A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)

The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one ignores normalizations, of positive operators. On the CFT side of the correspondence, any two positive operators $A,B$ will satisfy the trace inequality $\operatorname{Tr}(AB) \leq \operatorname{Tr}(A) \operatorname{Tr}(B)$. This relation holds on any Hilbert space ${\cal H}$ and is deeply associated with the fact that the algebra $B({\cal H})$ of bounded operators on ${\cal H}$ is a type I von Neumann factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate below. In particular, we argue that the Euclidean gravitational path integral respects this inequality at all orders in the semi-classical expansion and with arbitrary higher-derivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for Jackiw-Teitelboim gravity and we also motivate it for more general theories.Comment: 65 pages, 14 figure

A Rydberg tweezer platform with potassium atoms

Quantum simulation offers the possibility to study quantum mechanical problems which are untraceable on classical computers. This thesis introduces a novel platform for quantum simulation and presents the first experimental realisation of single potassium atoms trapped in optical tweezers. Interactions between individual atoms are induced by strong energy shifts of atoms excited to states with large principal quantum number, so-called Rydberg states. Either direct excitation to Rydberg states or off-resonant dressing can be used to induce these interactions. We argue that potassium is well-suited for the implementation of Rydberg dressing, enabling simultaneous dressing of both ground states to engineer complex interactions. Using techniques to cool and trap cold atoms, single potassium atoms are prepared in arrays of optical tweezers. Raman sideband cooling reduces vibrational excitations and prepares the atoms close to the motional ground state. This cooling technique mitigates severe limitations for Rydberg dressing, arising from thermal broadening and inhomogeneous light shifts in the array of atoms. To directly excite atoms to Rydberg states, a high power laser setup with two cavity-enhanced frequency doubling stages is constructed, generating up to one Watt of ulta-violet light at 286 nm. By exciting atoms to Rydberg states we observe Rabi oscillations with Rabi frequencies of up to 1 MHz, demonstrating coherent control of Rydberg atoms. Finally, we combine these techniques to observe interactions in two ways: First, we create a so-called superatom of up to four individual atoms using direct excitation and Rydberg-blockade and observe coherent oscillations to this collective state. We measure the expected square root scaling of the effective Rabi frequency with the number of individual atoms, confirming the creation of a many-body entangled state. Secondly, we off-resonantly dress the atoms prepared in a one-dimensional chain and measure correlated interaction shifts over multiple sites. In summary, we have developed a platform for quantum simulation with single atoms in optical tweezers. The presented results show coherent control of single atoms and interactions induced by Rydberg states. We have thus demonstrated that the system is well-suited for quantum simulation of many-body systems.Quantensimulationen bieten die Möglichkeit quantenmechanische Probleme zu untersuchen, welche auf klassischen Computern nicht berechenbar sind. Diese Arbeit stellt eine neue Plattform für Quantensimulationen vor und präsentiert die erste experimentelle Realisierung einzelner Kaliumatome in optischen Dipolfallen. Wechselwirkungen zwischen einzelnen neutralen Atomen werden durch die starken Energieverschiebungen von Zuständen mit großer Hauptquantenzahl verursacht, sogenannte Rydberg-Zustände. Wechselwirkungen können dabei entweder durch eine direkte Anregung in Rydberg-Zustände oder eine verstimmte optische Kopplung, so genanntes 'Rydberg dressing', erzeugt werden. Wir begründen, warum insbesondere Kalium für die Implementierung von 'Rydberg dressing' geeignet ist und insbesondere durch das gleichzeitige Koppeln beider Grundzustände das Erzeugen komplexer Wechselwirkungen ermöglicht. Kaliumatome werden mittels Laserkühlung abgebremst, gefangen und anschließend werden einzelne Atome in optischen Dipolfallen geladen. Zudem reduziert Raman Seitenbandkühlung die Schwingungsanregungen in den Fallenpotentialen und kühlt die Atome fast zum Bewegungsgrundzustand. Diese Kühltechnik ermöglicht 'Rydberg dressing', welches ansonsten durch thermische Verbreiterung und inhomogenen Fallenpotentiale limitiert wäre. Um Atome direkt in Rydberg-Zustände anzuregen, wird ein Lasersystem mit zwei resonanten Frequenz Verdopplungsstufen aufgebaut, mit welchem bis zu einem Watt ultravioletten Lichts bei 286 nm erzeugt wird. Durch Anregung von Atomen in Rydberg-Zustände beobachten wir Rabi-Oszillationen mit Rabi-Frequenzen von bis zu 1 MHz, was eine kohärente Kontrolle der Rydberg-Atome demonstriert. Zuletzt kombinieren wir diese Techniken, um Wechselwirkungen auf zwei verschiedene Arten zu beobachten: Erstens erzeugen wir durch direkte Anregung und Rydberg-Blockade ein sogenanntes 'Superatom' aus bis zu vier einzelnen Atomen und beobachten kohärente Oszillationen zu diesem kollektiven Zustand. Wir messen die erwartete Skalierung der effektiven Rabi-Frequenz mit der Wurzel der Anzahl der Atome und bestätigen die Erzeugung eines Quantenverschränkten Zustands. Zweitens induzieren wir Wechselwirkungen zwischen Atomen durch optische Beimischung mittels 'Rydberg dressing', die in einer eindimensionalen Kette optischer Dipolfallen gefangen wurden und messen korrelierte Wechselwirkungen über Distanzen von mehreren Fallenplätzen. Zusammenfassend haben wir eine Plattform für die Quantensimulation mittels einzelner Atome in optischen Dipolfallen entwickelt. Die vorgestellten Ergebnisse zeigen eine kohärente Kontrolle einzelner Atome und Wechselwirkungen, die durch Rydberg-Zustände induziert werden. Wir zeigen damit, dass das System für die Quantensimulation von Vielkörpersystemen gut geeignet ist

