Diese Dissertation berichtet über ein neuartiges Quantengasmikroskop, mit dem Vielteilchensysteme von fermionischen Atomen in optischen Gittern untersucht werden. Die einzelplatzaufgelöste Abbildung ultrakalter Gase im Gitter hat mächtige Experimente an bosonischen Vielteilchensystemen ermöglicht. Die Erweiterung dieser Fähigkeit auf Fermigase bietet neue Aussichten, komplexe Phänomene stark korrelierter Systeme zu erforschen, für die numerische Simulationen oft nicht möglich sind.

Mit Standardtechniken der Laserkühlung, optischen Fallen und Verdampfungskühlung werden ultrakalte Fermigase von 6Li präpariert und in ein 2D optisches Gitter mit flexibler Geometrie geladen. Die Atomverteilung wird mithilfe eines zweiten, kurzskaligen Gitters eingefroren. Durch Raman-Seitenbandkühlung wird an jedem Atom Fluoreszenz induziert, während seine Position festgehalten wird. Zusammen mit hochauflösender Abbildung erlaubt die Fluoreszenz die Rekonstruktion der ursprünglichen Verteilung mit Einzelplatzauflösung und hoher Genauigkeit.

Mithilfe von magnetisch angetriebener Verdampfungskühlung produzieren wir entartete Fermigase mit fast einheitlicher Füllung im ersten Gitter. Dies ermöglicht die ersten mikroskopischen Untersuchungen an einem ultrakalten Gas mit klaren Anzeichen von Fermi-Statistik. Durch die Präparation eines Ensembles spinpolarisierter Fermigase detektieren wir eine Abflachung im Dichteprofil im Zentrum der Wolke,

ein Charakteristikum bandisolierender Zustände.

In einem Satz von Experimenten weisen wir nach, dass Verluste von Atompaaren an einem Gitterplatz, bedingt durch lichtinduzierte Stöße, umgangen werden. Die Überabtastung des zweiten Gitters erlaubt eine deterministische Trennung der Atompaare in unterschiedliche Gitterplätze. Die Kompression einer dichten Wolke in der Falle vor dem Laden ins Gitter führt zu vielen Doppelbesetzungen von Atomen in unterschiedlichen Bändern, die wir ohne Anzeichen von paarweisen Verlusten abbilden können. Somit erhalten wir die wahre Besetzungsstatistik an jedem Gitterplatz.

Mithilfe dieser Besonderheit werten wir die lokale Besetzungsstatistik an einem Ensemble bandisolierenderWolken aus. Im Zentrum bei hoher Füllung sind die Atomzahlfluktuationen um eine Größenordnung unterdrückt, verglichen mit klassischen Gasen, eine Manifestation des Pauliverbots. Die Besetzungswahrscheinlichkeiten werden verwendet, um die lokale Entropie an jedem Gitterplatz zu messen. Eine niedrige Entropie pro Atom bis 0.34kB wird im Zentrum des Bandisolators gefunden.

Die Erweiterung der Quantengasmikroskopie auf entartete Fermigase eröffnet neue Möglichkeiten der Quantensimulation stark korrelierter Vielteilchensysteme und kann einzigartige Erkenntnisse über fermionische Systeme im und außerhalb vom Gleichgewicht, Quantenmagnetismus und verschiedene Phasen des Fermi-Hubbard-Modells

ergeben.

The observed accelerated expansion of the universe is successfully parameterized by a cosmological constant. However, since this parameter in Einstein's equations is not protected against quantum corrections, the observed and theoretically expected value vastly differ, thus giving rise to the cosmological constant problem. In this thesis, the issue is addressed by embedding our universe--represented by a brane--in a six-dimensional bulk spacetime, where the cosmological constant plays the role of a brane tension, which then no longer needs to imply an expansion of the three apparent spatial dimensions; rather, it curves the extra space and hence stays hidden from a brane observer. In this context, the crucial question is whether this so-called degravitation mechanism may be implemented in a phenomenologically viable and 't Hooft natural way. Corresponding answers will be given in the case of four different models.

The main part of this thesis has its focus on the 6D brane induced gravity model--a higher-dimensional generalization of the Dvali-Gabadadze-Porrati model--according to which a brane with sub-critical tension curves the bulk into a cone of infinite spatial extent.

First, it is shown that the model is free of ghost instabilities only if the tension is not unnaturally small.

This in turn opens a window of opportunity to study theoretically consistent modified cosmologies. In this context, it is shown that a homogeneous and isotropic brane acts as an antenna that emits and absorbs cylindrically symmetric Einstein-Rosen waves.

