Probing many-body localization with ultracold atoms in optical lattices

This thesis reports on first experiments on the observation of ergodicity breaking in a two-component, interacting fermionic gas of Potassium-40 subject to quasi-periodic optical lattices in one and two dimensions, demonstrating the breakdown of thermalization in highly excited states of isolated quantum systems. Our observations can be explained by the phenomenon of many-body localization, a non-ergodic phase of matter, whose properties can be detected with non-equilibrium probes. To probe such a phase, we first design a far-from-equilibrium initial state and then monitor how much the system remembers of this design during time evolution. This allows us to identify regimes and timescales where disorder can protect local quantum information and distinguish such cases from regimes where interactions amalgamate local information into highly nonlocal quantum correlations. We then describe how this treatment systematically breaks down in all real-world systems as the system is (necessarily) coupled to some bath-like structure. Following very recent developments, we are further able to show that order can exist even in driven quantum systems, which were earlier thought to exhibit no interesting features, corresponding to an infinite temperature state. We also extend the experimental realm to explore two dimensions and show that the dynamics emerge as a distinct interplay of interactions, disorder, and dimensions. Upon probing a putative MBL transition, we further show signatures of a new kind of slow relaxation, potentially arising due to randomness in the initial state. We close with some theoretical results on probing quantum dynamics ensuing in the absence of transport and a discussion of exciting areas for future experiments.Diese Doktorarbeit befasst sich mit der Realisierung nicht-ergodischer Zustände ultrakalter Atome in quasi-periodischen optischen Gittern mit einem zweikomponentigen, wechselwirkenden, fermionischen Gas aus Kalium-40-Atomen in einer und zwei Dimensionen. Die Ergebnisse zeigen hochangeregte, nicht-thermalisierende Zustände in isolierten Quantensystemen. Unsere Beobachtungen lassen sich mit dem Phänomen der Vielteilchenlokalisierung erklären – einer nicht-ergodischen Phase der Materie, deren Eigenschaften mittels dynamischer Observablen detektiert werden können. Zur Untersuchung einer solchen Phase präparieren wir zunächst einen Nichtgleichgewichtszustand und beobachten wie dessen Merkmale während der Zeitentwicklung verloren gehen. So können mehrere Parameterbereiche und Zeitskalen identifiziert werden, in denen lokale Quanteninformationen aufgrund der Unordnung erhalten bleiben und von Parameterbereichen unterschieden werden, in denen lokale Informationen mit Hilfe von Wechselwirkungen in hochgradig nichtlokale Quantenkorrelationen umgewandelt werden. Wir zeigen, wie die Beschreibung isolierter Quantensysteme in allen Experimenten systematisch zusammenbricht, da das System (notwendigerweise) an eine badähnliche Struktur gekoppelt ist. Des Weiteren wird gezeigt, dass Lokalisierung auch in periodisch getriebenen Quantensystemen existieren kann, von denen bis vor kurzem angenommen wurde, dass sie sich immer entsprechend einem Zustand unendlicher Temperatur verhalten. Wir ermöglichen die experimentelle Erforschung ungeordneter Systeme in zwei Dimensionen und zeigen die Existenz einer nicht-trivialen Dynamik, die als Zusammenspiel von Wechselwirkungen, Störungen und Dimensionen auftritt. Nach der Untersuchung eines mutmaßlichen Übergangs zeigen wir weitere Signaturen einer neuen Art langsamer Relaxation, die möglicherweise auf Unordnung im Anfangsszustand züruckzuführen ist. Wir schließen die Diskussion mit einigen theoretischen Ergebnissen zur Untersuchung der Quantendynamik in Abwesenheit von Transport und diskutieren vielversprechende zukünftige Experimente

