Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

In the first part of this thesis, we study classes of hybrid and chaotic inflation

models in four-dimensional N=1 supergravity. Therein, the eta-problem can be resolved relying on fundamental symmetries in the Kaehler potential.

Concretely, we investigate explicit realizations of superpotentials, in which the flatness of the inflaton potential is protected at tree level by a shift symmetry or a Heisenberg symmetry in the Kaehler potential. In the latter case, the associated modulus field can be stabilized during inflation by supergravity effects.

In the context of hybrid inflation, a novel class of models, to which we refer as

"tribrid inflation," turns out to be particularly compatible with such symmetry solutions to the eta-problem. Radiative corrections due to operators in the superpotential, which break the respective symmetry, generate the required small slope of the inflaton potential.

Additional effective operators in the Kaehler potential can reduce the predicted spectral index so that it agrees with latest observational data.

Within a model of chaotic inflation in supergravity with a quadratic potential,

we apply the Heisenberg symmetry to allow for viable inflation with super-Planckian field values, while the associated modulus is stabilized. We show that radiative corrections are negligible in this context.

In the second part, the tribrid inflation models are extended to realize gauge non-singlet inflation. This is applied to the matter sector of supersymmetric

Grand Unified Theories based on the Pati-Salam gauge group.

For the specific scenario in which the right-handed sneutrino is the inflaton,

we study the scalar potential in a D-flat valley. We show that despite potentially dangerous two-loop corrections, the required flatness of the potential can be maintained. The reason for this is the strong suppression of gauge interactions of the inflaton field due to its symmetry breaking vacuum

expectation value. In addition, the production of stable magnetic monopoles

at the end of the stage of inflation can be avoided.

Finally, we sketch how in tribrid inflation models the concepts discussed in the two parts can be combined to realize inflation via Heisenberg symmetry in local supersymmetric SO(10) grand unification.

In this work a new method for the detection of faint, both

point-like and extended, astronomical objects based on the

integrated treatment of source and background signals is described. This technique is applied to public data obtained by imaging methods of high-energy observational astronomy in the X-ray spectral regime.

These data are usually employed to address current astrophysical problems, e.g. in the fields of stellar and galaxy evolution and the large-scale structure of the universe. The typical problems encountered during the analysis of these data are: spatially varying cosmic background, large variety of source morphologies and intensities, data incompleteness, steep gradients in the data, and few photon counts per pixel.

These problems are addressed with the developed technique.

Previous methods extensively employed for the analysis of these data are, e.g., the sliding window and the wavelet based techniques. Both methods are known to suffer from: describing large variations in the background, detection of faint and extended sources and sources with complex

morphologies. Large systematic errors in object photometry and loss of faint sources may occur with these techniques.

The developed algorithm is based on Bayesian probability theory, which is a consistent probabilistic tool to solve an inverse problem for a given state of information.

The information is given by a parameterized model for the background and prior information about source intensity distributions quantified by probability distributions.

For the background estimation, the image data are not censored.

The background rate is described by a two-dimensional thin-plate spline function.

The background model is given by the product of the background rate and the exposure time which accounts for the variations of the integration time.

Therefore, the background as well as effects like vignetting, variations of detector quantum efficiency and strong gradients in the exposure time are being handled properly which results in improved detections with respect

to previous methods.

Source probabilities are provided for individual pixels as well as for correlations of neighboring pixels in a multi-resolution analysis.

Consequently, the technique is able of detecting

point-like and extended sources and their complex morphologies.

Furthermore, images of different spectral bands can be combined probabilistically to further increase the resolution in crowded regions. The developed method

characterizes all detected sources in terms of position, number of source counts, and shape including uncertainties.

The comparison with previous techniques shows that the developed method allows for an improved determination of background and source parameters.

