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

When the optical pulses emitted by a laser become so short in time that they encompass only a few cycles of the carrier wave, the phase between carrier and envelope becomes a crucial parameter. The ability to control this carrier-envelope phase (CEP) is elemental to experiments probing the fastest processes in the microcosm, occurring on the time-scale of attoseconds. More than a decade into the attosecond era, the limitations of the established CEP stabilisation technique have begun to curtail experimental progress. First, increasingly complex experiments require many hours of uninterrupted operation at the same waveform. Second, the pulses used in experiments are approaching the single-cycle boundary, calling for ever-decreasing CEP noise. With the conventional stabilisation technique, already these two requirements cannot be fulfilled simultaneously. Ultimately, the low efficiency of the underlying nonlinear processes can only be compensated by driver lasers at a higher repetition rate than available at present. In order to advance attosecond pulse generation, novel approaches to CEP control thus face a threefold challenge that outlines this thesis: To simultaneously provide low CEP noise and long-term operation to present-day few-cycle lasers and amplifiers, and to investigate CEP control capability in high average power sources that are currently under development.

This thesis describes the adaptation of cavity-external CEP stabilisation for use with few-cycle pulses. The intrinsic limitations of the conventional feed-back technique are lifted. A laser oscillator is demonstrated to maintain record-low CEP noise for tens of hours of operation free from phase discontinuities. In addition, a modification of the technique is presented that further enhances the applicability to amplified systems.

Two routes are investigated to achieve CEP control in system architectures that represent potential megahertz repetition rate driver sources. In combination with temporal pulse compression, a thin-disk laser is shown to yield few-cycle pulses. Experiments are presented that provide the groundwork towards the first CEP-stabilised thin-disk oscillator. The second approach targets the seed oscillator of a fibre chirped-pulse amplifier. The CEP noise properties of different amplification regimes are examined. Intensity enhancement of the output pulses in a passive resonator is shown to benefit greatly even from a coarse lock of the CEP slip rate.

For few-cycle pulse energy to reach the millijoule level and above, amplification and temporal compression will remain indispensable in the foreseeable future. Maintaining CEP stability across such stages is crucial, irrespective of the technology employed. Cavity-external CEP control is demonstrated to enable more than 24 hours of constant-CEP operation in chirped-pulse amplifiers. Furthermore, a novel actuator is introduced that, in conjunction with a fast means of measuring the CEP, is able to provide phase correction of the amplified waveform up to several kilohertz bandwidth. The result is a train of millijoule-level pulses with residual CEP noise comparable to that of state-of-the-art nanojoule oscillators. Eventually, an experiment is presented to examine the influence of different types of hollow-core fibre-based temporal compression on the CEP. The findings shed new light on the origin of adverse effects introduced by this technique, and point out ways towards effective compensation.

This thesis contributes to the understanding of impurity models. It is divided into two main parts, with a general introduction given in Part I and the research related to it presented in Part II, with the second part being subdivided into two main projects.

In the first project, the influence of two many-body effects, the Kondo effect and the Fermi edge singularity, on the absorption and emission spectra of self-assembled quantum dots (QDs) is examined. Whereas the Kondo effect so far was always examined with transport experiments, we show that it has been observed with optical methods for the first time, by comparing experimental data for the absorption line shapes of QDs to calculations with the numerical renormalization group. We continue by examining a QD with strong optical coupling of the energy levels. The resulting interplay of Rabi-oscillations and Kondo effect leads to a new many-body state, a secondary, outer Kondo effect, with Kondo-like correlations between the spin-Kondo and the trion state. The last work regarding optics at QDs addresses the Fermi edge singularity. We show that for QDs this phenomenon can be described numerically on a quantitative level.

