Realization of Floquet topological systems with ultracold atoms in optical honeycomb lattices

This thesis reports on the realization of Floquet topological systems with ultracold atoms in an optical honeycomb lattice. Using periodically driven quantum systems, topological phases of matter can be simulated by an effective, static Hamiltonian related to the time-evolution at integer multiples of the driving period, which is known as Floquet engineering. However, periodic driving can also give rise to genuinely time-dependent settings without static counterparts. One example is the anomalous Floquet phase in two dimensions, in which all bulk bands have a Chern number of zero but nevertheless robust chiral edge modes appear, which would be precluded by the bulk-edge correspondence in a static system. In an optical honeycomb lattice, anomalous Floquet systems can be created by continuous, periodic modulation of the laser intensities. This driving scheme results in different topological regimes, three of which are investigated, including the anomalous Floquet phase and a Haldane-like phase. Periodically driven systems feature periodic quasienergies and can be characterized in terms of winding numbers, which count the number of chiral edge modes in each quasienergy gap. By interferometric measurements of the quasienergy gaps between the first two Floquet bands, the topological phase transitions, emerging as gap closings, are located. For periodically driven systems, a modified bulk-edge correspondence can be formulated. In particular, the change of the winding number at a phase transition is related to the sign change of the local Berry curvature. The Berry curvature at the gap closing points is probed by Hall deflection measurements to obtain the winding numbers in each of the topological regimes, revealing the existence of chiral edge modes also in a setting with smooth boundaries as used in the experiments. The measured quasienergy gaps and transverse deflections are quantitatively well described by a numerical calculation of the Floquet bandstructure that includes coupling to higher bands during the driving period. To derive the spectrum of the modulated lattice in a geometry with edges, a tight-binding description of the system is discussed. Circular phase modulation of the honeycomb lattice can also give rise to an anomalous Floquet system when inversion symmetry is broken. The topological phase diagrams and the experimental feasibility are compared for both modulation schemes. Due to the vanishing Chern numbers, the bulk states in the anomalous Floquet regime can be fully localized by a disorder potential. This could prevent heating in interacting, periodically driven systems, resulting in a many-body localized bulk coexisting with thermalizing edge states. The experimental realization of disorder and strong interactions, as well as independent probes of the edge states are investigated. Bloch band geometry can be extended to multiband systems, using Wilson lines. The possible symmetry protection of their eigenvalues is discussed, along with measurements in the optical honeycomb lattice. Moreover, the onset of heating in weakly-interacting, periodically driven systems, triggered by parametric instabilities, is studied experimentally in a one-dimensional lattice.Diese Doktorarbeit beschreibt die Realisierung von topologischen Floquet-Systemen mit ultrakalten Atomen in einem optischen, zweidimensionalen hexagonalen Gitter. Topologische Phasen können mittels periodisch getriebener Quantensysteme simuliert werden. Dabei wird ein statisches System als Zeit-Mittel über eine Modulationsperiode dargestellt, was unter dem Begriff Floquet-Engineering bekannt ist. Periodische Modulation kann jedoch auch dazu verwendet werden, intrinsisch zeit-abhängige Konfigurationen zu erzeugen, die in keinem statischen System auftreten können. Ein Beispiel dafür sind zweidimensionale, anomale Floquet-Phasen, in denen die Chern-Zahlen aller Energiebänder gleich null sind, aber trotzdem robuste Randzustände existieren. Ein statisches System hingegen, in dem alle Chern-Zahlen verschwinden, ist topologisch trivial. Im optischen, hexagonalen Gitter können anomale Floquet-Systeme durch kontinuierliche, periodische Modulation der Laser-Intensitäten erzeugt werden. Das resultierende topologische Phasen-Diagramm beinhaltet unterschiedliche Bereiche, von denen drei genauer untersucht werden, unter anderem die anomale Floquet-Phase und eine Haldane-ähnliche Phase. Zeit-periodische Systeme besitzen periodische Quasi-Energien und können durch Windungszahlen beschrieben werden, welche die Anzahl der Randzustände in den Quasi-Energie-Lücken angeben. Das Schließen der Bandlücken definiert topologische Phasen-Übergänge, die mit Hilfe von interferometrischen Messungen nachgewiesen werden. Die entsprechende Änderung der Windungszahlen ist mit einem Vorzeichenwechsel der Berry-Krümmung an den Berührpunkten der Bänder verknüpft. Die Berry-Krümmung im Impulsraum wird anhand einer transversalen Ablenkung im Realraum gemessen, was die Bestimmung der Windungszahlen ermöglicht. Dies gibt direkt Aufschluss über die Existenz von Randzuständen, auch in einem System mit flachen Rändern, wie es im Experiment verwendet wird. Die gemessenen Bandlücken und transversalen Ablenkungen stimmen quantitativ sehr gut mit theoretischen Werten überein, die auf einer numerischen Berechnung der Floquet-Bandstruktur basieren. Um ein System mit Rändern zu beschreiben, wird außerdem ein Tight-Binding-Modell für das modulierte Gitter eingeführt. Anomale Floquet-Phasen können ebenfalls in frequenz-modulierten, zweidimensionalen hexagonalen Gittern auftreten, falls die Inversions-Symmetrie des Gitters gebrochen wird. Die beiden Modulations-Schemata werden hinsichtlich ihrer Phasen-Diagramme und der experimentellen Umsetzbarkeit verglichen. Die Zustände im Inneren eines anomalen Floquet-Systems können durch ein ungeordnetes Potential vollständig lokalisiert werden, was dazu verwendet werden könnte, wechselwirkende, periodisch getriebene Systeme gegen Heizeffekte zu stabilisieren. Die experimentelle Realisierung eines ungeordneten Potentials und starker Wechselwirkung wird diskutiert, ebenso wie eine direkte Messung der Randzustände. Darüber hinaus werden die Eigenwerte von Wilson-Linien im zweidimensionalen hexagonalen Gitter betrachtet, welche die geometrischen Eigenschaften von entarteten Bloch-Bändern beschreiben, sowie Heizeffekte in schwach-wechselwirkenden, getriebenen Systemen am Beispiel eines eindimensionalen Gitters untersucht

