Interband heating processes in a periodically driven optical lattice

We investigate multi-"photon" interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.Comment: 11 pages, 4 figure

Orbital-driven melting of a bosonic Mott insulator in a shaken optical lattice

In order to study the interplay between localized and dispersive orbital states in a system of ultracold atoms in an optical lattice, we investigate the possibility to coherently couple the lowest two Bloch bands by means of resonant periodic forcing. Considering bosons in one dimension, it is shown that a strongly interacting Floquet system can be realized, where at every lattice site two (and only two) near-degenerate orbital states are relevant. By smoothly tuning both states into resonance we find that the system can undergo an orbital-driven Mott-insulator-to-superfluid transition. As an intriguing consequence of the kinetic frustration in the system, this transition can be either continuous or first-order, depending on parameters such as lattice depth and filling.Comment: 7 pages, 3 figure

Non-equilibrum dynamics in the strongly excited inhomogeneous Dicke model

Using the exact eigenstates of the inhomogeneous Dicke model obtained by numerically solving the Bethe equations, we study the decay of bosonic excitations due to the coupling of the mode to an ensemble of two-level (spin 1/2) systems. We compare the quantum time-evolution of the bosonic mode population with the mean field description which, for a few bosons agree up to a relatively long Ehrenfest time. We demonstrate that additional excitations lead to a dramatic shortening of the period of validity of the mean field analysis. However, even in the limit where the number of bosons equal the number of spins, the initial instability remains adequately described by the mean-field approach leading to a finite, albeit short, Ehrenfest time. Through finite size analysis, we also present indications that the mean field approach could still provide an adequate description for thermodynamically large systems even at long times. However, for mesoscopic systems one cannot expect it to capture the behavior beyond the initial decay stage in the limit of an extremely large number of excitations.Comment: 9 pages, 7 figures, Phys. Rev. B in pres

Many-Body Floquet Engineering in Periodically Driven Optical Lattices

The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.Die vorliegende Arbeit behandelt Quantensimulationen von stark wechselwirkenden Systemen ultrakalter Atome in optischen Gittern. Dabei fokussiert sich diese theoretische Arbeit auf die Möglichkeit, diese Systeme mit Hilfe eines hochfrequenten Antriebs kohärent zu kontrollieren. Diese Form des Quantenengineering nennt man Floquet-Engineering. Experimentell wurden mit Hilfe eines zeitperiodischen Antriebs des optischen Gitters bereits viele physikalische Phänomene und Modelle realisiert, insbesondere im Bereich geringer Wechselwirkungen. Hier beschreiben wir zwei neue Vorschläge für interessante Phänomene im Bereich starker Wechselwirkungen, welche durch zeitperiodisches Gitterschütteln ermöglicht werden: Das Schmelzen eines Mott-Isolators in einen angeregte suprafluiden Zustand durch kohärentes Koppeln von Bloch-Bändern, sowie die Erzeugung von eindimensionalen Gitter-Anyonen. Außerdem wird die Rolle von Multiphoton-Übergängen in angetriebenen Gittern untersucht, da diese Prozesse zu ungewolltem Heizen und damit zur Verhinderung von erfolgreichem Floquet-Engineering führen können. Das einleitende Kapitel 1 gibt einen Überblick über das Feld der Quantensimulationen mit ultrakalten Atomen und beschreibt den experimentellen Fortschritt der letzten Jahre auf diesem Gebiet. In Kapitel 2 wird die Floquet-Theorie eingeführt, die einen exzellenten Rahmen dafür bietet zeitperiodische Hamiltonians zu behandeln und die Grundlage für die folgenden Kapitel ist. Kapitel 3 stellt den Vorschlag vor, Bloch-Bänder in optischen Gittern durch das Schütteln des Gitters kohärent miteinander zu koppeln. Insbesondere wird im Detail gezeigt, wie dieses Bandkoppeln zu einem orbital getriebenen Phasenübergang von einem Mott-Isolator zu einem Suprafluid führen kann. In Kapitel 4 wird der Vorschlag erläutert, wie eindimensionale Anyonen durch stark wechselwirkende Bosonen erzeugt werden können, indem das Gitter gekippt und geschüttelt wird. Außerdem wird vorgeschlagen, Friedel-Oszillationen im Ortsraum als im Experiment messbare Signatur für die Anyonisierung zu nutzen. Schließlich werden in Kapitel 5 Multiphoton-Übergänge in höhere Bloch-Bänder untersucht, im Falle eines geschüttelten und eines Amplitudenmodulierten Gitters. Die Stärke und die Lage der Resonanzen, welche zu Heizen führen, werden hierbei theoretisch und numerisch beschrieben