The method is applied to data obtained by the ROSAT and Chandra X-ray observatories whereas particularly the detection of faint and extended sources is improved with respect to previous analyses. This lead to the discovery of new galaxy clusters and quasars in the X-ray band which

are confirmed in the optical regime using additional observational data. The new technique developed in this work is particularly suited to the identification of objects featuring extended emission like clusters of galaxies.

The tremendous impact of Cosmic Microwave Background (CMB) radiation experiments on our understanding of the history and evolution of the universe is based on a tight connection between the observed fluctuations and the physical processes taking place in the very early universe. According to the prevalent paradigm, the anisotropies were

generated during the era of inflation. The simplest inflationary models predict almost perfectly Gaussian primordial perturbations, but competitive theories can naturally be constructed, allowing for a wide range in primordial non-Gaussianity. For this reason, the test for non-Gaussianity becomes a fundamental means to probe the physical processes of inflation.

The aim of the project is to develop a Bayesian formalism to infer the level of non-Gaussianity of local type. Bayesian statistics attaches great importance to a consistent formulation of the problem and properly calculates the error bounds of the measurements on the basis

of the actual data. As a first step, we develop an exact algorithm to generate simulated temperature and polarization CMB maps containing arbitrary levels of local non-Gaussianity. We derive an optimization scheme that allows us to predict and actively control the simulation

accuracy. Implementing this strategy, the code outperforms existing algorithms in computational efficiency by an order of magnitude. Then, we develop the formalism to extend the Bayesian approach to the calculation of the amplitude of non-Gaussianity. We implement an exact Hamiltonian Monte Carlo sampling algorithm to generate samples from the target probability distribution. These samples allow to construct the full posterior distribution of the level of non-Gaussianity given the data. The applicability of the scheme is demonstrated by means of a simplified data model. Finally, we fully implement the necessary equations considering a realistic CMB experiment dealing with partial

sky coverage and anisotropic noise. A direct comparison between the traditional frequentist estimator and the exact Bayesian approach shows the advantage of the newly developed method. For a significant detection of non-Gaussianity, the former suffers from excess variance whereas the Bayesian scheme always provides optimal error bounds.

The controlled generation of entanglement forms the basis for currently emerging ‘quantum technologies’, such as quantum simulation, computation, and metrology. In the field of quantum metrology, multi-particle entangled states, such as spin-squeezed states, are investigated as a means to improve measurement precision beyond the ‘standard quantum limit’. This limit arises from the quantum noise inherent in measurements on a finite number of uncorrelated particles and limits today’s best atomic clocks. Atom chips combine exquisite coherent control of ultracold atoms with a compact and robust setup, suggesting their use for quantum metrology with portable atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far.

In this thesis, I present experiments where we generate for the first time multi-particle entanglement on an atom chip. We achieve this by controlling elastic collisional interactions with a state-dependent potential. We employ this novel technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they

are a useful resource for quantum metrology, as they could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit.

The state-dependent potential is created with the help of a coplanar microwave guide, which is integrated on our atom chip. In the vicinity of this waveguide a microwave nearfield is formed. When a Bose-Einstein condensate of 87Rb is brought into this near-field, the hyperfine energy levels of the atoms are shifted differentially due to the AC Zeeman

effect. The strong gradients in the field can be used to state-selectively shift the minimum of a static magnetic atom trap and thus coherently split an ensemble of atoms which have been prepared in a superposition of two internal states.

During this process, nonlinear atomic interactions lead to the formation of a spinsqueezed state. I tomographically analyze the produced state, reconstruct its Wigner function, and deduce that it is at least four-particle entangled.

I compare our results with a dynamical multi-mode simulation which takes not only the atomic motion and internal state dynamics but also particle losses into account and find good agreement. Moreover, I use this comparison to identify technical noise sources in our experiment, which currently limit the achieved amount of squeezing, and make suggestions on how to eliminate them in future experiments. Our method can in principle create a very large amount of squeezing and entanglement and is applicable to a wide variety of atomic systems, in particular to those for which no convenient Feshbach resonance exists. We envisage the implementation of this technique in portable atomic clocks and interferometers operating beyond the standard quantum limit. Furthermore, it is a valuable tool for experiments on many-body quantum physics and could enable quantum information processing on atom chips.

