Strongly-correlated phases in trapped-ion quantum simulators

We study quantum (T = 0) phases of strongly-correlated matter, and their possible implementation in a quantum simulator. We focus on the non-perturbative regimes of 1D spin-boson models. As a reference physical system we consider trapped-ion chains. We realize complex many-body states, such as a ground state exhibiting magnetic frustration, a lattice gauge theory, and a topological insulator. The exquisite control over these phases offered by a quantum simulator opens up exciting possibilities for exploring the exotic phenomena emerging in these systems, such as enhanced fluctuations and correlations. We address the non-perturbative regimes of the phase diagrams by means of mean-field theories and the numerical algorithm DMRG. We have established the universality class of the continuous transition in the spin-boson chain, the existence of a first order phase transition when the system is endowed with a gauge symmetry, and the possibility of probing topological states of matter in these systems. Our results show that some of the most exotic phases of quantum matter can be readily realized in trapped-ion quantum simulators. This offers the possibility of exploring these physical models beyond their original realm of applicability, which may provide us with new insights on both theoretical and applied fields of physics, ranging from high-energy processes to low-energy cooperative phenomena

Dynamics of ion Coulomb crystals

The field of quantum simulations has achieved a remarkable success through the development of highly controllable and accessible quantum platforms, which pro- vide insights into the microscopic properties of complex large-scale systems that are otherwise difficult to analyze. Many of the platforms utilized in this pursuit are derived from the field of atomic, molecular, and optical physics. One particularly popular candidate is provided by trapped ions, whose vibrational and electronic degrees of freedom can be effectively combined through laser pulses to engineer desired model Hamiltonians or quantum circuits. Trapped ions constitute as well the basis for modern atomic clocks, the most precise frequency standards currently available. They find further applications in metrology, geodesy, and fundamental physics experiments. In this Thesis, we investigate the dynamics of vibrational modes in trapped ion crystals, utilizing them as a versatile platform to explore various many-body phenomena. We first focus on the expansion dynamics of local excitations and on heat transport within ion crystals hosting structural defects that undergo a sliding- to-pinned transition. We observe a significant reduction in conductivity when the crystal symmetry is spontaneously broken during the transition, and show that resonances between crystal eigenmodes lead to distinct softening signatures associated with energy localization. We then delve into the effects of thermal and quantum fluctuations on the vibrational modes of ion crystals near two distinct structural transitions. We observe the emergence of a prolonged symmetric phase stabilized by thermal and quantum fluctuations, and develop effective theories that reduce the degrees of freedom to the modes that drive the transitions. Finally, we discuss how to engineer spin-orbit coupling and on-site interaction energies for vibrational quantum excitations using two different external driving schemes. While the simulation of spin models with ions typically involves the use of two electronic states, we propose interpreting the two local oscillation modes in an ion crystal as a pseudospin. We show how using Floquet engineering ideas allows for spin flips in Coulomb-induced vibron hopping, resulting in a non-trivial coupling between spatial motion and spin evolution, that results in a markedly non-Abelian dynamics. Subsequently, we explore the simulation of Hubbard models in trapped ions by coupling the vibrational Fock states to an internal level system. Our findings include the observation of bound states in the strong interaction limit of the resulting Jaynes-Cummings-Hubbard model. By investigating these topics, we aim to contribute to the understanding of vibrational dynamics in trapped ion crystals, and shed light on their potential for simulating condensed matter systems, offering insights into phenomena that are otherwise challenging to explore.DFG/Sonderforschungsbereich 1227 DQ-mat/274200144/E

Electronic and photonic excitations in graphene nanostructures and hybrid systems

