Meshing Deforming Spacetime for Visualization and Analysis

We introduce a novel paradigm that simplifies the visualization and analysis of data that have a spatially/temporally varying frame of reference. The primary application driver is tokamak fusion plasma, where science variables (e.g., density and temperature) are interpolated in a complex magnetic field-line-following coordinate system. We also see a similar challenge in rotational fluid mechanics, cosmology, and Lagrangian ocean analysis; such physics implies a deforming spacetime and induces high complexity in volume rendering, isosurfacing, and feature tracking, among various visualization tasks. Without loss of generality, this paper proposes an algorithm to build a simplicial complex -- a tetrahedral mesh, for the deforming 3D spacetime derived from two 2D triangular meshes representing consecutive timesteps. Without introducing new nodes, the resulting mesh fills the gap between 2D meshes with tetrahedral cells while satisfying given constraints on how nodes connect between the two input meshes. In the algorithm we first divide the spacetime into smaller partitions to reduce complexity based on the input geometries and constraints. We then independently search for a feasible tessellation of each partition taking nonconvexity into consideration. We demonstrate multiple use cases for a simplified visualization analysis scheme with a synthetic case and fusion plasma applications

Optical Control of Josephson Coupling in Striped La_2-xBa_xCuO₄

High-TC cuprate superconductors display a rich phase diagram at low temperatures with coexisting and competing orders such as structural distortions of the crystal lattice, periodic charge- and spin-ordering, and superconductivity. The nature of interaction between these ordered phases (most of which are determined by strong electronic correlations) has been an intriguing area of research, as many believe it holds valuable insights into the mechanism behind the unusually high transition temperature of superconductivity in these materials, compared to those of conventional superconductors. The stripe order, a periodic ordering of charges and spins into one-dimensional stripes in the CuO2 planes, is commonly found in hole-doped compounds of the La-214 family, such as La2-x(Ba, Sr)xCuO4. This thesis is focused on investigating the relationship between the stripe order and superconductivity in the La-214 compounds using ultrashort laser pulses, with the aim of probing and potentially optimizing and stabilizing pre-existing superconducting fluctuations in the striped normal state. Earlier NIR pump - THz probe experiments found that photo-excitation induces a transient state with optical signatures of superconductivity in La2-xBaxCuO4. These tantalizing observations were interpreted as a result of photo-excitation melting away the stripe order which competes with superconductivity at equilibrium. The first experiment of the present thesis benchmarks this interpretation by performing NIR pump-THz probe measurements on La2-xBaxCuO4 in externally applied magnetic fields to finely control the delicate balance between the stripe order and the equilibrium superconducting phase, and maps out the dependence of the transiently enhanced/induced superconducting properties on the external magnetic field. Surprisingly, we found a significant increase in the lifetime of the transient superconducting response with increasing magnetic fields. These results were interpreted as an indication that the light-induced state originates not from simple optical melting of stripes, but rather emerges from activated tunnelling between optically excited superconducting stripes (the so-called Pair Density Wave) in adjacent planes. The second experiment of this thesis explores a different path towards understanding the relationship between the stripe order and superconductivity. In light of recent discovery of third harmonic generation of THz radiation by nonlinear Josephson tunnelling currents in the stripe phase of the same compound, numerical simulation predicts that more characteristic signatures of nonlinear Josephson