<p> This dissertation is an account of the first calorimetric detection of individual He*₂ excimers within a bath of superfluid ⁴He. When superfluid helium is subject to ionizing radiation, diatomic He molecules are created in both the singlet and triplet states. The singlet He molecules decay within nanoseconds, but due to a forbidden spin-flip the triplet molecules have a relatively long lifetime of 13 seconds in superfluid He. When He*₂ molecules decay, they emit a ~15 eV photon. Nearly all matter is opaque to these vacuum-UV photons, although they do propagate through liquid helium. The triplet state excimers propagate ballistically through the superfluid until they quench upon a surface; this process deposits a large amount of energy into the surface. The prospect of detecting both excimer states is the motivation for building a detector immersed directly in the superfluid bath.</p><p> The detector used in this work is a single superconducting titanium transition edge sensor (TES). The TES is mounted inside a hermetically sealed chamber at the baseplate of a dilution refrigerator. The chamber contains superfluid helium at 100 mK. Excimers are created during the relaxation of high-energy electrons, which are introduced into the superfluid bath either in situ via a sharp tungsten tip held above the field-emission voltage, or by using an external gamma-ray source to ionize He atoms. These excimers either propagate through the LHe bath and quench on a surface, or decay and emit vacuum-ultraviolet photons that can be collected by the detector.</p><p> This dissertation discusses the design, construction, and calibration of the TES-based excimer detecting instrument. It also presents the first spectra resulting from the direct detection of individual singlet and triplet helium excimers.</p>

<p> Engineered quantum systems are poised to revolutionize information science in the near future. A persistent challenge in applied quantum technology is creating controllable, quantum interactions while preventing information loss to the environment, decoherence. In this thesis, we realize mesoscopic superconducting circuits whose macroscopic collective degrees of freedom, such as voltages and currents, behave quantum mechanically. We couple these mesoscopic devices to microwave cavities forming a cavity quantum electrodynamics (QED) architecture comprised entirely of circuit elements. This application of cavity QED is dubbed Circuit QED and is an interdisciplinary field seated at the intersection of electrical engineering, superconductivity, quantum optics, and quantum information science. Two popular methods for taming active quantum systems in the presence of decoherence are discrete feedback conditioned on an ancillary system or quantum reservoir engineering. Quantum reservoir engineering maintains a desired subset of a Hilbert space through a combination of drives and designed entropy evacuation. Circuit QED provides a favorable platform for investigating quantum reservoir engineering proposals. A major advancement of this thesis is the development of a quantum reservoir engineering protocol which maintains the quantum state of a microwave cavity in the presence of decoherence. This thesis synthesizes strongly coupled, coherent devices whose solutions to its driven, dissipative Hamiltonian are predicted a <i>priori</i>. This work lays the foundation for future advancements in cavity centered quantum reservoir engineering protocols realizing hardware efficient circuit QED designs. </p>

<p> Cooper pairs are known to tunnel through a barrier between superconductors in a Josephson junction. The spin states of the pairs can be a mixture of singlet and triplet states when the barrier is an inhomogeneous magnetic material. The purpose of this thesis is to better understand the behavior of pair correlations in the ballistic regime for different magnetic configurations and varying physical parameters. We use a tight-binding Hamiltonian to describe the system and consider singlet-pair conventional superconductors. Using the Bogoliubov-Valatin transformation, we derive the Bogoliubov-de Gennes equations and numerically solve the associated eigenvalue problem. Pair correlations in the magnetic Josephson junction are obtained from the Green's function formalism for a superconductor. This formalism is applied to Josephson junctions composed of discrete and continuous magnetic materials. The differences between representing pair correlations in the time and frequency domain are discussed, as well as the advantages of describing the Gor'kov functions on a log scale rather than the commonly used linear scale, and in a rotating basis as opposed to a static basis. Furthermore, the effects of parameters such as ferromagnetic width, magnetization strength, and band filling will be investigated. Lastly, we compare results in the clean limit with known results in the diffusive regime.</p><p>

<p> We have investigated the Faraday effect of bismuth-doped rare-earth iron-garnets with varying doping levels of gallium from z = 1.0 to 1.35. We used lutetium to control the film's in-plane magnetic properties and found that gallium doping levels above the compensation point caused a loss of anisotropy control, a canted out-of-plane magnetization in the film, and an extremely weak but linear coercivity above 10 micro-Tesla fields. Using these results we focused on in-plane films to create 8 layer stacks of 500 um thick films to achieve a minimum detectable field of 50 pT at 1 kHz. Unlike previous Magneto-Optic (MO) studies that typically used thin films of approximately 1um thickness, we used approximately 400um thick films to allow experimentation with the final, robust, ideal form the MO sensor would take. We measured what most other MO studies with garnets neglected: the magnetic anisotropy axis or structure within the film. Knowledge of this structure is essential in improving the sensitivity of a stacked MO probe. Studying thick films proved to be key to understanding the magnetic anisotropy and domain properties that can degrade or enhance the sensitivity of the Faraday rotation in bismuth doped rare-earth iron-garnets to an applied magnetic field and to pointing the direction of future research to develop the conditions for rugged magnetometer sensors. </p><p>

