Experimentally Accessible Witnesses of Many-Body Localization

The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models

Many-Body Localization Implies that Eigenvectors are Matrix-Product States

The phenomenon of many-body localization has received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at nonzero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalization following out-of- equilibrium dynamics. In this work, we establish a novel link between dynamical properties—a vanishing group velocity and the absence of transport—with entanglement properties of individual eigenvectors. For systems with a generic spectrum, we prove that strong dynamical localization implies that all of its many-body eigenvectors have clustering correlations. The same is true for parts of the spectrum, thus allowing for the existence of a mobility edge above which transport is possible. In one dimension these results directly imply an entanglement area law; hence, the eigenvectors can be efficiently approximated by matrix-product states

Towards experimental quantum-field tomography with ultracold atoms

The experimental realization of large-scale many-body systems in atomic- optical architectures has seen immense progress in recent years, rendering full tomography tools for state identification inefficient, especially for continuous systems. To work with these emerging physical platforms, new technologies for state identification are required. Here we present first steps towards efficient experimental quantum-field tomography. Our procedure is based on the continuous analogues of matrix-product states, ubiquitous in condensed-matter theory. These states naturally incorporate the locality present in realistic physical settings and are thus prime candidates for describing the physics of locally interacting quantum fields. To experimentally demonstrate the power of our procedure, we quench a one- dimensional Bose gas by a transversal split and use our method for a partial quantum-field reconstruction of the far-from-equilibrium states of this system. We expect our technique to play an important role in future studies of continuous quantum many-body systems

Ein Einblick mittels Quanteninformationstheorie

This thesis investigates quantum-many body systems out of equilibrium in a variety of physically relevant and intriguing settings. It provides an overview of the recent developments in this field and based on the author’s recent review illuminates many interesting connections and summarises open questions. In this general framework, the various results of the author are embedded. While they often rely on advanced mathematics, great care is taken to present them in an intuitive way and most technical material is discussed separately in appendices. In the context of equilibration, work created as part of this thesis is able to capture the Gaussification of correlated initial states for a large class of free models. This allows to significantly extend equilibration results of free models, which are of crucial importance, as they provide reasonable relaxation time scales and immediately connect to our physical intuition in terms of ballistic spreading. Building on two surprising connections between static and dynamic features of Hamiltonians, which in general are hard to obtain, the results of this thesis further greatly contribute to the recent debate on the true nature of quantum many- body localisation. For those interacting models, we derive the localised structure of eigenstates from a dynamical suppression of information propagation on the low-energy sector. Further, we show how a non-degenerate spectrum, indicating the presence of interactions, and the existence of an approximately local constant of motion are sufficient to show information propagation, if arbitrary energies are allowed. In the context of quantum phase transitions, we continue such connections between static and dynamic features. We specifically investigate the Mott-superfluid transition of the Bose-Hubbard model and ask to what extent it has a universal dynamical signature. In a joint experimental, numerical and analytical effort, complex behaviour of these dynamics is uncovered, thus challenging the common believe that the Kibble-Zurek mechanism is sufficient to fully capture such transitions. We embed such experimental investigation in the recent debate on quantum simulators, which give the exciting perspective of solving notoriously and even provably hard problems efficiently in the laboratory. For such devices, we argue that the final read-out of the results is an important out- standing problem to be solved. We approach this issue in the case of a continuous quantum field, in which the notion of reconstructing the quantum state is even conceptually unclear. Based on tensor network methods, we demonstrate that in an experiment of ultra-cold atoms in a continuous setup, states can nevertheless efficiently be obtained. Thus, this thesis constitutes not only an important review of the field of quantum many-body systems out of equilibrium, but, using advanced mathematical and numerical tools, has significantly contributed to our understanding of various important out- standing questions in interacting many-body systems.In dieser Doktorarbeit werden Quantenvielteilchensysteme außerhalb des Equilibriums in verschiedenem physikalischen Kontext untersucht. Aufbauend auf einem Übersichtsartikel zu diesem Feld, an dem der Autor dieser Arbeit beteiligt war, werden wichtige Entwicklungen dargestellt, wesentliche Querverbindungen gezogen und offene Fragen präsentiert. In diesen Rahmen sind die analytischen und numerischen Arbeiten des Autors eingebettet. Trotz ihrer teils tiefgehend mathematischen Natur wurde großer Wert darauf gelegt, diese auf intuitive Weise zu präsentieren. Technische Details werden daher separat in Anhängen diskutiert. Im Bereich der Equilibrierung gelang es zu zeigen, dass korrelierte Anfangszustände durch die Entwicklung unter freien fermionischen Modellen lokal gegen einen Gaußschen Zustand streben. Damit können Gaußsche Equilibrierungsergebnisse verallgemeinert werden, woraus sich wichtige Intuition für den wechselwirkenden Fall ableiten lässt. Aufbauend auf zwei unerwarteten Verbindungen zwischen statischen und dynamischen Eigenschaften von Hamiltonoperatoren, welche im Allgemeinen schwer zu etablieren sind, trägt diese Arbeit signifikant zur Debatte bei, wie Vielteilchenlokalisierung zu fassen ist. Es wird gezeigt, dass Lokalisierungseigenschaften von Eigenzuständen aus einer dynamischen Lokalisierung unterhalb einer Energieschranke hergeleitet werden können. Darüber hinaus wird hergeleitet, dass die Anwesenheit einer lokalen Erhaltunsgröße zusammen mit einem nichtentarteten Spektrum ausreicht, um dynamische Ausbreitung von Information zu garantieren. Im Bereich der Quantenphasenübergänge wird der Zusammenhang von dynamischen und statischen Eigenschaften wechselwirkender Modelle tiefergehend untersucht. In einer vereinten experimentellen, analytischen und numerischen Arbeit wird die Dynamik des Phasenübergangs des Bose-Hubbard Modells analysiert. Hierbei tritt komplexes Verhalten zu Tage, das bisher weder durch den Kibble-Zurek Mechanismus, noch durch andere Theorien erklärt werden kann. Diese experimentelle Untersuchung wird in den weiter gefassten Rahmen von Quantensimulatoren eingebettet. Solche Simulatoren zeigen eine Perspektive auf, harte quantenmechanische Probleme im Labor effizient zu lösen. Der finale Schritt einer solchen Quantensimulation ist die Rekonstruktion der Simulationsergebnisse. Wir untersuchen diesen für ultrakalte Atome in einer kontinuierlichen Falle. Ausgehend von Tensornetzwerkmethoden zeigen wir, dass (trotz der Schwierigkeiten kontinuierlicher Architekturen) effiziente Quantenfeldtomographie durchgeführt werden kann und wir demonstrieren diese darüber hinaus auch direkt experimentell. Zusammenfassend gibt diese Arbeit nicht nur einen umfassenden Überblick über Quantenvielteilchensysteme außerhalb des Gleichgewichts, sondern nutzt darüber hinaus elaborierte mathematische Methoden und numerische Simulationen, um unser Verständnis von Vielteilchensystemen signifikant zu erweitern

Experimentally Accessible Witnesses of Many-Body Localization

The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models

Singularity methods for magnetohydrodynamics

Singular solutions for linearized MHD equations based on Oseen approximations have been obtained such as Oseenslet. Oseenrotlet, mass source, etc. By suitably distributing these singular solutions along the axes of symmetry of an axially symmetric bodies, we derive the approximate values for the velocity fields, the force and the momentum for the case of translational and rotational motions of such bodies in a steady flow of an incompressible viscous and magnetized fluid