We encounter two interesting types of solutions--sub-critical ones, which feature dynamical degravitation but are incompatible with observations, as well as compact super-critical ones, which still might be phenomenologically viable but certainly not technically natural. While this clearly shows that the cosmological constant problem cannot be solved in a 6D version of the model, our results point towards higher-dimensional constructions as the remaining playground for future research.

Next, we introduce a new two-brane model where a thick super-critical brane curves the extra space into a cigar that closes in a microscopically thin sub-critical brane, representing our universe. In the case both branes only host a tension, we derive fully analytic solutions, which correspond to a de Sitter phase on our brane and are hence phenomenologically promising. Unfortunately, as a fine-tuning of the brane tension is required, they are not technically natural. The failure is attributed to the compactness of the extra space.

To further exemplify the virtue of infinite volume extra dimensions, we devise a hybrid model where the brane is wrapped around an infinitely long cylinder of microscopic width. This construction turns out to be the minimal setup that features bulk waves as a dynamical ingredient of a modified cosmology. We find that, due to the existence of an infinitely large dimension, the system admits a degravitating solution. While being conceptually interesting, a supernova fit shows that the corresponding 4D cosmology cannot describe our universe.

Finally, we turn to the model of supersymmetric large extra dimensions that had been claimed to successfully address the cosmological constant problem. Here, a Maxwell flux stabilizes the extra space that has the shape of a rugby ball.

We critically review the corresponding mechanism, and find that a vanishing brane curvature--as required by the degravitation idea--is only ensured by a scale invariant brane sector, which however leads to an unavoidable parameter constraint due to a flux quantization condition.

In a second step, we generalize our analysis to solutions that admit a de Sitter phase on the brane. Provided the model parameters are not tuned, we find that either the brane curvature or the volume of the extra space exceeds its phenomenological bound by many orders of magnitude.

Our results significantly narrow down the s

Eine aussagekräftige theoretische Beschreibung des Infrarot (IR)-Schwingungsspektrums eines Biomoleküls in seiner nativen Umgebung durch Molekulardynamik (MD)-Simulationen benötigt hinreichend genaue Modelle sowohl für das Biomolekül, als auch für das umgebende Lösungsmittel. Die quantenmechanische Dichtefunktionaltheorie (DFT) stellt solche genauen Modelle zur Verfügung, zieht aber hohen Rechenaufwand nach sich. Daher ist dieser Ansatz nicht zur Simulation der MD ausgedehnter Biomolekül-Lösungsmittel-Komplexe einsetzbar. Solche Systeme können effizient mit polarisierbaren molekülmechanischen (PMM) Kraftfeldern behandelt werden, die jedoch nicht die zur Berechnung von IR-Spektren nötige Genauigkeit liefern.

Einen Ausweg aus dem skizzierten Dilemma bieten Hybridverfahren, die einen relevanten Teil eines Simulationssystems mit DFT, und die ausgedehnte Lösungsmittelumgebung mit einem (P)MM-Kraftfeld beschreiben. Im Rahmen dieser Arbeit wird, ausgehend von einer DFT/MM-Hybridmethode [Eichinger et al., J. Chem. Phys. 110, 10452-10467 (1999)], ein genaues und hocheffizientes DFT/PMM-Rechenverfahren entwickelt, das der wissenschaftlichen Ọ̈ffentlichkeit nun in Form des auf Großrechnern einsetzbaren Programmpakets IPHIGENIE/CPMD zur Verfügung steht.

Die neue DFT/PMM-Methode fußt auf der optimalen Integration des DFT-Fragments in die "schnelle strukturadaptierte Multipolmethode" (SAMM) zur effizienten approximativen Berechnung der Wechselwirkungen zwischen den mit gitterbasierter DFT bzw. mit PMM beschriebenen Subsystemen.

Dies erlaubt stabile Hamilton'sche MD-Simulationen sowie die Steigerung der Performanz (d.h. dem Produkt aus Genauigkeit und Recheneffizienz) um mehr als eine Größenordnung.

Die eingeführte explizite Modellierung der elektronischen Polarisierbarkeit im PMM-Subsystem durch induzierbare Gauß'sche Dipole ermöglicht die Verwendung wesentlich genauerer PMM-Lösungsmittelmodelle. Ein effizientes Abtastens von Peptidkonformationen mit DFT/ PMM-MD kann mit einer generalisierten Ensemblemethode erfolgen.