Realization of Floquet topological systems with ultracold atoms in optical honeycomb lattices

This thesis reports on the realization of Floquet topological systems with ultracold atoms in an optical honeycomb lattice. Using periodically driven quantum systems, topological phases of matter can be simulated by an effective, static Hamiltonian related to the time-evolution at integer multiples of the driving period, which is known as Floquet engineering. However, periodic driving can also give rise to genuinely time-dependent settings without static counterparts. One example is the anomalous Floquet phase in two dimensions, in which all bulk bands have a Chern number of zero but nevertheless robust chiral edge modes appear, which would be precluded by the bulk-edge correspondence in a static system. In an optical honeycomb lattice, anomalous Floquet systems can be created by continuous, periodic modulation of the laser intensities. This driving scheme results in different topological regimes, three of which are investigated, including the anomalous Floquet phase and a Haldane-like phase. Periodically driven systems feature periodic quasienergies and can be characterized in terms of winding numbers, which count the number of chiral edge modes in each quasienergy gap. By interferometric measurements of the quasienergy gaps between the first two Floquet bands, the topological phase transitions, emerging as gap closings, are located. For periodically driven systems, a modified bulk-edge correspondence can be formulated. In particular, the change of the winding number at a phase transition is related to the sign change of the local Berry curvature. The Berry curvature at the gap closing points is probed by Hall deflection measurements to obtain the winding numbers in each of the topological regimes, revealing the existence of chiral edge modes also in a setting with smooth boundaries as used in the experiments. The measured quasienergy gaps and transverse deflections are quantitatively well described by a numerical calculation of the Floquet bandstructure that includes coupling to higher bands during the driving period. To derive the spectrum of the modulated lattice in a geometry with edges, a tight-binding description of the system is discussed. Circular phase modulation of the honeycomb lattice can also give rise to an anomalous Floquet system when inversion symmetry is broken. The topological phase diagrams and the experimental feasibility are compared for both modulation schemes. Due to the vanishing Chern numbers, the bulk states in the anomalous Floquet regime can be fully localized by a disorder potential. This could prevent heating in interacting, periodically driven systems, resulting in a many-body localized bulk coexisting with thermalizing edge states. The experimental realization of disorder and strong interactions, as well as independent probes of the edge states are investigated. Bloch band geometry can be extended to multiband systems, using Wilson lines. The possible symmetry protection of their eigenvalues is discussed, along with measurements in the optical honeycomb lattice. Moreover, the onset of heating in weakly-interacting, periodically driven systems, triggered by parametric instabilities, is studied experimentally in a one-dimensional lattice.Diese Doktorarbeit beschreibt