The second project concerns transport properties of impurity models. First, we present a comprehensive study of the Kondo effect for an InAs-nanowire QD, a system for which the Kondo effect was observed only a few years ago. The second study regarding transport concerns the Kondo effect in bulk metals with magnetic impurities. Although nowadays the Kondo effect is often studied with QDs, it was discovered for iron impurities in noble metals like gold and silver. However, it was unknown for a long time which exact realization of Kondo model describes these systems. We identify the model by comparing numerical calculations for the magnetoresistivity and the dephasing rate for different models to experimental results. The third work about transport concerns the phenomenon that for a fixed type of Kondo model quantities like the magnetoresistivity or the conductivity, respectively, can be scaled onto a universal curve for different parameters, when energies are rescaled with the the Kondo temperature $T_K$, since it is the only relevant low energy scale of the problem. For finite bandwidth, however, different definitions of $T_K$ (which coincide in the limit of infinite bandwidth) lead to different $T_K$-values. We show that with a very common definition of $T_K$, finite bandwidth, which is always present at numerical calculations, can deteriorate the universality of rescaled curves, and we offer an alternative definition of $T_K$ which ensures proper scaling. In the last study presented in this thesis we calculate the Fermi-liquid coefficients for fully screened multi-channel Kondo models. For temperatures below $T_K$, these models show Fermi-liquid behavior, and the impurity density of states and certain quantities which depend on it, like resistivity, show quadratic dependencies on parameters like temperature or magnetic field, described by the Fermi-liquid coefficients. We calculate these coefficients both analytically and numerically.

Aerosols are an important part of our atmosphere. As they are very inhomogenously distributed both in time and space the estimation of their influence on the climate is very complex. So it is important to improve the knowledge about the aerosol distribution. In this study the distribution of aerosols above the region around Munich, Germany in the time period 2007 to 2010 is studied with measurements from remote sensing instruments. Thereby the main focus is set on the lidar data from the ground based lidar system MULIS of the Meteorological Institute Munich and the space lidar CALIOP onboard the satellite CALIPSO which both deliver aerosol information height resolved. As an addition and for a better comparison with previous studies, aerosol information from the AERONET Sunphotometer in Munich and the satellite spectroradiometer MODIS are used.

With help of these four datasets several aerosol parameters could be studied: on average the aerosol optical depth (AOD) above the Munich region is at 1064 nm about 0.05 to 0.06, at 532 nm about 0.12 to 0.17, and at 355 nm about 0.22 to 0.28. The height of the boundary layer top decreases from 1.68 km in spring to 0.73 km in winter, while the thickness of the elevated layers is more stable (spring: 1.43 km, winter: 1.02 km). The occurrence of ELs is highest in spring (in 75 % of all measurements), and lowest in winter (36 %). Measurements of the particle linear depolarization ratio and the Ångström exponent show that the aerosols in elevated layers clearly differ from the aerosols in the PBL. Especially in spring the average EL depolarization is large (25 %) indicating transportation of strongly depolarizing aerosols like Saharan dust in the free troposphere. The dominant aerosol type in the Munich region is smoke (also called biomass burning), polluted continental can occur in high concentrations especially during summer time. Dust occurs only in rare occasions, mainly mixed with other aerosol types (polluted dust).

One important finding from the comparison of the four datasets is that CALIPSO strongly underestimates the AOD. To study the significances of different causes for this, the CALIPSO extinction coefficient profiles are compared with coincidentally performed measurements of MULIS. The underestimation of the AOD above Munich by CALIPSO is mainly found to be due to the failure of the layer detection: its effect on the AOD underestimation is about 36 %. Also the wrong assumption of the lidar ratio contributes to the underestimation, though on a smaller account of about 5 %. The influence of clouds in the surroundings on the AOD is not quantifiable, but the analysis shows that clouds lead to an overestimation of the AOD. To compensate these reasons and to get detailed profiles from CALIPSO, it could be shown that -for case studies- it is very efficient to calculate the extinction coefficients from CALIPSO raw data (L1B) manually.

Convective phenomena in the atmosphere, such as convective storms, are characterized by very fast, intermittent and seemingly stochastic processes. They are thus difficult to predict with Numerical Weather Prediction (NWP) models, and difficult to estimate with data assimilation methods that combine prediction and observations. In this thesis, nonlinear data assimilation methods are tested on two idealized convective scale cloud models, developed in [58] and [59]. The aim of this work was to apply the particle filter, a method specifically designed for nonlinear models, to the two toy models that resemble some properties of convection. Potential problems and characteristic features of particle filter methodology were analyzed, having in mind possible tests on far more elaborate NWP models.