Durch die Entwicklung eines Gauß'schen polarisierbaren Sechspunktmodells (GP6P) für Wasser und die Parametrisierung der Modellpotentiale für van der Waals-Wechselwirkungen zwischen GP6P-Molekülen und der Amidgruppe (AG) von N-Methyl-Acetamid (NMA) wird ein DFT/PMM-Modell für (Poly-)Peptide und Proteine in wässriger Lösung konstruiert. Das neue GP6P-Modell kann die Eigenschaften von flüssigem Wasser mit guter Qualität beschreiben. Ferner können die mit DFT/PMM-MD berechneten IR-Spektren eines in GP6P gelösten DFT-Modells von NMA die experimentelle Evidenz mit hervorragender Genauigkeit reproduzieren. Somit ist nun ein hocheffizientes und ausgereiftes DFT/PMM-MD-Verfahren zur genauen Berechnung der Konformationslandschaften und IR-Schwingungsspektren von in Wasser gelösten Proteinen verfügbar.

A detailed study of alpha interactions on the passivated surface of a germanium detector is

presented. Germanium detectors can be used to search for both neutrinoless double beta

decay of 76Ge and direct interaction of dark matter. In order to increase the sensitivity to

both neutrinoless double beta decay and dark matter beyond the current state of the art,

the next generation of germanium-based experiments has to have a mass of about one ton

and has to reduce the background by a factor of ten. The choices of detector technology

facilitating both searches and the background reduction are one of the biggest challenges

for such an experiment. Surface contaminations on the material close to the detectors or

on the detectors themselves, can generate a background due to alpha particles, which was

found to be limiting in some experiments.

The characterization of events induced by alpha particles will help to identify such

events and thus eliminate them as sources of background. An especially designed segmented

true-coaxial detector was probed with alpha particles from an 241Am source inside the

test-stand GALATEA, located at the MPI f¨ur Physik in Munich. Pulse shape analysis was

performed to identify the characteristics of alpha events. The properties of the detector

directly underneath the passivation layer on the end-plate were also studied. As part of

the detector characterization, the thickness of the effective dead layer was determined.

The studies presented here suggest improvements on detector design, which would

allow an effective reduction of alpha background in next generation of germanium-based

experiments.

In this thesis, we investigate the gravitational consequences of theories in which the four spacetime dimensions of our universe are augmented by two spatial extra dimensions. More specifically, the focus is on braneworld scenarios, where our world is confined on a hypersurface in the higher-dimensional bulk, allowing the extra dimensions to be large or even infinite. Our main motivation for studying such models is that they could in principle be able to solve the cosmological constant (CC) problem via degravitation: the CC only curves the extra space, leaving the brane geometry flat.

A major difference to the simpler case of a codimension-one brane is that here, gravitational waves can be emitted into the bulk, even at the 3D homogeneous and isotropic level, as is relevant for cosmology. Therefore, we first analyze the question how an outgoing wave boundary condition can be implemented, which is necessary in order to obtain a closed set of modified Friedmann equations predicting the cosmological on-brane evolution. We find that a potential tool from the literature, provided by a certain decomposition of the Weyl tensor - while being applicable to plane gravitational waves - fails for cylindrical waves. This failure is related to the fact that it is already impossible to locally separate incoming from outgoing linear cylindrical waves (on flat spacetime), as we demonstrate by explicitly deriving the corresponding nonreflecting boundary condition, which is nonlocal in time.

We then consider a generalization of the Dvali-Gabadadze-Porrati (DGP) model, containing an additional compact on-brane dimension on top of the one infinite codimension. Since here the 3D maximally symmetric brane emits plane waves, the Weyl tensor criterion can be used to exclude incoming bulk waves, and we derive the resulting Friedmann equations. If the compact dimension is stabilized, DGP cosmology is recovered, but we find indications that the stabilization should break down when the CC starts to dominate, which would lead to additional, potentially interesting late time modifications. If, on the other hand, the compact direction is allowed to expand freely, there are dynamically degravitating solutions - which, however, lack a 4D regime and are thus ruled out, as we demonstrate by fitting to supernova data.

Next, we turn to the codimension-two version of the DGP model. By numerically solving the full nonlinear coupled bulk-brane system for cosmological symmetries on the (regularized) brane, we show that in some region of parameter space, a CC - but also any other fluid component - gets degravitated dynamically, and a static geometry is approached via the emission of Einstein-Rosen waves. For other model parameters, pathological super-accelerating solutions are encountered. The origin of this unstable behavior is traced back to a tachyonic ghost mode which is identified in this parameter region by studying linear metric perturbations around a nontrivial pure tension background. While confirming the ghost result on Minkowski from the literature, we gain the important insight that the ghost disappears if the brane tension is large enough, thereby reconciling the model with the physical expectation of a healthy low energy effective theory. Unfortunately, the healthy region is again incompatible with an appropriate 4D gravity regime, and therefore ruled out phenomenologically.