die Realisierung von topologischen Floquet-Systemen mit ultrakalten Atomen in einem optischen, zweidimensionalen hexagonalen Gitter. Topologische Phasen können mittels periodisch getriebener Quantensysteme simuliert werden. Dabei wird ein statisches System als Zeit-Mittel über eine Modulationsperiode dargestellt, was unter dem Begriff Floquet-Engineering bekannt ist. Periodische Modulation kann jedoch auch dazu verwendet werden, intrinsisch zeit-abhängige Konfigurationen zu erzeugen, die in keinem statischen System auftreten können. Ein Beispiel dafür sind zweidimensionale, anomale Floquet-Phasen, in denen die Chern-Zahlen aller Energiebänder gleich null sind, aber trotzdem robuste Randzustände existieren. Ein statisches System hingegen, in dem alle Chern-Zahlen verschwinden, ist topologisch trivial. Im optischen, hexagonalen Gitter können anomale Floquet-Systeme durch kontinuierliche, periodische Modulation der Laser-Intensitäten erzeugt werden. Das resultierende topologische Phasen-Diagramm beinhaltet unterschiedliche Bereiche, von denen drei genauer untersucht werden, unter anderem die anomale Floquet-Phase und eine Haldane-ähnliche Phase. Zeit-periodische Systeme besitzen periodische Quasi-Energien und können durch Windungszahlen beschrieben werden, welche die Anzahl der Randzustände in den Quasi-Energie-Lücken angeben. Das Schließen der Bandlücken definiert topologische Phasen-Übergänge, die mit Hilfe von interferometrischen Messungen nachgewiesen werden. Die entsprechende Änderung der Windungszahlen ist mit einem Vorzeichenwechsel der Berry-Krümmung an den Berührpunkten der Bänder verknüpft. Die Berry-Krümmung im Impulsraum wird anhand einer transversalen Ablenkung im Realraum gemessen, was die Bestimmung der Windungszahlen ermöglicht. Dies gibt direkt Aufschluss über die Existenz von Randzuständen, auch in einem System mit flachen Rändern, wie es im Experiment verwendet wird. Die gemessenen Bandlücken und transversalen Ablenkungen stimmen quantitativ sehr gut mit theoretischen Werten überein, die auf einer numerischen Berechnung der Floquet-Bandstruktur basieren. Um ein System mit Rändern zu beschreiben, wird außerdem ein Tight-Binding-Modell für das modulierte Gitter eingeführt. Anomale Floquet-Phasen können ebenfalls in frequenz-modulierten, zweidimensionalen hexagonalen Gittern auftreten, falls die Inversions-Symmetrie des Gitters gebrochen wird. Die beiden Modulations-Schemata werden hinsichtlich ihrer Phasen-Diagramme und der experimentellen Umsetzbarkeit verglichen. Die Zustände im Inneren eines anomalen Floquet-Systems können durch ein ungeordnetes Potential vollständig lokalisiert werden, was dazu verwendet werden könnte, wechselwirkende, periodisch getriebene Systeme gegen Heizeffekte zu stabilisieren. Die experimentelle Realisierung eines ungeordneten Potentials und starker Wechselwirkung wird diskutiert, ebenso wie eine direkte Messung der Randzustände. Darüber hinaus werden die Eigenwerte von Wilson-Linien im zweidimensionalen hexagonalen Gitter betrachtet, welche die geometrischen Eigenschaften von entarteten Bloch-Bändern beschreiben, sowie Heizeffekte in schwach-wechselwirkenden, getriebenen Systemen am Beispiel eines eindimensionalen Gitters untersucht

Feasibility of single breath-hold left ventricular function with 3 Tesla TSENSE acquisition and 3D modeling analysis