tunnelling can be found after excitation by large-amplitude THz driving pulses. Electric Field Induced Second Harmonic (EFISH) is employed as an ultrafast voltmeter to monitor the voltage drop across the Josephson coupled CuO2 planes in La2-xBaxCuO4. It is found that voltage anomalies associated with 2π phase slips are detected not only in the superconducting state but also in the normal, striped phase. The results presented in this thesis produce further evidence for pre-existing Josephson coupling in the stripe phase which can be activated by optical excitation or in a highly nonlinear driving regime.Hochtemperatursupraleiter zeigen bei tiefen Temperaturen ein reichhaltiges Phasendiagramm, mit vielen nebeneinander bestehenden und konkurrierenden Ordnungen auf, wie z. B. strukturelle Verzerrungen des Kristallgitters, periodische Ladungs- und Spin-Ordnung und Supraleitfähigkeit. Die Art der Wechselwirkung zwischen diesen geordneten Phasen, von denen die meisten durch starke elektronische Korrelationen bestimmt werden, ist ein faszinierendes Forschungsgebiet, da es wertvolle Einblicke in den Mechanismus der hohen Übergangstemperatur der Supraleitung in diesen Materialien zu erlangen ermöglicht. Die Streifenordnung, eine periodische Anordnung von Ladungen und Spins in eindimensionalen Streifen in den CuO2-Ebenen, findet sich häufig in hochdotierten Verbindungen der La-214-Familie, wie La2-x(Ba, Sr)xCuO4. In dieser Arbeit wird die Beziehung zwischen dieser Streifenanordnung und der Supraleitung in den La-214-Verbindungen mit ultrakurzen Laserpulsen untersucht, um die bereits vorhandenen supraleitenden Fluktuationen im streifenförmigen Normalzustand zu charakterisieren und möglicherweise zu optimieren und stabilisieren. Frühere NIR-Pump- und THz-Probe Experimente zeigen, dass die Photoanregung einen vorübergehenden Zustand mit optischen Signaturen der Supraleitung in La2-xBaxCuO4 hervorruft. Diese Beobachtungen wurden als Resultat der Photoanregung interpretiert, die die Streifenordnung schmilzt, die mit der Supraleitung im Gleichgewicht konkurriert. Das erste Experiment der vorliegenden Arbeit überprüft diese Interpretation, mittels NIR-Pump-THz-Probe Experimenten an La2-xBaxCuO4 in extern angelegten Magnetfeldern. Es wurde dabei versucht, dass empfindliche Gleichgewicht zwischen der Streifenordnung und der supraleitenden Gleichgewichtsphase zu verändern, und die Abhängigkeit der vorübergehend verstärkten/induzierten supraleitenden Eigenschaften vom externen Magnetfeld aufzuzeigen. Es stellte sich heraus, dass sich die Lebensdauer des vorübergehenden supraleitenden Zustandes mit zunehmenden Magnetfeldern signifikant erhöht. Diese Ergebnisse werden als Hinweis darauf interpretiert, dass der lichtinduzierte Zustand nicht durch einfaches optisches Schmelzen der Streifen entsteht, sondern vielmehr durch aktiviertes Tunneln zwischen optisch angeregten supraleitenden Streifen (die so genannte Pair Density Wave) in benachbarten Ebenen. Das zweite Experiment dieser Arbeit hat einen anderen Ansatz um das Verständnis der Beziehung zwischen der Streifenordnung und der Supraleitung zu untersuchen. Ausgehend von der Entdeckung der Existenz einer dritten Harmonischen der THz-Strahlung, welche durch nichtlineare Josephson-Tunnelströme in der Streifenphase erzeugt werden, sagen numerische Simulationen voraus, dass durch die Anregung der Probe mittels eines THz-Pump Pulses große Amplituden eines nichtlinearen Josephson-Tunnelns gefunden werden können. Die dabei durch elektrische Felder induzierte zweite Harmonische (EFISH) wird als ultraschnelles Voltmeter eingesetzt, um den Spannungsabfall über die durch den Josephson Effekt gekoppelten CuO2-Ebenen in La2-xBaxCuO4 zu überwachen. Es zeigt sich, dass Spannungsanomalien, die mit 2π-Phasenverschiebungen verbunden sind, nicht nur im supraleitenden Zustand, sondern auch in der normalen, gestreiften Phase nachgewiesen werden können. Die Ergebnisse in dieser Arbeit vorgestellten liefern weitere Beweise für eine bereits existierende Josephson-Kopplung in der Streifenphase, die durch optische Anregung oder in einem hochgradig nichtlinearen Antriebsregime aktiviert werden kann

