and nonequilibrium dynamics in a homogeneous two-dimensional quantum gas.

This licentiate thesis describes an investigation of participation and achievement in undergraduate physics courses with a discourse analytical lens. Issues of unequal participation have been a growing concern for the physics education research community. At the same time, these issues have not been explored to any large extent using already developed theoretical tools from fields of social science and humanities. This thesis builds on earlier studies in physics education research but crosses disciplinary boundaries to bring in perspectives from gender studies. The two papers use a discourse theoretical framework to explore what it might mean to participate in physics, whether that is one’s primary subject or not, in courses in electromagnetism and quantum physics. A general conclusion that can be drawn from these empirical studies is that physics courses may often be taught from a narrow physics perspective, and that this may limit the possibilities for identification for many students. For instance, engineering students whose main area was not physics failed to see much significance in studying electromagnetism and then just “studied to pass”. Additionally, students on physics programmes may find that the limited positions in quantum physics which can be characterized as mainly focused on “calculating”, are hard to reconcile with their interest in physics. Using a discourse perspective, I broaden this critique to a discussion of the culture of physics: What does it mean to become a physicist and what physics culture follows from different “productions” of physicists? These results inform continued research in physics education by raising issues of identity and providing critical frameworks for exploring them. They also point to the importance of including broad views of physics in courses. Critically examining participation in physics, this thesis aims at widening the discussion and provide new ways to talk about these issues in physics education research.

This thesis is concerned with the generation of non-classical quantum states of light, the photon-level manipulation of quantum states and the accurate tomography of both quantum states and quantum processes. In optics, quantum information can be encoded and processed in both discrete and continuous variables. Hybrid approaches combining for example homodyne detection with conditional state preparation and manipulation are gaining increasing prominence. The development and characterization of a time-domain balanced homodyne detector (BHD) is presented. The detector has a bandwidth of 80 MHz, a signal-to-noise ratio of 14.5 dB and an efficiency of 86% making it well-suited to pulse-to-pulse measurement of quantum optical states. The BHD is employed to perform quantum state tomography (QST) of non-classical multi-photon Fock states generated by spontaneous parametric down-conversion. A detailed investigation of the mode-matching between the local oscillator used for homodyne detection and the generated Fock states is presented. The one-, two- and three-photon Fock states are reconstructed with a combined preparation and detection efficiency exceeding 50%. Fock states have a number of applications in quantum state engineering, where non-classical ancilla states and conditional measurements enable photon-level manipulation of quantum states. Fock state filtration (FSF) is investigated - an example of a post-selected beam splitter which is a basic building block for many quantum state engineering protocols. A model is developed incorporating the effect of experimental imperfections. An experimental implementation of a Fock state filter is fully characterized by means of coherent-state quantum process tomography (QPT). The reconstructed process is found to be consistent with the model. The filter preferentially removes the single-photon component from an arbitrary input quantum state. Calibration of optical detectors in the quantum regime is discussed. Quantum detector tomography (QDT) is reviewed and contrasted with a new technique for performing QST with a calibrated detector known as the fitting of data patterns (FDP). The first experimental characterization of a BHD is performed by probing the detector with phase-averaged coherent states. The FDP method is shown to be applicable to the estimation of quantum processes, where a detector response is not assumed - thus demonstrating the versatility of the FDP approach as a new method in the quantum tomography toolbox.

In this thesis, we study persistent currents and quantum critical phenomena in the systems of mesoscopic physics. As an introduction in Chapter 1 we familiarize the reader with the area of mesoscopic physics. We explain how mesoscopic systems are different from quantum systems of single atoms and molecules and bulk systems with an Avogadro number of elements. We also describe some important mesoscopic phenomena. One of the mathematical tools that we extensively use in our studies is Random Matrix Theorty. This theory is not a part of standard physics courses and for educational purposes we provide the basics of Random Matrix Theory in Chapter 2. In Chapter 3 we study the persistent current of noninteracting electrons in quantum billiards. We consider simply connected chaotic Robnik-Berry quantum billiard and its annular analog. The electrons move in the presence of a point-like magnetic flux at the center of the billiard. For the simply connected billiard, we find a large diamagnetic contribution to the persistent current at small flux, which is independent of the flux and is proportional to the number of electrons (or equivalently the density since we keep the area fixed). The size of this diamagnetic contribution is much larger than the previously studied mesoscopic fluctuations in the persistent current in the simply connected billiard. This behavior of persistent current can ultimately be traced to the response of the angular-momentum l = 0 levels (neglected in semiclassical expansions) on the unit disk to a point-like flux at its center. We observe the same behavior for the annular billiard when the inner radius is much smaller than the outer one. We also find that the usual fluctuating persistent current and Anderson-like localization due to boundary scattering are seen when the annulus tends to a one-dimensional ring. We explore the conditions for the observability of this phenomenon. In Chapter 4 we study quantum critical phenomena in a system of two coupled quantum dots connected by a hopping bridge. Both the dots and connecting region are assumed to be in universal Random Matrix crossover regimes between Gaussian orthogonal and unitary ensembles (defined in Chapter 2). We exploit a diagrammatic approach appropriate for energy separations much larger than the level spacing, to obtain the ensemble-averaged one- and two-particle Greens functions. We find that two main components of the twoparticle Green’s function (diffuson and Cooperon) can be described by separate scaling functions. We then use this information to investigate a model interacting system in which one dot has an attractive s-wave reduced Bardeen-Cooper-Schrieffer interaction, while the other is noninteracting but subject to an orbital magnetic field. We find that the critical temperature TC of the mean-field transition into the superconducting state in the first dot is non-monotonic in the flux through the second dot in a certain regime of interdot coupling. Likewise, the fluctuation magnetization above the critical temperature is also non-monotonic in this regime, can be either diamagnetic or paramagnetic, and can be deduced from the Cooperon scaling function. We end this thesis with conclusion in Chapter 5.