<p>Abstract</p> <p>Background</p> <p>A single breath-hold evaluation of ventricular function would allow assessment in cases where scan time or patient tolerance is limited. Spatiotemporal acceleration techniques such as TSENSE decrease cardiovascular MR acquisition time, but standard slice summation analysis requires enough short axis slices to cover the left ventricle (LV). By reducing the number of short axis slices, incorporating long axis slices, and applying a 3D model based analysis, it may be possible to obtain accurate LV mass and volumes. We evaluated LV volume, mass and ejection fraction at 3.0T using a 3D modeling analysis in 9 patients with a history of myocardial infarction and one healthy volunteer. Acquisition consisted of a standard short axis SSFP stack and a 15 heart-beat single breath-hold six slice multi-planar (4 short and 2 long axis) TSENSE SSFP protocol with an acceleration factor of <it>R </it>= 4.</p> <p>Results</p> <p>Differences (standard minus accelerated protocol mean ± s.d.) and coefficients of variation (s.d. of differences as a percentage of the average estimate) were 7.5 ± 9.6 mL and 6% for end-diastolic volume (p = 0.035), 0.4 ± 5.1 mL and 7% for end-systolic volume (p = NS), 7.1 ± 8.1 mL and 9% for stroke volume (p = 0.022), 2.2 ± 2.8% and 5% for ejection fraction (p = 0.035), and -7.1 ± 6.2 g and 4% for LV mass (p = 0.005), respectively. Intra- and inter-observer errors were similar for both protocols (p = NS for all measures).</p> <p>Conclusion</p> <p>These results suggest that clinically useful estimates of LV function can be obtained in a TSENSE accelerated single breath-hold reduced slice acquisition at 3T using 3D modeling analysis techniques.</p

Parametric Instabilities of Interacting Bosons in Periodically Driven 1D Optical Lattices

Periodically-driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and inter-particle interactions are well controlled. The combination of interactions and time-periodic driving, however, often leads to uncontrollable heating and instabilities, potentially preventing practical applications of Floquet-engineering in large many-body quantum systems. In this work, we experimentally identify the existence of parametric instabilities in weakly-interacting Bose-Einstein condensates in strongly-driven optical lattices through momentum-resolved measurements. Parametric instabilities can trigger the destruction of weakly-interacting Bose-Einstein condensates through the rapid growth of collective excitations, in particular in systems with weak harmonic confinement transverse to the lattice axis

Dynamic and Static Magnetic Resonance Angiography of the Supra-aortic Vessels at 3.0 T Intraindividual Comparison of Gadobutrol, Gadobenate Dimeglumine, and Gadoterate Meglumine at Equimolar Dose

Purpose: The purpose of this study was the intraindividual comparison of a 1.0 M and two 0.5 M gadolinium-based contrast agents (GBCA) using equimolar dosing in dynamic and static magnetic resonance angiography (MRA) of the supra-aortic vessels. Materials and Methods: In this institutional review board-approved study, a total of 20 healthy volunteers (mean +/- SD age, 29 +/- 6 years) underwent 3 consecutive supra-aortic MRA examinations on a 3.0 T magnetic resonance system. The order of GBCA (Gadobutrol, Gadobenate dimeglumine, and Gadoterate meglumine) was randomized with a minimum interval of 48 hours between the examinations. Before each examination and 45 minutes after each examination, circulatory parameters were recorded. Total GBCA dose per MRA examination was 0.1 mmol/kg with a 0.03 mmol/kg and 0.07 mmol/kg split for dynamic and static MRA, respectively, injected at a rate of 2 mL/s. Two blinded readers qualitatively assessed static MRA data sets independently using pairwise rankings (superior, inferior, and equal). In addition, quantitative analysis was performed with signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) evaluation as well as vessel sharpness analysis of static MRA using an in-house-developed semiautomated tool. Dynamic MRA was evaluated for maximal SNR. Statistical analysis was performed using the Cohen kappa, the Wilcoxon rank sum tests, and mixed effects models. Results: No significant differences of hemodynamic parameters were observed. In static MRA, Gadobutrol was rated superior to Gadoterate meglumine (P 0.05). Maximal SNR in dynamic MRA using Gadobutrol was significantly higher than both comparators at the level of the proximal and distal internal carotid artery (P < 0.05 and P < 0.05; P < 0.05 and P < 0.05). Conclusions: At equimolar doses, 1.0 M Gadobutrol demonstrates higher SNR/CNR than do Gadobenate dimeglumine and Gadoterate meglumine, with superior image quality as compared with Gadoterate meglumine for dynamic and static carotid MRA. Despite the shortened bolus with Gadobutrol, no blurring of vessel edges was observed