Mit der Fourierdomänen Modenkopplung (FDML) wurde vor kurzem ein neuer Operationsmodus für sehr schnell in der Wellenlänge abstimmbare Laser entdeckt, bei dem ein schmalbandiger Spektralfilter resonant zur Lichtumlaufzeit im Resonator abgestimmt wird. Diese FDML-Laser, deren genaue Funktionsweise noch unverstanden ist, gehören zu den schnellsten weit abstimmbaren Lichtquellen und eignen sich besonders für die optische Kohärenztomografie (OCT), die ein junges dreidimensionales Bildgebungsverfahren darstellt. In dieser Arbeit wurden zwei Ziele parallel verfolgt. Zum einen sollten durch Optimierungen und Erweiterungen des Lasers neue Anwendungsmöglichkeiten insbesondere in der OCT ermöglicht, gleichzeitig aber auch neue Erkenntnisse über die genaue Funktionsweise der Fourierdomänen Modenkopplung auf physikalischer Ebene gewonnen werden.

In dem eher anwendungsorientierten Teil dieser Arbeit wurde zunächst eine neue Methode entwickelt, mit der es in der OCT mit schnell abstimmbaren Lasern möglich ist, zweidimensionale Schnitte bei einer bestimmten Tiefe, sogenannte en face Schnitte, ohne aufwändige Computerberechnung zu erhalten. Während diese Schnitte bisher nur sehr rechenintensiv durch Nachbearbeitung und Extraktion aus einem vollständig aufgenommenen dreidimensionalen Datensatz gewonnen werden konnten, lassen diese sich nun um ein Vielfaches schneller aufnehmen und darstellen. Weiterhin wurde durch den Eigenbau eines auf Abstimmgeschwindigkeit optimierten Spektralfilters die Aufnahmegeschwindigkeit eines mit einem FDML-Laser betriebenen OCT-Systems um über eine Größenordnung erhöht, so dass dieses nun mit Abstand zu den schnellsten Systemen gehört. Obwohl bei diesen hohen Geschwindigkeiten das Signal-Rausch-Verhältnis durch Schrotrauschen bereits limitiert wird, konnten Aufnahmen sehr hoher Qualität erzeugt werden, was a priori nicht selbstverständlich war.

Im Grundlagenteil dieser Arbeit wurde das Verständnis der Operationsweise der Fourierdomänen Modenkopplung erweitert. Da FDML-Laser vollständig aus Glasfaserkomponenten aufgebaut sind und Längen von mehreren Kilometern aufweisen, wurde der Einfluss der Faserdispersion auf sowohl Linienbreite und Rauschverhalten untersucht. Mit einer speziellen dispersionskompensierten Resonatorgeometrie konnte dabei ein einfaches Modell des Einflusses der Dispersion auf die Kohärenzlänge validiert und eine deutliche Erhöhung dieser erreicht werden. Ein umfassenderes Modell der Operationsweise von FDML-Lasern ist wünschenswert, um experimentell schwer zugängliche Fragestellungen beantworten zu können. Auf dem Weg dahin müssen zunächst alle physikalischen Effekte im Resonator, welche zur Lasertätigkeit beitragen, aufgeklärt werden. Hierzu wurde die zeitabhängige Leistung eines FDML-Lasers durch verschiedene Terme in der nichtlinearen Schrödingergleichung modelliert, numerisch ausgewertet und mit experimentellen Daten verglichen. Dadurch konnten wichtige an der Laseroperation beteiligte Prozesse aufgeklärt und eine Basis für weitergehende Simulationen geschaffen werden.

In this thesis, we investigate the electronic coupling in quantum dot (QD) solids, optical anisotropies of nanowires (NWs) with diameters comparable to the wavelength of light, and the propagation of light in nanoribbon waveguides. In particular, we demonstrate a new mechanism to control the electronic coupling in QD solids thermomechanically, and how size controls the optical anisotropies in NWs.