Mon projet de thèse a eu pour objectif l'étude des propriétés magnétiques de condensats de Bose-Einstein d'atomes de Sodium confinés dans un piège optique. Dans la première partie, nous présentons le dispositif expérimental et le protocole suivi pour la production tout-optique de condensats. La première étape consiste dans le chargement d'un piège dipolaire croisé désaccordé vers le rouge à partir d'atomes pré-refroidis dans un piège magnéto-optique. La deuxième étape est le refroidissement évaporatif dans un piège dipolaire composite, combinaison du piège dipolaire croisé avec un faisceau fortement focalisé. Nous sommes ainsi capables de réaliser des condensats de Bose-Einstein quasi-purs contenant environ 3000 atomes. Dans la deuxième partie, nous nous intéressons aux propriétés magnétiques qui découlent de la présence de trois espèces de spin simultanément piégées. Nous présentons des méthodes de contrôle de la magnétisation des nuages ultra-froids, ainsi que des procédures de diagnostic de la composition de spin. Nous utilisons ces échantillons pour explorer le diagramme de phase à basse température, en fonction de la magnétisation et du champ magnétique. Nous montrons l'accord satisfaisant de ces résultats expérimentaux avec une théorie de champ champ moyen dans l'approximation de mode commun. Enfin, nous observons des fluctuations anormales des populations à bas champ et basse magnétisation. On les relie à des fluctuations collectives tendant à restaurer la symmétrie de spin, qui disparaissent à la limite thermodynamique mais sont présentes dans nos échantillons de taille finie.

Many quantum information tasks require measurements to distinguish between different quantum-mechanically entangled states (Bell states) of a particle pair. In practice, measurements are often limited to linear evolution and local measurement (LELM) of the particles. We investigate LELM distinguishability of the Bell states of two qubits (two-state particles) and qutrits (three-state particles), via standard projective measurement and via generalized measurement, which allows detection channels beyond the number of orthogonal single-particle states. Projective LELM can only distinguish 3 of 4 qubit Bell states; we show that generalized measurement does no better. We show that projective LELM can distinguish only 3 of 9 qutrit Bell states that generalized LELM allows at most 5 of 9. We have also made progress on distinguishing qubit $\times$ qutrit hyperentangled Bell states, which are made up of tensor products of the qubit Bell states and the qutrit Bell states, showing that the maximum number distinguishable with projective LELM measurements is between 9 and 11.

<p>Atomic ions trapped in microfabricated surface traps can be utilized as a physical platform with which to build a quantum computer. They possess many of the desirable characteristics of such a device, including high fidelity state preparation and readout, universal logic gates, and long coherence times, and can be readily entangled with each other through photonic interconnects. The use of optical cavities integrated with trapped ion qubits as a photonic interface presents the possibility for order of magnitude improvements in performance in several key areas for their use in quantum computation. The first part of this thesis describes the design and fabrication of a novel surface trap for integration with an optical cavity. The trap is custom made on a highly reflective mirror surface and includes the capability of moving the ion trap location along all three trap axes with nanometer scale precision. The second part of this thesis demonstrates the suitability of small microcavities formed from laser ablated, fused silica substrates with radii of curvature in the 300-500 micron range for use with the mirror trap as part of an integrated ion trap cavity system. Quantum computing applications for such a system include dramatic improvements in the photon entanglement rate of up to 10 kHz, the qubit measurement time down to 1 microsecond, and the qubit measurement error rate down to the 1e-5 range. The final part of this thesis describes a performance simulator for exploring the physical resource requirements and performance demands to scale a quantum computer to sizes capable of implementing quantum algorithms beyond the limits of classical computation.</p> / Dissertation

Phase lies at the heart of quantum physics and quantum information theory. A quantum bit is qualitatively different from a classical bit as it allows for the coherent superposition of possibilities, which demonstrate different behaviours depending on the phase between them. These behaviours constitute as interference phenomena, and lie behind the existence of algorithms in quantum computing which are arguably faster than the best classical alternatives. The concept of phase is deeply steeped in the structure of Hilbert spaces: the mathematical framework that underlies quantum theory. What if quantum theory did not hold in all scenarios, or was only a limiting case of some broader theory? In this case, would we still be able to meaningfully talk about phase and interference? In this thesis, we will adopt an operational generalisation of quantum theory known as the framework of generalised probabilistic theories. We will provide a reasonable definition of phase in this framework. Using this, we shall explore single-particle interferometry set-ups (particularly Mach-Zehnder interferometers): experiments whose output is highly dependent on the phase between the spatially disjoint branches through which a particle might be traversing. By applying physically-motivated locality considerations, we identify the crucial role that the uncertainty principle and its generalisations play in quantum theory as an enabler of non-trivial interference. By taking into account relativity of simultaneity, we will also provide a physical motivation for why standard quantum theory provides the best description of the location of a particle traversing such a system. Finally, we apply our generalised definition of phase in the related context of particle exchange behaviour, and identify a method for classifying post-quantum particles. All of this will demonstrate that phase between possibilities and its consequences are not uniquely quantum phenomena. Much of the behaviour we might ascribe to phase in quantum theory in fact holds generally true for phase in probabilistic theories.