Efficiency and instabilities of financial markets

[Excerpt from the abstract]: In this thesis, we consider two topics in the field of high frequency financial econometrics. The first one is the measurement of market efficiency from high frequency data, within an information theory framework. The study of this topic is performed with an analytical and empirical combined approach. The second topic is that of financial market systemic instabilities at high frequency level and is analysed mainly with an empirical and modelling approach. [...

Superconductivity in Iron Compounds

Kamihara and coworkers' report of superconductivity at Tc = 26 K in fluorine-doped LaFeAsO inspired a worldwide effort to understand the nature of the superconductivity in this new class of compounds. These iron pnictide and chalcogenide (FePn/Ch) superconductors have Fe electrons at the Fermi surface, plus an unusual Fermiology that can change rapidly with doping, which lead to normal and superconducting state properties very different from those in standard electron-phonon coupled 'conventional' superconductors. Clearly superconductivity and magnetism/magnetic fluctuations are intimately related in the FePn/Ch - and even coexist in some. Open questions, including the superconducting nodal structure in a number of compounds, abound and are often dependent on improved sample quality for their solution. With Tc values up to 56 K, the six distinct Fe-containing superconducting structures exhibit complex but often comparable behaviors. The search for correlations and explanations in this fascinating field of research would benefit from an organization of the large, seemingly disparate data set. This review attempts to provide an overview, using numerous references, with a focus on the materials and their superconductivity.Comment: 30 figures, 4 tables, approximately 600 references; to appear in Rev. Mod. Phy

First International Conference on Laboratory Research for Planetary Atmospheres

Proceedings of the First International Conference on Laboratory Research for Planetary Atmospheres are presented. The covered areas of research include: photon spectroscopy, chemical kinetics, thermodynamics, and charged particle interactions. This report contains the 12 invited papers, 27 contributed poster papers, and 5 plenary review papers presented at the conference. A list of attendees and a reprint of the Report of the Subgroup on Strategies for Planetary Atmospheres Exploration (SPASE) are provided in two appendices

Quantum correlations in continuous variable mixed states : from discord to signatures

This thesis studies continuous variable mixed states with the aim of better understanding the fundamental behaviour of quantum correlations in such states, as well as searching for applications of these correlations. I first investigate the interesting phenomenon of discord increase under local loss and explain the behaviour by considering the non-orthogonality of quantum states. I then explore the counter-intuitive result where entanglement can be created by a passive optical beamsplitter, even if the input states are classical, as long as the input states are part of a larger globally nonclassical system. This result emphasises the importance of global correlations in a quantum state, and I propose an application of this protocol in the form of quantum dense coding. Finally, I develop a quantum digital signature protocol that can be described entirely using the continuous variable formalism. Quantum digital signatures provide a method to ensure the integrity and provenance of a message using quantum states. They follow a similar method to quantum key distribution (QKD), but require less post-processing, which means they can sometimes be implemented over channels that are inappropriate for QKD. The method I propose uses homodyne measurement to verify the signature, unlike previous protocols that use single photon detection. The single photon detection of previous methods is designed to give unambiguous results about the signature, but this comes at the cost of getting no information much of the time. Using homodyne detection has the advantage of giving results all the time, but this means that measurement results always have some ambiguity. I show that, even with this ambiguity, the signature protocol based on homodyne measurement outperforms previous protocols, with the advantage enhanced when technical considerations are included. Therefore this represents an interesting new direction in the search for a practical quantum digital signature scheme