Plasmonische Resonanzen in photonischen Nanoantennen erlauben eine beispiellose Verstärkung und örtliche Konzentrierung elektrischer Felder und finden vielseitige Anwendungen in der Nanotechnologie. Viele Jahre waren die Edelmetalle die Treiber der Nanoplasmonik. In letzter Zeit erfreuen sich aber vor allem niedrigdimensionale Werkstoffe zunehmender Beliebtheit als plasmonische Materialien. Vor allem die einzigartige Bandstruktur von zweidimensionalem Graphen bietet die Möglichkeit, Resonanzen auch nach der Herstellung der Struktur durch elektrisches Dotieren oder optisches Pumpen spektral zu verschieben. Neben Graphen diskutieren wir in dieser Arbeit im Rahmen des Su-Schrieffer-Heeger-Modells (SSH) zudem eindimensionale Polyen- und Polyacetylen-Moleküle, um konzeptionelle Einblicke in die Wesensart optischer Moden in Nanoantennen zu erlangen. Nanoantennen verändern allein durch ihre Präsenz die lokale photonische Umgebung und beeinflussen die optischen Eigenschaften von Quantenemittern in der Nähe, z. B. deren spontane Emissionsraten oder Rabi-Oszillationen. Zur Modellierung der optischen Eigenschaften hybrider Systeme, die aus Nanoantennen und Emittern bestehen, ist die führende Simulationsmethode die Dichtefunktionaltheorie. Sie ist jedoch sehr rechenintensiv und kann nicht auf Strukturen relevanter Größe angewandt werden. Um diese Beschränkung zu überwinden, entwickeln wir eine tight-binding-Methode (TB) im Zeitbereich, die die quantenoptischen Phänomene im Emitter und seine chemische Wechselwirkung mit der Nanoantenne beschreiben kann. In dieser Arbeit diskutieren wir zwei Probleme, die auftreten, wenn eine klassische Beschreibung für die oben beschriebenen Systeme nicht mehr anwendbar ist und stattdessen eine quantenmechanische Beschreibung erforderlich wird. Das erste Problem betrifft die TB-Simulationsmethodik hybrider Systeme, die aus einer Nanoantenne und einem adsorbierten Atom (Adatom) bestehen, das als Emitter fungiert. Der üblicherweise verwendete Purcell-Formalismus zur Modellierung solcher Systeme vernachlässigt allerdings elektronisches Tunneln zwischen der Nanoantenne und dem Adatom. Unsere Simulationen zeigen, dass sich unter Berücksichtigung dieses Wechselwirkungskanals die optischen Eigenschaften des Systems maßgeblich verändern. Sowohl die Wechselwirkungsstärke zwischen Adatom und Nanoantenne, als auch deren relative Position sind hierfür entscheidend. Wir finden zwei qualitativ verschiedene Wechselwirkungs-Regime, wenn das Adatom am Rand oder an den Mittelteil der Nanoantenne gekoppelt wird. Umgekehrt ändern sich auch die dem Adatom zugehörigen Phänomene. Insbesondere beobachten wir eine Reduzierung sowohl der spontanen Emissionsrate, als auch der Rabi-Frequenz optischer Übergänge im hybriden Gesamtsystem. Die zweite Problematik behandelt die Frage, was ein Plasmon in Nanosystemen wirklich ist. Wir zeigen auf, dass es in der Literatur verschiedene Konzepte für plasmonische Resonanzen gibt. Die meisten stützen sich bei ihrer Definition auf die induzierte Ladungsverteilung der Resonanz oder auf die Anzahl der beteiligten Ein - Teilchen - Übergänge. Unser Beitrag zu dieser wissenschaftlichen Diskussion, der energy-based plasmonicity index (EPI), klassifiziert eine Resonanz anhand der Zeitentwicklung der Kohärenzen im Dichteoperator des Systems, ausgewertet im Energie-Raum. Der EPI wird hier eingeführt, validiert und auf SSH-Ketten und Graphen-Nanoantennen angewandt. Wir stellen fest, dass der EPI Klassifikationsergebnisse liefert, die mit jenen der Coulomb-Skalierungs-Methode übereinstimmen. Der generalized plasmonicity index, welcher auf Auswertungen im Ortsraum basiert, liefert allerdings keine deckungsgleichen Resultate. Der EPI ergänzt daher die bestehenden Klassifizierungsmethoden und hilft, bisher wenig beachtete Aspekte plasmonischer Resonanzen in den Mittelpunkt zu rücken

Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering

We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper-Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer-Wolff transformation extending the latter to driven systems.Comment: 84 pages, 25 figures, 4 appendice