Optical Control of Josephson Coupling in Striped La_2-xBa_xCuO₄

High-TC cuprate superconductors display a rich phase diagram at low temperatures with coexisting and competing orders such as structural distortions of the crystal lattice, periodic charge- and spin-ordering, and superconductivity. The nature of interaction between these ordered phases (most of which are determined by strong electronic correlations) has been an intriguing area of research, as many believe it holds valuable insights into the mechanism behind the unusually high transition temperature of superconductivity in these materials, compared to those of conventional superconductors. The stripe order, a periodic ordering of charges and spins into one-dimensional stripes in the CuO2 planes, is commonly found in hole-doped compounds of the La-214 family, such as La2-x(Ba, Sr)xCuO4. This thesis is focused on investigating the relationship between the stripe order and superconductivity in the La-214 compounds using ultrashort laser pulses, with the aim of probing and potentially optimizing and stabilizing pre-existing superconducting fluctuations in the striped normal state. Earlier NIR pump - THz probe experiments found that photo-excitation induces a transient state with optical signatures of superconductivity in La2-xBaxCuO4. These tantalizing observations were interpreted as a result of photo-excitation melting away the stripe order which competes with superconductivity at equilibrium. The first experiment of the present thesis benchmarks this interpretation by performing NIR pump-THz probe measurements on La2-xBaxCuO4 in externally applied magnetic fields to finely control the delicate balance between the stripe order and the equilibrium superconducting phase, and maps out the dependence of the transiently enhanced/induced superconducting properties on the external magnetic field. Surprisingly, we found a significant increase in the lifetime of the transient superconducting response with increasing magnetic fields. These results were interpreted as an indication that the light-induced state originates not from simple optical melting of stripes, but rather emerges from activated tunnelling between optically excited superconducting stripes (the so-called Pair Density Wave) in adjacent planes. The second experiment of this thesis explores a different path towards understanding the relationship between the stripe order and superconductivity. In light of recent discovery of third harmonic generation of THz radiation by nonlinear Josephson tunnelling currents in the stripe phase of the same compound, numerical simulation predicts that more characteristic signatures of nonlinear Josephson tunnelling can be found after excitation by large-amplitude THz driving pulses. Electric Field Induced Second Harmonic (EFISH) is employed as an ultrafast voltmeter to monitor the voltage drop across the Josephson coupled CuO2 planes in La2-xBaxCuO4. It is found that voltage anomalies associated with 2π phase slips are detected not only in the superconducting state but also in the normal, striped phase. The results presented in this thesis produce further evidence for pre-existing Josephson coupling in the stripe phase which can be activated by optical excitation or in a highly nonlinear driving regime.Hochtemperatursupraleiter zeigen bei tiefen Temperaturen ein reichhaltiges Phasendiagramm, mit vielen nebeneinander bestehenden und konkurrierenden Ordnungen auf, wie z. B. strukturelle Verzerrungen des Kristallgitters, periodische Ladungs- und Spin-Ordnung und Supraleitfähigkeit. Die Art der Wechselwirkung zwischen diesen geordneten Phasen, von denen die meisten durch starke elektronische Korrelationen bestimmt werden, ist ein faszinierendes Forschungsgebiet, da es wertvolle Einblicke in den Mechanismus der hohen Übergangstemperatur der Supraleitung in diesen Materialien zu erlangen ermöglicht. Die Streifenordnung, eine periodische Anordnung von Ladungen und Spins in eindimensionalen Streifen in den CuO2-Ebenen, findet sich häufig in hochdotierten Verbindungen der La-214-Familie, wie La2-x(Ba, Sr)xCuO4. In dieser Arbeit wird die Beziehung zwischen dieser Streifenanordnung und der Supraleitung in den La-214-Verbindungen mit ultrakurzen Laserpulsen untersucht, um die bereits vorhandenen supraleitenden Fluktuationen im streifenförmigen Normalzustand zu charakterisieren und möglicherweise zu optimieren und stabilisieren. Frühere NIR-Pump- und THz-Probe Experimente zeigen, dass die Photoanregung einen vorübergehenden Zustand mit optischen Signaturen der Supraleitung in La2-xBaxCuO4 hervorruft. Diese Beobachtungen wurden als Resultat der Photoanregung interpretiert, die die Streifenordnung schmilzt, die mit der Supraleitung im Gleichgewicht konkurriert. Das erste Experiment der vorliegenden Arbeit überprüft diese Interpretation, mittels NIR-Pump-THz-Probe Experimenten an La2-xBaxCuO4 in extern angelegten Magnetfeldern. Es wurde dabei versucht, dass empfindliche Gleichgewicht zwischen der Streifenordnung und der supraleitenden Gleichgewichtsphase zu verändern, und die Abhängigkeit der vorübergehend verstärkten/induzierten supraleitenden Eigenschaften vom externen Magnetfeld aufzuzeigen. Es stellte sich heraus, dass sich die Lebensdauer des vorübergehenden supraleitenden Zustandes mit zunehmenden Magnetfeldern signifikant erhöht. Diese Ergebnisse werden als Hinweis darauf interpretiert, dass der lichtinduzierte Zustand nicht durch einfaches optisches Schmelzen der Streifen entsteht, sondern vielmehr durch aktiviertes Tunneln zwischen optisch angeregten supraleitenden Streifen (die so genannte Pair Density Wave) in benachbarten Ebenen. Das zweite Experiment dieser Arbeit hat einen anderen Ansatz um das Verständnis der Beziehung zwischen der Streifenordnung und der Supraleitung zu untersuchen. Ausgehend von der Entdeckung der Existenz einer dritten Harmonischen der THz-Strahlung, welche durch nichtlineare Josephson-Tunnelströme in der Streifenphase erzeugt werden, sagen numerische Simulationen voraus, dass durch die Anregung der Probe mittels eines THz-Pump Pulses große Amplituden eines nichtlinearen Josephson-Tunnelns gefunden werden können. Die dabei durch elektrische Felder induzierte zweite Harmonische (EFISH) wird als ultraschnelles Voltmeter eingesetzt, um den Spannungsabfall über die durch den Josephson Effekt gekoppelten CuO2-Ebenen in La2-xBaxCuO4 zu überwachen. Es zeigt sich, dass Spannungsanomalien, die mit 2π-Phasenverschiebungen verbunden sind, nicht nur im supraleitenden Zustand, sondern auch in der normalen, gestreiften Phase nachgewiesen werden können. Die Ergebnisse in dieser Arbeit vorgestellten liefern weitere Beweise für eine bereits existierende Josephson-Kopplung in der Streifenphase, die durch optische Anregung oder in einem hochgradig nichtlinearen Antriebsregime aktiviert werden kann