<p> The fractional quantum Hall effect (FQHE) in the half-filled second Landau level (filling factor &nu; = 5/2) offers new insights into the physics of exotic emergent quasi-particles. The FQHE is due to the collective interactions of electrons confined to two-dimensions, cooled to sub-Kelvin temperatures, and subjected to a strong perpendicular magnetic field. Under these conditions a quantum liquid forms displaying quantized plateaus in the Hall resistance and chiral edge flow. The leading candidate description for the FQHE at 5/2 is provided by the Moore-Read Pfaffian state which supports non-Abelian anyonic low-energy excitations with potential applications in fault-tolerant quantum computation schemes. The Moore-Read Pfaffian is the exact zero-energy ground state of a particular three-body Hamiltonian and explicitly breaks particle-hole symmetry. In this thesis we investigate the role of two and three body interaction terms in the Hamiltonian and the role of particle hole symmetry (PHS) breaking at &nu; = 5/2. We start with a PHS two body Hamiltonian (<i>H</i>₂) that produces an exact ground state that is nearly identical with the Moore-Read Pfaffian and construct a Hamiltonian H(&alpha;) = (1 &ndash; &alpha;)<i>H</i>₃ + &alpha; <i>H</i>₂ that tunes continuously between <i>H</i>₃ and <i> H</i>₂. We find that the ground states, and low-energy excitations, of <i>H</i>₂ and <i>H</i>₃ are in one-to-one correspondence and remain adiabatically connected indicating they are part of the same universality class and describe the same physics in the thermodynamic limit. In addition, evidently three body PHS breaking interactions are not a crucial ingredient to realize the FQHE at 5/2 and the non-Abelian quasiparticle excitations.</p><p>

Microorganisms have evolved in a low Reynolds number environment and have adapted their behaviour to its viscosity. Here, we consider some features of behaviour observed in microorganisms and use hydrodynamic models to show that these behaviours emerge from physical interactions, including hydrodynamic friction, hydrodynamic interactions and mechanical constraints. Swimming behaviour is affected by surfaces and observations of Vibrio cholerae show that it swims near a surface with two distinct motility modes. We develop a model which shows that friction between pili and the surface gives the two motility modes. The model is extended to study the behaviour of bacteria which are partially attached to a surface. Observations of Shewanella constrained by a surface show several different behaviours. The model shows that different degrees of surface constraint lead to different types of behaviour; the flexibility of the flagellar hook and the torque exerted by the flagellar motor also cause different behaviours. Near surface behaviour is important for understanding the initial stages of biofilm formation. Chlamydomonas swims using synchronous beating of its two flagella. A simple model of Chlamydomonas is developed to study motility and synchronisation. This model shows that the stability of synchronisation is sensitive to the beat pattern. Run-and-tumble behaviour emerges when we include intrinsic noise, without the need for biochemical signalling. The model is also used to show how observed responses of the flagella to light stimuli produce phototaxis. Finally we study hydrodynamic synchronisation of many cilia and consider the stability of metachronal waves in arrays of hydrodynamically coupled cilia. This thesis shows that physical interactions are responsible for many behavioural features and that physical models provide a useful technique for exploring open questions in biology.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Nas Ãltimas dÃcadas, a dinÃmica de pacotes de ondas tem sido objeto de vÃrios estudos teÃricos e experimentais em diversos tipos de sistemas, tais como semicondutores, supercondutores, sÃlidos cristalinos e Ãtomos frios. Com a descoberta do grafeno, surge agora um novo sistema para a comunidade cientÃfica investigar a evoluÃÃo temporal de pacotes de onda e a possibilidade de observar-se o fenÃmeno zitterbewegung (ZBW), um movimento trÃmulo previsto teoricamente por SchrÃdinger para pacotes de onda descrevendo partÃculas que obedecem à equaÃÃo de Dirac, como à o caso de elÃtrons de baixa energia neste material. Neste trabalho, apresentamos uma descriÃÃo detalhada da dinÃmica de partÃculas carregadas descritas por um pacote de onda Gaussiano em monocamada e bicamada de grafeno de forma analitica. Primeiramente, obtivemos analiticamente um Hamiltoniano aproximado 2x2 para uma monocamada de grafeno, generalizando-o, em seguida, para o caso de n-camadas com empilhamento ABC. A partir deste Hamiltoniano, encontramos as funÃÃes de onda para as sub-redes A e B. Uma vez conhecidas as funÃÃes de onda, determinamos a densidade de probabilidade eletrÃnica e o valor mÃdio das coordenadas do centro de massa com o objetivo de verificar o comportamento da propagaÃÃo do pacote de onda, bem como as oscilaÃÃes devido ao fenÃmeno ZBW. Foram analisados diferentes casos de polarizaÃÃo inicial de pseudo-spin, relacionados a diferentes amplitudes de probabilidade das funÃÃes de onda das sub-redes A e B que compÃem as camadas do grafeno. Por fim, comparamos os resultados obtidos analiticamente com um mÃtodo computacional tight-binding, encontrando um casamento perfeito entre os resultados para o caso da monocamada.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.