Out-of-time-ordered measurements as a probe of quantum dynamics

Probing the out-of-equilibrium dynamics of quantum matter has gained renewed interest owing to immense experimental progress in artifcial quantum systems. Dynamical quantum measures such as the growth of entanglement entropy (EE) and out-of-time ordered correlators (OTOCs) have been shown, theoretically, to provide great insight by exposing subtle quantum features invisible to traditional measures such as mass transport. However, measuring them in experiments requires either identical copies of the system, an ancilla qubit coupled to the whole system, or many measurements on a single copy, thereby making scalability extremely complex and hence, severely limiting their potential. Here, we introduce an alternate quantity $-$ the out-of-time-ordered measurement (OTOM) $-$ which involves measuring a single observable on a single copy of the system, while retaining the distinctive features of the OTOCs. We show, theoretically, that OTOMs are closely related to OTOCs in a doubled system with the same quantum statistical properties as the original system. Using exact diagonalization, we numerically simulate classical mass transport, as well as quantum dynamics through computations of the OTOC, the OTOM, and the EE in quantum spin chain models in various interesting regimes (including chaotic and many-body localized systems). Our results demonstrate that an OTOM can successfully reveal subtle aspects of quantum dynamics hidden to classical measures, and crucially, provide experimental access to them.Comment: 7 pages, 4 figure

Probing many-body localization with ultracold atoms in optical lattices

This thesis reports on first experiments on the observation of ergodicity breaking in a two-component, interacting fermionic gas of Potassium-40 subject to quasi-periodic optical lattices in one and two dimensions, demonstrating the breakdown of thermalization in highly excited states of isolated quantum systems. Our observations can be explained by the phenomenon of many-body localization, a non-ergodic phase of matter, whose properties can be detected with non-equilibrium probes. To probe such a phase, we first design a far-from-equilibrium initial state and then monitor how much the system remembers of this design during time evolution. This allows us to identify regimes and timescales where disorder can protect local quantum information and distinguish such cases from regimes where interactions amalgamate local information into highly nonlocal quantum correlations. We then describe how this treatment systematically breaks down in all real-world systems as the system is (necessarily) coupled to some bath-like structure. Following very recent developments, we are further able to show that order can exist even in driven quantum systems, which were earlier thought to exhibit no interesting features, corresponding to an infinite temperature state. We also extend the experimental realm to explore two dimensions and show that the dynamics emerge as a distinct interplay of interactions, disorder, and dimensions. Upon probing a putative MBL transition, we further show signatures of a new kind of slow relaxation, potentially arising due to randomness in the initial state. We close with some theoretical results on probing quantum dynamics ensuing in the absence of transport and a discussion of exciting areas for future experiments.Diese Doktorarbeit befasst sich mit der Realisierung nicht-ergodischer Zustände ultrakalter Atome in quasi-periodischen optischen Gittern mit einem zweikomponentigen, wechselwirkenden, fermionischen Gas aus Kalium-40-Atomen in einer und zwei Dimensionen. Die Ergebnisse zeigen hochangeregte, nicht-thermalisierende Zustände in isolierten Quantensystemen. Unsere Beobachtungen lassen sich mit dem Phänomen der Vielteilchenlokalisierung erklären – einer nicht-ergodischen Phase der Materie, deren Eigenschaften mittels dynamischer Observablen detektiert werden können. Zur Untersuchung einer solchen Phase präparieren wir zunächst einen Nichtgleichgewichtszustand und beobachten wie dessen Merkmale während der Zeitentwicklung verloren gehen. So können mehrere Parameterbereiche und Zeitskalen identifiziert werden, in denen lokale Quanteninformationen aufgrund der Unordnung erhalten bleiben und von Parameterbereichen unterschieden werden, in denen lokale Informationen mit Hilfe von Wechselwirkungen in hochgradig nichtlokale Quantenkorrelationen umgewandelt werden. Wir zeigen, wie die Beschreibung isolierter Quantensysteme in allen Experimenten systematisch zusammenbricht, da das System (notwendigerweise) an eine badähnliche Struktur gekoppelt ist. Des Weiteren wird gezeigt, dass Lokalisierung auch in periodisch getriebenen Quantensystemen existieren kann, von denen bis vor kurzem angenommen wurde, dass sie sich immer entsprechend einem Zustand unendlicher Temperatur verhalten. Wir ermöglichen die experimentelle Erforschung ungeordneter Systeme in zwei Dimensionen und zeigen die Existenz einer nicht-trivialen Dynamik, die als Zusammenspiel von Wechselwirkungen, Störungen und Dimensionen auftritt. Nach der Untersuchung eines mutmaßlichen Übergangs zeigen wir weitere Signaturen einer neuen Art langsamer Relaxation, die möglicherweise auf Unordnung im Anfangsszustand züruckzuführen ist. Wir schließen die Diskussion mit einigen theoretischen Ergebnissen zur Untersuchung der Quantendynamik in Abwesenheit von Transport und diskutieren vielversprechende zukünftige Experimente

Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice

A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states localize for arbitrarily weak disorder strengths. However, if correlations are present in the disorder potential, the localization transition can occur at a finite disorder strength and SPMEs become possible. In this work, we find experimental evidence for the existence of such a SPME in a one-dimensional quasi-periodic optical lattice. Specifically, we find a regime where extended and localized single-particle states coexist, in good agreement with theoretical simulations, which predict a SPME in this regime

Coupling Identical one-dimensional Many-Body Localized Systems

We experimentally study the effects of coupling one-dimensional many-body localized systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artificially prepare an initial charge density wave in an array of 1D tubes with quasirandom on-site disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between many-body localization and Anderson localization. While the noninteracting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system

Observation of many-body localization of interacting fermions in a quasi-random optical lattice

We experimentally observe many-body localization of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the many-body localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. We connect this dependence to the ubiquitous logarithmic growth of entanglement entropy characterizing the generic many-body localized phase.Comment: 6 pages, 6 figures + supplementary informatio

Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems.

In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasiperiodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point. We discuss possible microscopic origins of these slow dynamics

Signatures of Many-Body Localization in a Controlled Open Quantum System

In the presence of disorder, an interacting closed quantum system can undergo many-body localization (MBL) and fail to thermalize. However, over long times, even weak couplings to any thermal environment will necessarily thermalize the system and erase all signatures of MBL. This presents a challenge for experimental investigations of MBL since no realistic system can ever be fully closed. In this work, we experimentally explore the thermalization dynamics of a localized system in the presence of controlled dissipation. Specifically, we find that photon scattering results in a stretched exponential decay of an initial density pattern with a rate that depends linearly on the scattering rate. We find that the resulting susceptibility increases significantly close to the phase transition point. In this regime, which is inaccessible to current numerical studies, we also find a strong dependence on interactions. Our work provides a basis for systematic studies of MBL in open systems and opens a route towards extrapolation of closed-system properties from experimentsWe acknowledge financial support by the European Commission (UQUAM, AQuS) and the Nanosystems Initiative Munich (NIM). Work at Strathclyde is supported by the EOARD via AFOSR Grant No. FA2386-14-1-5003. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. M. H. F. acknowledges additional support from the Swiss Society of Friends of the Weizmann Institute of Science and S. S. H. acknowledges additional support from the Australian Research Council through Discovery Early Career Research Award No. DE150100315

Periodically driving a many-body localized quantum system

We experimentally study a periodically driven many-body localized system realized by interacting fermions in a one-dimensional quasi-disordered optical lattice. By preparing the system in a far-from-equilibrium state and monitoring the remains of an imprinted density pattern, we identify a localized phase at high drive frequencies and an ergodic phase at low ones. These two distinct phases are separated by a dynamical phase transition which depends on both the drive frequency and the drive strength. Our observations are quantitatively supported by numerical simulations and are directly connected to the change in the statistical properties of the effective Floquet Hamiltonian.We acknowledge support from Technical University of Munich - Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under grant agreement 291763, from the DFG grant no. KN 1254/1-1, the European Commission (UQUAM, AQuS) and the Nanosystems Initiative Munich (NIM)