The preceding analysis only covered sub-critical brane tensions, meaning that the deficit angle of the exterior conical geometry is less than 2π. In the following chapter, we investigate super-critical tensions (first in 4D), and find that the (regularized) static solution is no longer stable. Instead, the axial direction expands at an asymptotically constant rate, and the exterior geometry (which is necessarily compact) takes the form of a growing cigar. We are able to derive an analytic relation between the expansion rate and the tension, which - when adapted to the 6D s

We formulate a quantum theory of classical solutions in gravity and field theory in terms of a large number of constituent degrees of freedom. The description is realized in two different ways.

In the first part we introduce the so-called auxiliary current description. The basic idea is to represent the true quantum state of the solution one considers in terms of a multi- local composite operator of the fields of the microscopic theory. Although the approach is completely general, we will be mostly interested in representing black holes as bound states of a large number of gravitons. We show how the mass of the black hole arises microscopically as a collective effect of N gravitons composing the bound state. For that purpose we compute observables associated to the black hole interior such as the constituent density of gravitons and their energy density, respectively. As a next step, it is shown how these observables can be embedded within S-matrix processes. In particular, it is demonstrated that an outside observer has access to the black hole interior doing scattering experiments. Measuring the cross section for the scattering of particles on black holes, the outside observer is sensitive to the distribution of gravitons in the black hole. Possible implications concerning the information paradox are discussed. Finally, we show how geometric concepts, and in particular the Schwarzschild solution emerge as an effective description derived from our construction.

In the second part, an alternative approach based on coherent states in presented. First, we apply our reasoning to solitons in field theory. In particular, we explicitly show how well-known properties of solitons such as interactions, false vacuum decay or conservation of topological charge follow easily from the basic properties of coherent states. Secondly, we develop in detail a similar quantum picture of instantons. Since instantons can be understood in terms of solitons in one more spatial dimension evolving in Euclidean time, a coherent state description of the latter implies a similar description of the former. Using the coherent state picture we develop a novel quantum mechanical understanding of the physics of instanton-induced transitions and the concept of resurgence. Finally, we consider solitons in supersymmetric theories. It is shown that the corpuscular effects lead to a novel mechanism of supersymmetry breaking which can never be accounted for in the semi- classical approach.

In the last part of the thesis we resolve anti-de Sitter (AdS) space-time as a coherent state. On the one hand, we explain how well-known holographic and geometric properties can easily be understood in terms of the occupation number of gravitons in the state. On the other hand, we explicitly compute corpuscular corrections to the scalar propagator in AdS. Furthermore, it is shown that corpuscular effects lead to deviations from thermality an Unruh observer in AdS measures.

In this thesis we introduce a novel approach viewing spacetime geometry as an emergent

phenomenon based on the condensation of a large number of quanta on a distinguished

flat background. We advertise this idea with regard to investigations of spacetime singularities

within a quantum field theoretical framework and semiclassical considerations

of black holes.

Given that in any physical theory apart from General Relativity the metric background

is determined in advance, singularities are only associated with observables and

can either be removed by renormalization techniques or are otherwise regarded as unphysical.

The appearance of singularities in the spacetime structure itself, however, is

pathological. The prediction of said singularities in the sense of geodesic incompleteness

culminated in the famous singularity theorems established by Hawking and Penrose.

Though these theorems are based on rather general assumptions we argue their physical

relevance. Using the example of a black hole we show that any classical detector theory

breaks down far before geodesic incompleteness can set in. Apart from that, we point

out that the employment of point particles as diagnostic tools for spacetime anomalies

is an oversimplification that is no longer valid in high curvature regimes.

In view of these results the question arises to what extent quantum objects are

affected by spacetime singularities. Based on the definition of geodesic incompleteness

customized for quantum mechanical test particles we collect ideas for completeness

concepts in dynamical spacetimes. As it turns out, a further development of these

ideas has shown that Schwarzschild black holes, in particular, allow for a evolution of

quantum probes that is well-defined all over.

This fact, however, must not distract from such semiclassical considerations being

accompanied by many so far unresolved paradoxes. We are therefore compelled to take

steps towards a full quantum resolution of geometrical backgrounds.