We firstly demonstrate that the electronic coupling in QD solids can be controlled by a new thermomechanical mechanism. This mechanism is realized by controlling the expansion and shrinkage of the interstitial material in the QD solids, which in turn controls the distance and distance-dependent electronic coupling between semiconductor nanocrystals (SNCs). Photoluminescence (PL) and TEM investigation demonstrate the tuning of the band gap emission in individual polycrystalline NWs and densely packed SNCs via this mechanism. At low temperature, temperature-induced blueshift in densely packed SNC film and redshift in polycrystalline NWs were realized. This is qualitatively different from bulk CdTe and isolated CdTe SNCs. The electronic coupling between the nearest SNCs for sub-nm distances agrees well with semiempirical calculations.

Size dependence of optical anisotropies in NWs is demonstrated in this work. We found optical anisotropies in NWs with diameters comparable to the wavelength of light in the NW, i.e., beyond the electrostatic limit, are much lower than those of NWs in electrostatic limit. Finite-difference time domain calculations, with realistic parameters for the CdTe NWs, for excitation and PL anisotropy were carried out. It was found that the optical anisotropies of NWs display a strong size dependence when the NW is beyond the electrostatic limit. Changing the diameter allows tuning the polarization anisotropy from its maximum, predicted by the electrostatic limit, to zero. The optical anisotropies of a NW are determined by the diameter-wavelength ratio, the material dispersion, as well as the local refractive index of the surrounding. In addition, the optical anisotropies can be transferred into macroscopically aligned NW arrays, and the anisotropies of the NW arrays are determined by the optical anisotropies of isolated NWs, the disorder of the NWs in the film, the local environment and multiple scattering in the thick film.

Furthermore, we show that self-assembled nanoribbons can serve as single-mode waveguides for the propagation of PL light. Calculations show that the minimum width needed for single-mode operation is approximately 150 nm, which agrees well with SEM measurements. The loss in the nanoribbon waveguides was quantitatively determined. Re-absorption was demonstrated in the nanoribbon waveguides to be a major contribution in the loss mechanism. Losses in the nanoribbon waveguide are on the same order of magnitude as for plasmon waveguides.

This thesis presents the experimental investigation of the phase state of two-dimensional complex plasmas by means of their dynamical and kinetic properties. The two-dimensional complex plasma consists of negatively charged micron-sized plastic spheres, levitated in the sheath of a radio-frequency noble gas discharge in a single horizontal layer.

In two different experiments the thermodynamical state of a crystalline complex plasma (``plasma crystal''), and the process of recrystallization of a molten complex plasma is studied.

The experiments were performed on strictly two-dimensional particle systems, and all data analysis builds on the examination of particle coordinates and trajectories.

One important aspect of the data analysis is the estimation of uncertainties. A procedure has been developed to obtain reliable estimations of the measurement uncertainties introduced by the recording method and the particle tracking algorithm. The implications of the uncertainties on the scientific interpretation of the experimental results will be considered throughout the thesis.

The first experiment aims to estimate the coupling parameter of a two-dimensional, crystalline complex plasma. The coupling parameter of an ensemble of particles is the ratio of their mean potential energy to their mean kinetic energy. It describes the thermodynamical state of the system, and is therefore an important quantity to characterize such a system. To calculate it, not only the particle temperature has to be estimated, but also an expression for the interparticle potential has to be known. For charged particles, this depends on the particle charge, which can often only be obtained with additional experimental effort, and its measurement is usually subject to large uncertainties.

A simple, new method to calculate the coupling parameter from solely the spatial particle coordinates will be presented in this thesis, and verified to be consistent with the conventional estimation by charge and temperature measurements.