Neutral Atom Quantum Computing Hardware: Performance and End-User Perspective

We present an industrial end-user perspective on the current state of quantum computing hardware for one specific technological approach, the neutral atom platform. Our aim is to assist developers in understanding the impact of the specific properties of these devices on the effectiveness of algorithm execution. Based on discussions with different vendors and recent literature, we discuss the performance data of the neutral atom platform. Specifically, we focus on the physical qubit architecture, which affects state preparation, qubit-to-qubit connectivity, gate fidelities, native gate instruction set, and individual qubit stability. These factors determine both the quantum-part execution time and the end-to-end wall clock time relevant for end-users, but also the ability to perform fault-tolerant quantum computation in the future. We end with an overview of which applications have been shown to be well suited for the peculiar properties of neutral atom-based quantum computers

Multimodality Imaging in the Evaluation of Cardiovascular Manifestations of Malignancy

Up to one third of the population will die as a direct result of cancer. Accurate and timely diagnosis of disease often requires multiple different approaches including the use of modern imaging techniques. Prompt recognition of adverse consequences of some anti-cancer therapies also requires a knowledge of the optimum imaging strategy for the problem at hand. The purpose of this article is to review not only some of the commoner cardiovascular manifestations of malignancy but also to discuss the strengths, weaknesses and appropriate use of cardiovascular imaging modalities

Free Breathing Real-Time Cardiac Cine Imaging With Improved Spatial Resolution at 3 T

Objectives: The aim of this study was to evaluate free-breathing single-shot real-time cine imaging for functional cardiac imaging at 3 +/- with increased spatial resolution. Special emphasis of this study was placed on the influence of parallel imaging techniques. Materials and Methods: Gradient echo phantom images were acquired with GRAPPA and modified SENSE reconstruction using both integrated and separate reference scans as well as TGRAPPA and TSENSE. In vivo measurements were performed for GRAPPA reconstruction with an integrated and a separate reference scan, as well as TGRAPPA using balanced steady-state free precession protocols. Three clinical protocols, rtLRInt (T-res = 51.3 milliseconds; voxel, 2.5 x 5.0 x 10 mm(3)), rtMRSep (T-res = 48.8 milliseconds; voxel, 1.9 x 3.1 x 10 mm(3)), and rtHRSep ((Tres) = 48.3 milliseconds; voxel, 1.6 x 2.6 x 10 mm(3)), were investigated on 20 volunteers using GRAPPA reconstruction with internal as well as separate reference scans. End-diastolic volume, end-systolic volume, ejection fraction, peak ejection rate, peak filling rate, and myocardial mass were evaluated for the left ventricle and compared with an electrocardiogram-triggered segmented readout cine protocol used as standard of reference. All studies were performed at 3 T. Results: Phantom and in vivo data demonstrate that the combination of GRAPPA reconstruction with a separate reference scan provides an optimal compromise of image quality as well as spatial and temporal resolution. Functional values (P values) for the standard of reference, rtLRInt, rtMRSep, and rtHRSep end-diastolic volume were 141 +/- 24 mL, 138 +/- 21 mL, 138 +/- 19 mL, and 128 +/- 33 mL, respectively (P = 0.7, 0.7, 0.4); end-systolic volume, 55 +/- 15 mL, 61 +/- 14 mL, 58 +/- 12 mL, and 55 +/- 20 mL, respectively (P = 0.23, 0.43, 0.62); ejection fraction, 61% +/- 5%, 57% +/- 5%, 58% +/- 4%, and 56% +/- 8%, respectively (P = 0.01, 0.11, 0.06); peak ejection rate, 481 +/- 73 mL/s, 425 +/- 62 mL/s, 434 +/- 67 mL/s, and 381 +/- 86 mL/s, respectively (P = 0.03, 0.04, 0.01); peak filling rate, 555 +/- 80 mL/s, 480 +/- 70 mL/s, 500 +/- 70 mL/s, and 438 +/- 108 mL/s, respectively (P = 0.007, 0.05, 0.004); and myocardial mass, 137 +/- 26 g, 141 T 25 g, 141 +/- 23 g, and 130 +/- 31 g, respectively (P = 0.62, 0.54, 0.99). Conclusions: Using a separate reference scan and high acceleration factors up to R = 6, single-shot real-time cardiac imaging offers adequate temporal and spatial resolution for accurate assessment of global left ventricular function in free breathing with short examination times