First steps towards such a microscopic description are made by means of a non-relativistic

scalar toy model mimicking properties of General Relativity. In particular, we model

black holes as quantum bound states of a large number N of soft quanta subject to

a strong collective potential. Operating at the verge of a quantum phase transition

perturbation theory naturally breaks down and a numerical analysis of the model becomes

inevitable. Though indicating 1/N corrections as advertised in the underlying

so-called Quantum-N portrait relevant for a possible purification of Hawking radiation

and henceforth a resolution of the long-standing information paradox we recognize that

such a non-relativistic model is simply not capable of capturing all relevant requirements

of a proper black hole treatment.

We therefore seek a relativistic framework mapping spacetime geometry to large-N quantum bound states. Given a non-trivial vacuum structure supporting graviton condensation

this is achieved via in-medium modifications that can be linked to a collective

binding potential. Viewing Minkowski spacetime as fundamental, the classical notion of

any other spacetime geometry is recovered in the limit of an infinite constituent number

of the corresponding bound state living on Minkowski. This construction works

in analogy to the description of hadrons in quantum chromodynamics and, in particular,

also uses non-perturbative methods like the auxiliary current description and the

operator product expansion. Concentrating on black holes we develop a bound state description

in accordance with the isometries of Schwarzschild spacetime. Subsequently,

expressions for the constituent number density and the energy density are reviewed.

With their help, it can be concluded that the mass of a black hole at parton level is

proportional to its constituent number. Going beyond this level we then consider the

scattering of a massless scalar particle off a

This thesis reports on experimental demonstrations of a novel direct frequency-comb spectroscopic technique for the measurement of one- and two-photon excitation spectra. An optical-frequency-comb generator emits a multitude of highly coherent laser modes whose oscillation frequencies are evenly spaced and uniquely determined by only two measurable and adjustable radio-frequency parameters and the integer-valued mode number. Direct frequency-comb spectroscopy can traditionally be performed by scanning the comb lines of the frequency comb across the transitions of interest and measuring a signal that is proportional to the excitation by all comb lines in concert. Since the modes that contribute to the excitation cannot be singled out, transition frequencies can only be measured modulo the comb-line spacing with this scheme. The so arising limitations are overcome by the technique presented here, where the first frequency comb is spatially overlapped with a second frequency comb. Both combs of this so-called dual-comb setup are ideally identical except for having different carrier-envelope frequencies and slightly different repetition rates. The interference between the two combs leads to beat notes between adjacent comb lines, forming pairs (with one line from each comb) with an effectively modulated excitation amplitudes. Consequently the probability of excitation by any given comb-line pair is also modulated at the respective beat-note frequency. These beat-note frequencies are spaced by the repetition-rate difference and uniquely encode for individual comb-line pairs, thus enabling the identification of the comb lines causing an observed excitation.

In a first demonstration, Doppler-limited one-photon excitation spectra of the transitions 5S_{1/2}-5P_{3/2} (at 384 Thz/780 nm), 5P_{3/2}-5D_{3/2}, and 5P_{3/2}-5D_{5/2} (both at 386 Thz/776 nm), and two-photon spectra of the 5S_{1/2}-5D_{5/2} (at 2x385 Thz/2x778 nm) transition, agreeing well with simulated spectra, are simultaneously measured for both stable Rb isotopes.

Within an 18-s measurement time, a spectral range of more than 10 THz (20 nm) is covered at a signal-to-noise ratio (SNR) of up to 550. To my knowledge, this is the first demonstration of both dual-comb-based two-photon spectroscopy and fluorescence-based dual-comb spectroscopy.

In a follow-up experiment probing the same sample and two-photon transitions, the Doppler-resolution limit is overcome by implementation of an anti-resonant ring configuration. Cancellation of the first-order Doppler effect makes it possible to resolve 33 hyperfine two-photon transitions. The highly resolved (1 MHz point spacing), narrow transition-linewidth (5 MHz), accurate (systematic uncertainty of ~340 kHz), high-SNR (10^4) spectra are shown to be consistent with basic simulation-based predictions. As the spectral span is, in principle, only limited by the bandwidths of the excitation sources, the acquisition of Doppler-free two-photon spectra spanning 10s of THz appears to be in reach. To my knowledge, this is the first demonstration of Doppler-free Fourier-transform spectroscopy.

Lastly, the possibility of extending the technique's scope to applications in the field of biochemistry, such as two-photon microscopy, are explored. To that end, first high-speed, low-resolution (>>1 GHz) experiments are carried out identifying comb-stabilization requirements and measurement constraints due to the limited dynamic range of the presented highly multiplexed spectroscopic technique.