The first model, the stochastic cloud model, is a one-dimensional birth-death model initialized by a Poisson distribution, where clouds randomly appear or die independently from each other on a set of grid-points. This purely stochastic model is physically unreal- istic, but since it is highly nonlinear and non-Gaussian, it contains minimal requirements for representing main features of convection. The derivation of the transition probability density function (PDF) of the stochastic cloud model made it possible to understand better the weighting mechanism involved in the particle filter. This mechanism, which associates a weight to particles (state vectors) according to their likelihood with respect to observa- tions and to their evolution in time, is followed by resampling, where particles with high probability are replicated, and others eliminated. The ratio between magnitudes of the ob- servation probability distribution and the transition probability is shown to determine the selection process of particles at each time step, where data and prediction are combined. Further, a strong sensitivity of the filter to the observation density and to the speed of the cloud variability (given by the cloud life time) is demonstrated. Thus, the particle filter can outperform some simpler methods for certain observation densities, whereas it does not bring any improvement when using others. Similarly, it leads to good results for stationary cloud fields while having difficulties to follow fast varying cloud fields, because any change in the model state variable is potentially penalized. The main difficulty for the filter is the fact that this model is discrete, while the filter was designed for data assimilation of continuous fields.

However, by representing an extreme testbed for the particle filter, the stochastic cloud model shows the importance of the observation and model error densities for the selection of particles, and it stresses the influence of the chosen model parameters on the filter’s performance.

The second model considered was the modified shallow water model. It is based on the shallow water equations, to which is added a small stochastic noise in order to trigger convection, and an equation for the evolution of rain. It contains spatial correlations and is represented by three dynamical variables - wind speed, water height and rain concentration - which are linked together. A reduction of the observation coverage and of the number of updated variables leads to a relative error reduction of the particle filter compared to an ensemble of particles that are only continuously pulled (nudged) to observations, for a certain range of nudging parameters. But not surprisingly, reducing data coverage in- creases the absolute error of the filter. We found that the standard deviation of the error density exponents is a quantity that is responsible for the relative success of the filter with respect to nudging-only. In the case where only one variable is assimilated, we formulated a criterion that determines whether the particle filter outperforms the nudged ensemble. A theoretical estimate is derived for this criterion. The theoretical value

Wir untersuchen stark gekoppelte Phänomene unter Verwendung der Dualität

zwischen Eich- und Gravitationstheorien. Dabei liegt ein besonderer Fokus

einerseits auf Vortex Lösungen, die von einem magnetischem Feld verursacht

werden, und andererseits auf zeitabhängigen Problemen in holographischen

Modellen. Das wichtigste Ergebnis ist die Entdeckung eines unerwarteten Effektes

in einem einfachen holografischen Modell: ein starkes nicht abelsches

magnetisches Feld verursacht die Entstehung eines Grundzustandes in der Form

eines dreieckigen Gitters von Vortices.

Die Dualität zwischen Eich- und Gravitationstheorien ist ein mächtiges Werkzeug

welches bereits verwendet wurde um stark gekoppelte Systeme vom Quark-Gluonen

Plasma in Teilchenbeschleunigern bis hin zu Festkörpertheorien zu beschreiben.

Die wichtigste Idee ist dabei die der Dualität: Eine stark gekoppelte

Quantenfeldtheorie kann untersucht werden, indem man die Eigenschaften eines aus

den Einsteinschen Feldgleichungen folgenden Gravitations-Hintergrundes bestimmt.

Eine der Gravitationstheorien, die in dieser Arbeit behandelt werden, ist eine

Einstein--Yang--Mills Theorie in einem AdS--Schwarzschild Hintergrund mit

SU(2)-Eichsymmetrie. Der Ansatz für das Eichfeld ist so gewählt, dass die

zugehörige Quantenfeldtheorie einem externen Magnetfeld ausgesetzt ist. Oberhalb

eines kritischen Magnetfeldes wird die Konfiguration instabil und zeigt einen

Phasenübergang zu einem Supraleiter.