Semi-synthetic zigzag optical lattice for ultracold bosons

We consider a one-dimensional "zigzag" lattice, pictured as a two-site wide single strip taken from a triangular lattice, affected by a tunable homogeneous magnetic flux piercing its triangular plaquettes. We focus on a semi-synthetic lattice produced by combining a one-dimensional spin-dependent lattice in the long direction with laser-induced transitions between atomic internal states that define the short synthetic dimension. In contrast to previous studies on semi-synthetic lattices, the atom-atom interactions are nonlocal in both lattice directions. We investigate the ground-state properties of the system for the case of strongly interacting bosons, and find that the interplay between the frustration induced by the magnetic field and the interactions gives rise to an exotic gapped phase at fractional filling factors corresponding to one particle per magnetic unit cell.Comment: 9 pages, 6 figures; v3: final version to appear in PR

Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence

We present a numerical approach which allows the solving of Bethe equations whose solutions define the eigenstates of Gaudin models. By focusing on a new set of variables, the canceling divergences which occur for certain values of the coupling strength no longer appear explicitly. The problem is thus reduced to a set of quadratic algebraic equations. The required inverse transformation can then be realized using only linear operations and a standard polynomial root finding algorithm. The method is applied to Richardson's fermionic pairing model, the central spin model and generalized Dicke model.Comment: 10 pages, 3 figures, published versio

Interaction dependent heating and atom loss in a periodically driven optical lattice

Periodic driving of optical lattices has enabled the creation of novel band structures not realizable in static lattice systems, such as topological bands for neutral particles. However, especially driven systems of interacting bosonic particles often suffer from strong heating. We have systematically studied heating in an interacting Bose-Einstein condensate in a driven one-dimensional optical lattice. We find interaction dependent heating rates that depend on both the scattering length and the driving strength and identify the underlying resonant intra- and interband scattering processes. By comparing the experimental data and theory, we find that, for driving frequencies well above the trap depth, the heating rate is dramatically reduced by the fact that resonantly scattered atoms leave the trap before dissipating their energy into the system. This mechanism of Floquet evaporative cooling offers a powerful strategy to minimize heating in Floquet engineered quantum gases.This work was financially supported by the Deutsche Forschungsgemeinschaft (FOR2414), the European Commission (UQUAM, AQuS), and the Nanosystems Initiative Munich

