Artificial gauge fields with ultracold atoms in optical lattices

Diese Doktorarbeit befasst sich mit der Erzeugung von künstlichen Magnetfeldern für ultrakalte Atome in optischen Gittern mithilfe von Laser-induziertem Tunneln sowie mit der ersten experimentellen Bestimmung der Chernzahl in einem nicht-elektronischen System. Kalte Atome in optischen Gittern lassen sich experimentell sehr gut kontrollieren, was sie zu guten Modellsystemen für die Simulation von Festkörpern macht, wobei die Atome die Rolle der Elektronen übernehmen. Allerdings können Magnetfeldeffekte in diesen Systemen nicht direkt im Experiment simuliert werden, da die Atome elektrisch neutral sind, weshalb auf sie keine Lorentzkraft wirkt. Im Rahmen dieser Doktorarbeit wird eine neue Methode vorgestellt künstliche Magnetfelder basierend auf Laser-induziertem Tunneln zu erzeugen um somit die Physik geladener Teilchen in realen Magnetfeldern nachzuahmen. Dabei verursachen Laserstrahlen eine periodische Modulation der einzelnen Gitterplätze, deren Phase von der Gitterposition abhängt und dadurch zu komplexen Tunnelkopplungen führt. Ein Atom, welches sich entlang einer geschlossenen Bahn in diesem System bewegt, erfährt eine Phase, die als Aharonov-Bohm-Phase eines geladenen Teilchens in einem Magnetfeld interpretiert werden kann. Das modulierte Gitter wird durch einen zeitabhängigen Hamilton-Operator beschrieben, der typischerweise durch einen effektiven zeitunabhängigen Floquet Hamilton-Operator genähert wird. Im Rahmen dieser Arbeit wird darüber hinaus die vollständige Zeitabhängigkeit innerhalb einer Modulationsperiode beschrieben und mit den experimentellen Daten verglichen. Mithilfe des Laser-induzierten Tunnelns wurden alternierende sowie gleichgerichtete Magnetfelder im Experiment erzeugt, wobei letztere eine Realisierung des Harper-Hofstadter-Modells für einen Fluss Phi=pi/2 pro Gittereinheitszelle darstellen. Durch die Verwendung eines zusätzlichen Pseudospin-Freiheitsgrades konnte zudem der Spin-Hall-Effekt in einem optischen Gitter beobachtet werden. Unter Benutzung der einzigartigen Detektions- und Manipulationstechniken eines zweidimensionalen Übergitters konnte die Stärke und Verteilung des künstlichen Magnetfeldes auf lokaler Ebene durch die Beobachtung von Zyklotronorbits experimentell bestimmt werden. Die Bandstruktur in einem periodischen Potential mit externem Magnetfeld weist interessante topologische Eigenschafen auf, die durch Chernzahlen beschrieben werden, welche beispielsweise dem Quanten-Hall-Effekt zugrunde liegen. Um topologische Bandeigenschaften mit kalten Atomen beobachten zu können, wurden die genannten experimentellen Techniken weiterentwickelt. Mit einem neuen Aufbau, der nur auf optischen Potentialen beruht, konnte erstmals die Chernzahl in einem nicht-elektronischen System bestimmt werden. Die vorgestellten experimentellen Methoden eröffnen einzigartige Möglichkeiten die Eigenschaften von topologischen Materialien mit kalten Atomen in optischen Gittern zu untersuchen. Die Techniken wurden mit bosonischen Atomen implementiert, sie lassen sich allerdings ohne weiteres auch auf fermionische Systeme anwenden.This thesis reports on the generation of artificial magnetic fields with ultracold atoms in optical lattice potentials using laser-assisted tunneling, as well as on the first Chern-number measurement in a non-electronic system. The high experimental controllability of cold atoms in optical lattices makes them suitable candidates to study condensed matter Hamiltonians, where the atoms play the role of the electrons. However, the observation of magnetic field effects in these systems is challenging because the atoms are charge neutral and do not experience a Lorentz force. In the context of this thesis a new experimental technique for the generation of effective magnetic fields with laser-assisted tunneling was demonstrated, which mimics the physics of charged particles in real magnetic fields. The applied laser beams create a periodic on-site modulation whose phase depends on the position in the lattice and leads to complex tunnel couplings. An atom that hops around a closed loop in this system picks up a non-zero phase, which is reminiscent of the Aharonov-Bohm phase acquired by a charged particle in a magnetic field. The corresponding time-dependent Hamiltonian is typically described in terms of an effective time-independent Floquet Hamiltonian. In this work a theoretical description of the underlying full-time dynamics that occurs within one driving period and goes beyond the simple time-independent picture is presented. In the experiment the laser-assisted-tunneling method was implemented for staggered as well as uniform flux distributions, where the latter is a realization of the Harper-Hofstadter model for a flux Phi=pi/2 per lattice unit cell. By exploiting an additional pseudo-spin degree of freedom the same experimental setup led to the observation of the spin Hall effect in an optical lattice. Using the unique experimental detection and manipulation techniques offered by a two-dimensional bichromatic superlattice potential the strength of the artificial magnetic field and its spatial distribution could be determined through the observation of quantum cyclotron orbits on the level of isolated four-site square plaquettes. The band structure in the presence of a uniform magnetic field is topologically non-trivial and is characterized by the Chern number, a 2D topological invariant, which is at the origin of the quantized Hall conductance observed in electronic systems. In order to probe the topology of the bands the techniques mentioned above were refined by developing a new all-optical laser-assisted tunneling setup, which enabled the first experimental determination of the Chern number in a non-electronic system. The presented measurements and techniques offer a unique setting to study the properties of topological systems with ultracold atoms. All experimental techniques that were developed in the context of this thesis with bosonic atoms can be directly applied to fermionic systems