Die Instabilität wird mit zwei Ansätzen untersucht. Zum einen werden

Fluktuationen des Hintergrunds betrachtet und die Quasinormalmoden analysiert.

Zum anderen zeigt die numerische Analyse der Bewegungsgleichungen, dass das

effektive Schrödinger-Potential mit stärker werdendem Magnetfeld sich so lange

verändert, bis ein gebundener Zustand möglich wird. Der sich ergebende

supraleitende Grundzustand ist durch ein dreieckiges Vortexgitter gegeben, wie

eine störungstheoretische Entwicklung über einem kleinen Parameter proportional

zur Größe des Kondensats zeigt. Zur Bestimmung des energetisch bevorzugten

Zustands wird mithilfe der holographischen Übersetzungsvorschrift die

Gesamtenergie verschiedener Lösungen berechnet. Hierfür wird die Lösung der

Bewegungsgleichungen zur dritten Ordnung in oben genanntem Parameter berechnet.

Zusätzlich wird gezeigt, dass dieses Ergebnis auch für den Fall einer AdS--hard

wall Geometrie gilt, also einer Feldtheorie mit Confinement.

Als nächstes erweitern wir das einfache Gravitationsmodell um ein chemisches

Potential und wiederholen die Untersuchung. Sind das chemische Potential, das

magnetische Feld oder beide groß genug, so befindet sich das System in einer

supraleitenden Phase. Wir berechnen das Phasendiagramm des Systems numerisch.

Der Grundzustand der supraleitenden Phase nahe dem Phasenübergang ist ein

dreieckiges Vortexgitter, wobei der Gitterabstand nur von der Stärke des

magnetischen Feldes abhängt. Die Relevanz dieser Ergebnisse wird im Zusammenhang

mit inhomogenen Grundzuständen in holographischen Supraleitern diskutiert, einem

Themengebiet welches in letzter Zeit viel Interesse auf sich gezogen hat. Die

erhaltenen Resultate sind nicht nur aufgrund der vorher unbekannten inhomogenen

Lösung der Gravitationstheorie mit Schwarzem Loch neuartig. Es ist auch

interessant, dass ein großes magnetisches Feld die Vortexstruktur im

Grundzustand induziert anstatt sie zu unterdrücken.

Des Weiteren untersuchen wir zeitabhängige Phänomene in einer holographischen

Erweiterung des Kondomodells. Letzteres beschreibt ein einfaches Modell in der

Festkörperphysik, in welchem eine magnetische Verunreinigung stark an ein

Elektronenreservoir koppelt. Die holographische Beschreibung erfordert Techniken

der numerischen Relativitätstheorie und erlaubt uns die Entwicklung des Systems

nach einem plötzlichen Sprung in der Kopplungskonstante zu simulieren.

Diese Doktorarbeit basiert

Deep radio observations provide a dust unbiased view of both black hole (BH) and star

formation (SF) activity and therefore represent a powerful tool to investigate their evolution

and their possible mutual influence across cosmic time. Radio astronomy is therefore

becoming increasingly important for galaxy evolution studies thanks also to the many new

radio facilities under construction or being planned. To maximise the potentiality of these

new instruments it is crucial to make predictions on what they will observe and to see how

best to complement the radio data with multi-wavelength information.

These are the motivations of my Thesis in which I studied a sample of 900 sources

detected in one of the deepest radio surveys ever made. The observations have been

performed at 1.4 GHz with the Very Large Array on the Extended Chandra Deep Field

South. I developed a multi-wavelength method to identify the optical-infrared counterparts

of the radio sources and to classify them as radio-loud active galactic nuclei (RL AGNs),

radio-quiet (RQ) AGNs, and star forming galaxies (SFGs). I was able for the first time to

quantify the relative contribution of these different classes of sources down to a radio flux

density limit of ∼30 μJy.

I characterized the host galaxy properties (stellar masses, optical colors, and morphology)

of the radio sources; RQ AGN hosts and SFGs have similar properties with disk

morphology and blue colors while radio-loud AGN hosts are more massive, redder and

mostly ellipticals. This suggests that the RQ and RL activity occurs at two different evolutionary

stages of the BH-host galaxy co-evolution. The RQ phase occurs at earlier times

when the galaxy is still gas rich and actively forming stars while the radio activity of the

BH appears when the galaxy has already formed the bulk of its stellar population, the gas

supply is lower, and the SF is considerably reduced.