The cold atom toolbox in momentum space

The many weird properties of quantum mechanics at the very small scale have led to surprising and useful discoveries that manifest at the macroscopic level, like the quantum Hall effect and high temperature superconductivity. Yet trying to understand the origin of correlated behavior from interacting quantum systems via classical simulation requires an infeasible level of computing power. Instead, we can use an easily tunable, clean quantum system as a quantum simulation of a more unwieldy system, building the same model to study the same physics, but in a more controlled environment. Our field of cold neutral atoms in optical lattices has seen success over many years as a platform for quantum simulation of various lattice models from condensed matter physics. The recent (2015) implementation of lattices not in position, but in a synthetic dimension by coupling individual quantum states with lasers has led to a more bottom-up approach to engineering lattice models. In this thesis, we present our "momentum-space lattice" technique in which we use individual laser frequencies to couple the momentum states of a rubidium-87 Bose-Einstein condensate, in order to create lattices with site-by-site and link-by-link precision. This technique is simple to implement experimentally, requiring just two additional common optical components (acousto-optic modulators) compared to a real-space lattice, yet is incredibly versatile. Using momentum-space lattices, we have studied the physics of artificial magnetic fields, disorder and pseudodisorder-induced localization, and atomic interactions across eight works described in this thesis. More interesting are the not-so-well-known effects that arise in the interplay among these three components of topology, disorder, and interactions, and we have made headway towards studying physics in this regime. To be more specific, in our studies we have generated an artificial magnetic field for neutral atoms, and directly observed the resulting chiral currents in both a square ladder and zigzag lattice geometry. We have further monitored the quantum walk behavior of atoms under disordered and pseudodisordered lattices, observing a transition to localization under a quasiperiodic potential. We have been able to introduce a tunable energy dependence to this localization transition (single-particle mobility edge) in two ways: with the addition of more tunneling pathways, and by modifying the form of the potential. Finally, we have studied the effects of nonlinear inter-atomic interactions in the momentum-space lattice, observing self-trapping in a double well system as well as on a full lattice, showing a skewed current-phase relationship in an analog to Josephson junction arrays, and investigating an interaction-induced shift in localization behavior under pseudodisorder. In constructing the momentum-space lattice apparatus, Eric, Bryce, and I have created a promising new platform for Hamiltonian engineering. The studies described here not only show off the capabilities of the technique, but also realize new models, reveal new physics, and provide a new perspective complementary to both real-space lattice techniques and real materials. We have observed topological edge states more directly than previous works and engineered precise lattice parameter variations unavailable to other techniques, and yet the best is still to come. With our ongoing experimental upgrades comes access to the regime of strong inter-particle interactions, which promises more challenging yet more rewarding experiments

Zigzag Solitons and Spontaneous Symmetry Breaking in Discrete Rabi Lattices with Long-Range Hopping

A new type of discrete soliton, which we call zigzag solitons, is founded in two-component discrete Rabi lattices with long-range hopping. The spontaneous symmetry breaking (SSB) of zigzag solitons is also studied. Through numerical simulation, we found that by enhancing the intensity of the long-range linearly-coupled effect or increasing the total input power, the SSB process from the symmetric soliton to the asymmetric soliton will switch from the supercritical to subcritical type. These results can help us better understand both the discrete solitons and the Rabi coupled effect

Quantum Electrodynamics in a Topological Waveguide

While designing the energy-momentum relation of photons is key to many linear, nonlinear, and quantum optical phenomena, a new set of light-matter properties may be realized by employing the topology of the photonic bath itself. In this work we experimentally investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model. We explore topologically induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects. Addition of qubits to this waveguide system also enables direct quantum control over topological edge states that form in finite waveguide systems, useful for instance in constructing a topologically protected quantum communication channel. More broadly, our work demonstrates the opportunity that topological waveguide-QED systems offer in the synthesis and study of many-body states with exotic long-range quantum correlations

Quantum Electrodynamics in a Topological Waveguide

While designing the energy-momentum relation of photons is key to many linear, nonlinear, and quantum optical phenomena, a new set of light-matter properties may be realized by employing the topology of the photonic bath itself. In this work we experimentally investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model. We explore topologically induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects. Addition of qubits to this waveguide system also enables direct quantum control over topological edge states that form in finite waveguide systems, useful for instance in constructing a topologically protected quantum communication channel. More broadly, our work demonstrates the opportunity that topological waveguide-QED systems offer in the synthesis and study of many-body states with exotic long-range quantum correlations