Artificial gauge fields with ultracold atoms in optical lattices

Diese Doktorarbeit befasst sich mit der Erzeugung von künstlichen Magnetfeldern für ultrakalte Atome in optischen Gittern mithilfe von Laser-induziertem Tunneln sowie mit der ersten experimentellen Bestimmung der Chernzahl in einem nicht-elektronischen System. Kalte Atome in optischen Gittern lassen sich experimentell sehr gut kontrollieren, was sie zu guten Modellsystemen für die Simulation von Festkörpern macht, wobei die Atome die Rolle der Elektronen übernehmen. Allerdings können Magnetfeldeffekte in diesen Systemen nicht direkt im Experiment simuliert werden, da die Atome elektrisch neutral sind, weshalb auf sie keine Lorentzkraft wirkt. Im Rahmen dieser Doktorarbeit wird eine neue Methode vorgestellt künstliche Magnetfelder basierend auf Laser-induziertem Tunneln zu erzeugen um somit die Physik geladener Teilchen in realen Magnetfeldern nachzuahmen. Dabei verursachen Laserstrahlen eine periodische Modulation der einzelnen Gitterplätze, deren Phase von der Gitterposition abhängt und dadurch zu komplexen Tunnelkopplungen führt. Ein Atom, welches sich entlang einer geschlossenen Bahn in diesem System bewegt, erfährt eine Phase, die als Aharonov-Bohm-Phase eines geladenen Teilchens in einem Magnetfeld interpretiert werden kann. Das modulierte Gitter wird durch einen zeitabhängigen Hamilton-Operator beschrieben, der typischerweise durch einen effektiven zeitunabhängigen Floquet Hamilton-Operator genähert wird. Im Rahmen dieser Arbeit wird darüber hinaus die vollständige Zeitabhängigkeit innerhalb einer Modulationsperiode beschrieben und mit den experimentellen Daten verglichen. Mithilfe des Laser-induzierten Tunnelns wurden alternierende sowie gleichgerichtete Magnetfelder im Experiment erzeugt, wobei letztere eine Realisierung des Harper-Hofstadter-Modells für einen Fluss Phi=pi/2 pro Gittereinheitszelle darstellen. Durch die Verwendung eines zusätzlichen Pseudospin-Freiheitsgrades konnte zudem der Spin-Hall-Effekt in einem optischen Gitter beobachtet werden. Unter Benutzung der einzigartigen Detektions- und Manipulationstechniken eines zweidimensionalen Übergitters konnte die Stärke und Verteilung des künstlichen Magnetfeldes auf lokaler Ebene durch die Beobachtung von Zyklotronorbits experimentell bestimmt werden. Die Bandstruktur in einem periodischen Potential mit externem Magnetfeld weist interessante topologische Eigenschafen auf, die durch Chernzahlen beschrieben werden, welche beispielsweise dem Quanten-Hall-Effekt zugrunde liegen. Um topologische Bandeigenschaften mit kalten Atomen beobachten zu können, wurden die genannten experimentellen Techniken weiterentwickelt. Mit einem neuen Aufbau, der nur auf optischen Potentialen beruht, konnte erstmals die Chernzahl in einem nicht-elektronischen System bestimmt werden. Die vorgestellten experimentellen Methoden eröffnen einzigartige Möglichkeiten die Eigenschaften von topologischen Materialien mit kalten Atomen in optischen Gittern zu untersuchen. Die Techniken wurden mit bosonischen Atomen implementiert, sie lassen sich