Simulation of Transient Effects in High-Temperature Superconducting Magnets

Particle colliders for high-energy physics are important tools for investigating the fundamental structure of matter. In circular accelerators, the collision energy of particles is proportional to the bending magnetic field and the radius of the machine. As a consequence, circular accelerators such as the Large Hadron Collider at CERN have traditionally relied on high-field magnets made of low-temperature superconductors, confining the particle beams within a complex of acceptable dimensions. This class of superconductors shows a practical limit in the achievable magnetic field in the magnet aperture of about 8 T for a Nb-Ti alloy, and 16 T for a Nb3Sn compound. Overcoming these limits requires the use of high-temperature superconductors (HTS) in accelerator magnets, in particular rare-earth barium copper oxide (ReBCO) tapes. With respect to the low-temperature counterpart, accelerator magnets based on ReBCO tapes are known to behave differently in terms of magnetic field quality and protection from quench events. The tapes are equivalent to wide and anisotropic mono-filaments, resulting in screening currents detrimentally affecting the magnetic field quality, in particular at low currents. At the same time, quenches are less likely to occur due to the enhanced thermal stability of the tapes, but are more difficult to detect and mitigate. Moreover, the dynamic behavior of accelerator magnets is also affected by the surrounding circuitry which must be taken into account, leading to multiphysics, multirate and multiscale problems. Numerical methods play a crucial role for overcoming the challenges related to magnetic field quality and quench protection. In this work, the magnetothermal dynamics in high-temperature superconducting magnets is modeled by means of an eddy-current problem in the time domain. A mixed field formulation is developed to cope with the nonlinear resistivity law of superconducting materials. The formulation is complemented with distribution functions for the coupling of external voltage and/or current source quantities. Further simplifications are discussed in case of tapes with high aspect ratio, and multifilamentary conductors. Moreover, a field-circuit coupling interface is derived as an optimized Schwarz transmission condition, such that the formulation can be used in field-circuit coupled problems by means of co-simulation methods. The implementation of the formulation in the finite element method is verified against analytical and reference solutions available in literature, and validated against measurements on the HTS-based dipole magnet Feather-M2. As a case-study, the formulation is applied to proof-of-concept ReBCO screens for the passive field-error cancellation in accelerator magnets. The proposed design is called HALO (harmonics-absorbing layered object) as it is made of stacks of tapes arranged in layers which are fully scalable and expandable. The screens are positioned such that their persistent magnetization shapes the magnetic field in the magnet aperture, canceling the undesired field imperfections. Experimental measurements at 77 K in liquid nitrogen show a significant reduction of the field error, up to a factor of four. Moreover, numerical extrapolation for accelerator-like conditions shows that a careful design of the superconducting screens allows matching the typical field quality requirements for accelerator magnets

Cryogenic Near-field Nanoscopy at Terahertz Frequency

This dissertation reports on data acquisition method and the application of world’s first cryogenic apertureless near-field microscope designed for terahertz frequencies. The dissertation briefly summarizes the commonly used data acquisition methods and the existing challenges in applying near-field technology using broadband terahertz sources. We devised, implemented, and validated a novel measurement technique to resolve the challenges. The novel method improves the traditional method by providing the information of the carrier-envelop-phase of the terahertz pulse. The physical properties of WTe₂ microcrystals depend sensitively on the layer number. By applying both the traditional and the novel techniques, we systematically explored the layer-dependent electromagnetic response of mono-layer and few-layer tungsten ditelluride (WTe₂ microcrystals. On tri-layer WTe₂, we discovered the plasmonic response and imaged the real-space pattern of the terahertz plasmon using the novel measurement technique. On bi-layer WTe₂, our measurements support that the band alignment is semi-metallic instead of semi-conducting. Near-field technology at terahertz frequency is sensitive to the Drude behavior of condensed matters. We imaged the electromagnetic response of the transition of cadmium osmate (Cd₂Os₂O₇) crystals from a high temperature metal to a low temperature magnetic insulator. The result is consistent with the temperature dependence in the direct-current conductivity. In the end, the dissertation discusses the theory and simulation of imaging hydrodynamic flow of materials with viscous electron systems via nano-photocurrent technique. In anisotropic material, nano-photocurrent measures the geometrical properties of the Shockley-Ramo auxiliary field or flux. As a result, the nano-photocurrent is a good candidate to detect the boundary layer and vortex flow pattern of a viscous electron system