The second experiment involves the creation of a two-dimensional plasma crystal and its shock melting by the application of a short electric pulse. The following phase of rapid recrystallization gives insight into the nature of a non-equilibrium transition of a two-dimensional system of interacting particles from a disordered to an ordered state. The measurements have been performed at a high temporal resolution to ensure the possibility to obtain kinetic energies from particle velocity distributions.

The process is investigated thoroughly by means of the time-dependent development of the kinetic particle energy and structural properties of the system, such as translational and orientational long range order, defects fraction and spatial defect arrangements.

Finally the connection of structural order parameters to the kinetic energy -- in comparison with conventional models and theories -- gives novel insights into the underlying physical processes determining the two-dimensional phase transition.

The climate of the stratosphere is known to be subject to long-term changes induced

by anthropogenic emissions of long-lived greenhouse gases (GHGs) as well as by emissions

of ozone depleting substances (primarily chlorofluorocarbons, CFCs). Enhanced

concentrations of CFCs have led to strong ozone depletion over the last decades. Thanks

to the Montreal Protocol and its amendments and adjustments, the stratospheric halogen

loading is expected to retreat again in the future. Emissions of GHGs, on the

other hand, are not yet controlled sufficiently, and concentrations of GHGs are projected

to increase further in the future. The effects of enhanced GHG concentrations

on the stratosphere include decreasing temperatures, as well as changes in the dynamical

balances and interactions with the troposphere, and thus changes in the large-scale

circulation. In particular, the stratospheric meridional circulation is projected to be

subject to changes. These GHG-induced changes will also affect stratospheric ozone

chemistry and transport of ozone. Therefore, the expected recovery of ozone due to decreasing

CFC concentrations will coincide with alterations of the ozone layer by climate

change.

This study aims to diagnose and explain long-term changes in the stratospheric

meridional circulation using the chemistry-climate model E39CA. The dynamical causes

for these changes are identified, and the impact of changes in the meridional circulation

on the future development of ozone is quantified.

In a changing climate, the meridional circulation is found to strengthen in the tropical

lower stratosphere. In particular, tropical upwelling in the lowermost stratosphere

intensifies at a rate of about 3% per decade over the analysed period of 1960 to 2049.

This enhanced upwelling is balanced by downwelling in the subtropics at latitudes

around 20-40°N/S. The increase in tropical upwelling can be explained by stronger local

forcing by large scale waves. It is shown that enhanced tropical upwelling is driven

by processes induced by increases in tropical sea surface temperatures (SSTs). Higher

tropical SSTs cause both a) a strengthening of the subtropical jets and b) modifications

of deep convection, leading to changes in the strength and location of latent heat release.

While the former (a) can modify wave propagation and dissipation, the latter (b)

affects tropical wave generation. Evidence is presented that the dominating mechanism

leading to enhanced vertical wave propagation into the lower stratosphere is an upward

shift of the easterly shear zone due to the strengthening and upward and equatorward

shifts of the subtropical jets.

In addition to the increase in tropical upwelling caused by climate change, the

changes in CFC concentrations also affect the dynamical forcing of the meridional circulation.

The CFC-induced depletion of ozone in the past has led to changes in the

background wind field in the southern hemisphere in summer, which cause enhanced

wave propagation into the middle stratosphere and thus a strengthening of the meridional

circulation. This effect is reversed in the future, when CFC concentrations decline.

The future development of ozone is found to be dominated by changes in local

chemistry in most regions of the stratosphere. Both decreasing CFC concentrations and

stratospheric cooling due to enhanced GHG concentrations lead to less efficient ozone

destruction, and thus increasing ozone concentrations. However, changes in transport

of ozone due to the strengthening of the meridional circulation play an important role in

the tropical lower stratosphere, where ozone concentrations decrease due to more export

of ozone. Furthermore, it is found that the chemically induced positive ozone trend

in southern high latitudes in the future is counteracted by decreased ozone transport

from middle to high latitudes. This decrease in transport is due to the weakening of

the meridional circulation in the southern hemisphere in summer, which, in