I quantified the star formation rate (SFR) of the radio sources using two independent

tracers, the radio and far-infrared luminosities. I found evidence that the main contribution

to the radio emission of RQ AGNs is the SF activity in their host galaxy. This result

demonstrates the remarkable possibility of using the radio band to estimate the SFR even in

the hosts of bright RQ AGNs where the optical-to-mid-infrared emission can be dominated

by the AGN. I have shown that deep radio surveys can be used to study the cosmic star

formation history; I estimated the contribution of the so-called ”starburst” mode to the

total SFR density and quantified the AGN occurrence in galaxies with different levels of

SF.

Few-cycle laser pulses are an important tool for investigating laser-matter interactions. Apart

from the mere resolution used in time-resolved processes, owing to this approach table-top

sources nowadays can reach the limits of the perturbative regime and therewith enable extreme

nonlinear optics. In the visible domain, femtosecond technology over the last decades has quickly developed, in recent years leading to the routine generation of carrier-envelope phase (CEP) stable few-cycle laser pulses at high energies, using ubiquitous Ti:Sapphire amplifiers.

Near to mid-infrared few-cycle pulses in contrast can be employed for investigating interactions

in the tunneling regime. The ponderomotive potential of the infrared light field allows quivered charged particles to acquire large energies, leading to applications like the generation of isolated attosecond pulses in the water window. In this wavelength regime however, the required sources are yet to be demonstrated or at least matured. The best candidate for few-cycle pulses in this domain is optical parametric amplification.

This work describes the development of an optical parametric chirped pulse amplifier (OPCPA),

used to create CEP-stable few-cycle pulses in the near infrared (NIR). It covers all essential parts of the system. First the signal pulses are generated from ultrashort lasers using spectral broadening techniques in chapter 2. After compression of these white light continua, intra-pulse broadband difference frequency generation yields CEP stable infrared

pulses spanning over more than one octave.

A thin-disk-based pump laser provides ample pump energy (20 mJ) at pulse durations around

1.5 ps. Its characterization and optimization for OPCPA is performed in chapter 3. The high

peak energy of this pump laser leads to the buildup of optical nonlinearities and consequently

shows distinct influence on the OPCPA system performance.

The synchronization of the OPCPA pump and seed laser system is the topic of chapter 4. This

chapter is not limited to NIR systems, but demonstrates enhanced (actively stabilized) synchronization of the jitter between pump and seed pulses to σ = 24 fs, which later results in improved output stability.

The NIR OPCPA centered at 2.1 μm is described in chapter 5. This combines the efforts of

the previous chapters and describes the generation and characterization of 100 μJ sub-two-cycle CEP-stable pulses, the shortest published to date at this energy level.

As a first prototype (cutting edge) experiment, CEP dependent sub-fs currents in a dielectric are

generated in chapter 6 using the developed light source. The results compared well to visible

few-cycle laser sources and demonstrate the usability of the OPCPA system (beyond the charac-

terizations of chapter 5) for investigating sub-cycle carrier dynamics in dielectrics.

For the same purpose, to generate the currently most broadband NIR continua at kHz repetition

rates and mJ-level pulse energies, the OPCPA system is further boosted and efficiently broadened to three optical octaves using a hollow core fiber setup (described in chapter 7). The spectral phase is characterized and demonstrates self-compression in the NIR around 1.3 μm. The process provides CEP-stable sub-2-cycle pulses in this regime directly, the shortest and most powerful reported to date.

Furthermore, the spectral broadening in the infrared shows enhanced low-order harmonic gen-

eration and cross-phase-modulation as the dominant mechanism. Experimentally the limited

influence on the driver bandwidth is investigated. It is found that the processes allow using more efficient many-cycle infrared sources to generate several-octave spanning, compressible continua in the future. Even partial compression of these would then provide NIR transients for high-field experiments.