allerdings ohne weiteres auch auf fermionische Systeme anwenden.This thesis reports on the generation of artificial magnetic fields with ultracold atoms in optical lattice potentials using laser-assisted tunneling, as well as on the first Chern-number measurement in a non-electronic system. The high experimental controllability of cold atoms in optical lattices makes them suitable candidates to study condensed matter Hamiltonians, where the atoms play the role of the electrons. However, the observation of magnetic field effects in these systems is challenging because the atoms are charge neutral and do not experience a Lorentz force. In the context of this thesis a new experimental technique for the generation of effective magnetic fields with laser-assisted tunneling was demonstrated, which mimics the physics of charged particles in real magnetic fields. The applied laser beams create a periodic on-site modulation whose phase depends on the position in the lattice and leads to complex tunnel couplings. An atom that hops around a closed loop in this system picks up a non-zero phase, which is reminiscent of the Aharonov-Bohm phase acquired by a charged particle in a magnetic field. The corresponding time-dependent Hamiltonian is typically described in terms of an effective time-independent Floquet Hamiltonian. In this work a theoretical description of the underlying full-time dynamics that occurs within one driving period and goes beyond the simple time-independent picture is presented. In the experiment the laser-assisted-tunneling method was implemented for staggered as well as uniform flux distributions, where the latter is a realization of the Harper-Hofstadter model for a flux Phi=pi/2 per lattice unit cell. By exploiting an additional pseudo-spin degree of freedom the same experimental setup led to the observation of the spin Hall effect in an optical lattice. Using the unique experimental detection and manipulation techniques offered by a two-dimensional bichromatic superlattice potential the strength of the artificial magnetic field and its spatial distribution could be determined through the observation of quantum cyclotron orbits on the level of isolated four-site square plaquettes. The band structure in the presence of a uniform magnetic field is topologically non-trivial and is characterized by the Chern number, a 2D topological invariant, which is at the origin of the quantized Hall conductance observed in electronic systems. In order to probe the topology of the bands the techniques mentioned above were refined by developing a new all-optical laser-assisted tunneling setup, which enabled the first experimental determination of the Chern number in a non-electronic system. The presented measurements and techniques offer a unique setting to study the properties of topological systems with ultracold atoms. All experimental techniques that were developed in the context of this thesis with bosonic atoms can be directly applied to fermionic systems

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux-attachment to Z2 lattice gauge theories

Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highly-controllable environment. Despite being dynamically tunable, such artificial gauge fields are genuinely classical and exhibit no back-action from the neutral particles. Here we go beyond this paradigm, and demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices. Specifically, we propose a protocol by which atoms of one species carry a magnetic flux felt by another species, hence realizing an instance of flux-attachment. This is obtained by combining coherent lattice modulation techniques with strong Hubbard interactions. We demonstrate how this setting can be arranged so as to implement lattice models displaying a local Z2 gauge symmetry, both in one and two dimensions. We also provide a detailed analysis of a ladder toy model, which features a global Z2 symmetry, and reveal the phase transitions that occur both in the matter and gauge sectors. Mastering flux-attachment in optical lattices envisages a new route towards the realization of strongly-correlated systems with properties dictated by an interplay of dynamical matter and gauge fields.Comment: 11 pages, 6 figures, 11 pages supplement

Dissemination activity and impact of maternal and newborn health projects in Ethiopia, India and Nigeria

This study aimed to document the key messages, dissemination activities and impacts of selected projects within the Bill & Melinda Gates Foundation Maternal, Neonatal and Child Health strategy portfolio, and consider how these might contribute toward the learning agenda for the strategy

Experimental realization of strong effective magnetic fields in an optical lattice

We use Raman-assisted tunneling in an optical superlattice to generate large tunable effective magnetic fields for ultracold atoms. When hopping in the lattice, the accumulated phase shift by an atom is equivalent to the Aharonov-Bohm phase of a charged particle exposed to a staggered magnetic field of large magnitude, on the order of one flux quantum per plaquette. We study the ground state of this system and observe that the frustration induced by the magnetic field can lead to a degenerate ground state for non-interacting particles. We provide a measurement of the local phase acquired from Raman-induced tunneling, demonstrating time-reversal symmetry breaking of the underlying Hamiltonian. Furthermore, the quantum cyclotron orbit of single atoms in the lattice exposed to the magnetic field is directly revealed.Comment: 6 pages, 5 figure

The cold-atom elevator: From edge-state injection to the preparation of fractional Chern insulators

Optical box traps for cold atoms offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activate energy-selective chiral edge currents, but also, to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly-correlated and topological phases.Comment: 15 pages, 11 figures including Supplementary materia

Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms

We propose a scheme to implement Kitaev's honeycomb model with cold atoms, based on a periodic (Floquet) drive, in view of realizing and probing non-Abelian chiral spin liquids using quantum simulators. We derive the effective Hamiltonian to leading order in the inverse-frequency expansion, and show that the drive opens up a topological gap in the spectrum without mixing the effective Majorana and vortex degrees of freedom. We address the challenge of probing the physics of Majorana fermions, while having only access to the original composite spin degrees of freedom. Specifically, we propose to detect the properties of the chiral spin liquid phase using gap spectroscopy and edge quenches in the presence of the Floquet drive. The resulting chiral edge signal, which relates to the thermal Hall effect associated with neutral Majorana currents, is found to be robust for realistically-prepared states. By combining strong interactions with Floquet engineering, our work paves the way for future studies of non-Abelian excitations and quantized thermal transport using quantum simulators

Observation of many-body localization in a one-dimensional system with single-particle mobility edge

We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL, when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-Andr\'{e} model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase

Floquet topological phase transitions induced by uncorrelated or correlated disorder

The impact of weak disorder and its spatial correlation on the topology of a Floquet system is not well understood so far. In this study, we investigate a model closely related to a two-dimensional Floquet system that has been realized in experiments. In the absence of disorder, we determine the phase diagram and identify a new phase characterized by edge states with alternating chirality in adjacent gaps. When weak disorder is introduced, we examine the disorder-averaged Bott index and analyze why the anomalous Floquet topological insulator is favored by both uncorrelated and correlated disorder, with the latter having a stronger effect. For a system with a ring-shaped gap, the Born approximation fails to explain the topological phase transition, unlike for a system with a point-like gap.Comment: 6+3 pages, 3 + 2 figure