Many-Body Floquet Engineering in Periodically Driven Optical Lattices

The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.Die vorliegende Arbeit behandelt Quantensimulationen von stark wechselwirkenden Systemen ultrakalter Atome in optischen Gittern. Dabei fokussiert sich diese theoretische Arbeit auf die Möglichkeit, diese Systeme mit Hilfe eines hochfrequenten Antriebs kohärent zu kontrollieren. Diese Form des Quantenengineering nennt man Floquet-Engineering. Experimentell wurden mit Hilfe eines zeitperiodischen Antriebs des optischen Gitters bereits viele physikalische Phänomene und Modelle realisiert, insbesondere im Bereich geringer Wechselwirkungen. Hier beschreiben wir zwei neue Vorschläge für interessante Phänomene im Bereich starker Wechselwirkungen, welche durch zeitperiodisches Gitterschütteln ermöglicht werden: Das Schmelzen eines Mott-Isolators in einen angeregte suprafluiden Zustand durch kohärentes Koppeln von Bloch-Bändern, sowie die Erzeugung von eindimensionalen Gitter-Anyonen. Außerdem wird die Rolle von Multiphoton-Übergängen in angetriebenen Gittern untersucht, da diese Prozesse zu ungewolltem Heizen und damit zur Verhinderung von erfolgreichem Floquet-Engineering führen können. Das einleitende Kapitel 1 gibt einen Überblick über das Feld der Quantensimulationen mit ultrakalten Atomen und beschreibt den experimentellen Fortschritt der letzten Jahre auf diesem Gebiet. In Kapitel 2 wird die Floquet-Theorie eingeführt, die einen exzellenten Rahmen dafür bietet zeitperiodische Hamiltonians zu behandeln und die Grundlage für die folgenden Kapitel ist. Kapitel 3 stellt den Vorschlag vor, Bloch-Bänder in optischen Gittern durch das Schütteln des Gitters kohärent miteinander zu koppeln. Insbesondere wird im Detail gezeigt, wie dieses Bandkoppeln zu einem orbital getriebenen Phasenübergang von einem Mott-Isolator zu einem Suprafluid führen kann. In Kapitel 4 wird der Vorschlag erläutert, wie eindimensionale Anyonen durch stark wechselwirkende Bosonen erzeugt werden können, indem das Gitter gekippt und geschüttelt wird. Außerdem wird vorgeschlagen, Friedel-Oszillationen im Ortsraum als im Experiment messbare Signatur für die Anyonisierung zu nutzen. Schließlich werden in Kapitel 5 Multiphoton-Übergänge in höhere Bloch-Bänder untersucht, im Falle eines geschüttelten und eines Amplitudenmodulierten Gitters. Die Stärke und die Lage der Resonanzen, welche zu Heizen führen, werden hierbei theoretisch und numerisch beschrieben

Many-Body Floquet Engineering in Periodically Driven Optical Lattices

The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.Die vorliegende Arbeit behandelt Quantensimulationen von stark wechselwirkenden Systemen ultrakalter Atome in optischen Gittern. Dabei fokussiert sich diese theoretische Arbeit auf die Möglichkeit, diese Systeme mit Hilfe eines hochfrequenten Antriebs kohärent zu kontrollieren. Diese Form des Quantenengineering nennt man Floquet-Engineering. Experimentell wurden mit Hilfe eines zeitperiodischen Antriebs des optischen Gitters bereits viele physikalische Phänomene und Modelle realisiert, insbesondere im Bereich geringer Wechselwirkungen. Hier beschreiben wir zwei neue Vorschläge für interessante Phänomene im Bereich starker Wechselwirkungen, welche durch zeitperiodisches Gitterschütteln ermöglicht werden: Das Schmelzen eines Mott-Isolators in einen angeregte suprafluiden Zustand durch kohärentes Koppeln von Bloch-Bändern, sowie die Erzeugung von eindimensionalen Gitter-Anyonen. Außerdem wird die Rolle von Multiphoton-Übergängen in angetriebenen Gittern untersucht, da diese Prozesse zu ungewolltem Heizen und damit zur Verhinderung von erfolgreichem Floquet-Engineering führen können. Das einleitende Kapitel 1 gibt einen Überblick über das Feld der Quantensimulationen mit ultrakalten Atomen und beschreibt den experimentellen Fortschritt der letzten Jahre auf diesem Gebiet. In Kapitel 2 wird die Floquet-Theorie eingeführt, die einen exzellenten Rahmen dafür bietet zeitperiodische Hamiltonians zu behandeln und die Grundlage für die folgenden Kapitel ist. Kapitel 3 stellt den Vorschlag vor, Bloch-Bänder in optischen Gittern durch das Schütteln des Gitters kohärent miteinander zu koppeln. Insbesondere wird im Detail gezeigt, wie dieses Bandkoppeln zu einem orbital getriebenen Phasenübergang von einem Mott-Isolator zu einem Suprafluid führen kann. In Kapitel 4 wird der Vorschlag erläutert, wie eindimensionale Anyonen durch stark wechselwirkende Bosonen erzeugt werden können, indem das Gitter gekippt und geschüttelt wird. Außerdem wird vorgeschlagen, Friedel-Oszillationen im Ortsraum als im Experiment messbare Signatur für die Anyonisierung zu nutzen. Schließlich werden in Kapitel 5 Multiphoton-Übergänge in höhere Bloch-Bänder untersucht, im Falle eines geschüttelten und eines Amplitudenmodulierten Gitters. Die Stärke und die Lage der Resonanzen, welche zu Heizen führen, werden hierbei theoretisch und numerisch beschrieben