Synthesis and surface modification of semiconductor nanocrystals

The last decade has witnessed an exponential growth of activities in the field of nanoscience and nanotechnology worldwide, driven both by the excitement of understanding new science and by the potential hope for applications and economic impacts. The largest activity in this field up to date has been in the synthesis and characterization of new materials consisting of particles with dimensions in the order of a few nanometers, so-called nanocrystalline materials. [1-8] Semiconductor nanomaterials such as III/V or II/VI compound semiconductors exhibit strong quantum confinement behavior in the size range from 1 to 10 nm. Therefore, preparation of high quality semiconductor nanocrystals has been a challenge for synthetic chemists, leading to the recent rapid progress in delivering a wide variety of semiconducting nanomaterials. Semiconductor nanocrystals, also called quantum dots, possess physical properties distinctly different from those of the bulk material. Typically, in the size range from 1 to 10 nm, when the particle size is changed, the band gap between the valence and the conduction band will change, too. In a simple approximation a particle in a box model has been used to describe the phenomenon[9]: at nanoscale dimensions the degenerate energy states of a semiconductor separate into discrete states and the system behaves like one big molecule. The size-dependent transformation of the energy levels of the particles is called “quantum size-effect”. Quantum confinement of both the electron and hole in all three dimensions leads to an increase in the effective bandgap of the material with decreasing crystallite size. Consequently, both the optical absorption and emission of semiconductor nanaocrystals shift to the blue (higher energies) as the size of the particles gets smaller. This color tuning is well documented for CdSe nanocrystals whose absorption and emission covers almost the whole visible spectral range. As particle sizes become smaller the ratio of surface atoms to those in the interior increases, which has a strong impact on particle properties, too. Prominent examples are the low melting point [8] and size/shape dependent pressure resistance [10] of semiconductor nanocrystals. Given the size dependence of particle properties, chemists and material scientists now have the unique opportunity to change the electronic and chemical properties of a material by simply controlling the particle size. In particular, CdSe nanocrystals have been widely investigated. Mainly due to their size-dependent optoelectronic properties [11, 12] and flexible chemical processibility [13], they have played a distinguished role for a number of seminal studies [11, 12, 14, 15]. Potential technical applications have been discussed, too. [8, 16-27] Improvement of the optoelectronic properties of semiconductor nanocrystals is still a prominent research topic. One of the most important approaches is fabricating composite type-I core-shell structures which exhibit improved properties, making them attractive from both a fundamental and a practical point of view. Overcoating of nanocrystallites with higher band gap inorganic materials has been shown to increase the photoluminescence quantum yields by eliminating surface nonradiative recombination sites. [28] Particles passivated with inorganic shells are more robust than nanocrystals covered by organic ligands only and have greater tolerance to processing conditions necessary for incorporation into solid state structures or for other applications. Some examples of core-shell nanocrystals reported earlier include CdS on CdSe [29], CdSe on CdS, [30], ZnS on CdS, [31] ZnS on CdSe[28, 32], ZnSe on CdSe [33] and CdS/HgS/CdS [34]. The characterization and preparation of a new core-shell structure, CdSe nanocrystals overcoated by different shells (CdS, ZnS), is presented in chapter 4. Type-I core-shell structures as mentioned above greatly improve the photoluminescence quantum yield and chemical and photochemical stability of nanocrystals. The emission wavelengths of type-I core/shell nanocrystals typically only shows a small red-shift when compared to the plain core nanocrystals. [30, 31, 35] In contrast to type-I core-shell nanocrystals, only few studies have been conducted on colloidal type-II core/shell structures [36-38] which are characterized by a staggered alignment of conduction and valence bands giving rise to a broad tunability of absorption and emission wavelengths, as was shown for CdTe/CdSe core-shell nanocrystals. [36] The emission of type-II core/shell nanocrystals mainly originates from the radiative recombination of electron-hole pairs across the core-shell interface leading to a long photoluminescence lifetime. Type-II core/shell nanocrystals are promising with respect to photoconduction or photovoltaic applications as has been discussed in the literature.[39] Novel type-II core-shell structures with ZnTe cores are reported in chapter 5. The recent progress in the shape control of semiconductor nanocrystals opens new fields of applications. For instance, rod shaped CdSe nanocrystals can enhance the photo-electro conversion efficiency of photovoltaic cells, [40, 41] and also allow for polarized emission in light emitting diodes. [42, 43] Shape control of anisotropic nanocrystals can be achieved by the use of surfactants, [44, 45] regular or inverse micelles as regulating agents, [46, 47] electrochemical processes, [48] template-assisted [49, 50] and solution-liquid-solution (SLS) growth mechnism. [51-53] Recently, formation of various CdSe nanocrystal shapes has been reported by the groups of Alivisatos [54] and Peng, [55] respectively. Furthermore, it has been reported by the group of Prasad [56] that noble metal nanoparticles can induce anisotropic growth of CdSe nanocrystals at lower temperatures than typically used in other methods for preparing anisotropic CdSe structures. Although several approaches for anisotropic crystal growth have been reported by now, developing new synthetic methods for the shape control of colloidal semiconductor nanocrystals remains an important goal. Accordingly, we have attempted to utilize a crystal phase control approach for the controllable synthesis of colloidal ZnE/CdSe (E = S, Se, Te) heterostructures in a variety of morphologies. The complex heterostructures obtained are presented in chapter 6. The unique optical properties of nanocrystals make them appealing as in vivo and in vitro fluorophores in a variety of biological and chemical investigations, in which traditional fluorescence labels based on organic molecules fall short of providing long-term stability and simultaneous detection of multiple emission colours [References]. The ability to prepare water soluble nanocrystals with high stability and quantum yield has led to promising applications in cellular labeling, [57, 58] deep-tissue imaging, [59, 60] and assay labeling [61, 62]. Furthermore, appropriately solubilized nanocrystals have been used as donors in fluorescence resonance energy transfer (FRET) couples. [63-65] Despite recent progress, much work still needs to be done to achieve reproducible and robust surface functionalization and develop flexible (bio-) conjugation techniques. Based on multi-shell CdSe nanocrystals, several new solubilization and ligand exchange protocols have been developed which are presented in chapter 7. The organization of this thesis is as follows: A short overview describing synthesis and properties of CdSe nanocrystals is given in chapter 2. Chapter 3 is the experimental part providing some background information about the optical and analytical methods used in this thesis. The following chapters report the results of this work: synthesis and characterization of type-I multi-shell and type-II core/shell nanocrystals are described in chapter 4 and chapter 5, respectively. In chapter 6, a high–yield synthesis of various CdSe architectures by crystal phase control is reported. Experiments about surface modification of nanocrystals are described in chapter 7. At last, a short summary of the results is given in chapter 8.

Strukturelle, chemische und isotopische Analysen nanoskaliger präsolarer und früher solarer Kondensate

Neben astronomischen Beobachtungen mittels boden- und satellitengestützer Instrumente existiert ein weiterer experimenteller Zugang zu astrophysikalischen Fragestellungen in Form einer Auswahl extraterrestrischen Materials, das für Laboruntersuchungen zur Verfügung steht. Hierzu zählen interplanetare Staubpartikel, Proben, die von Raumfahrzeugen zur Erde zurückgebracht wurden und primitive Meteorite. Von besonderem Interesse sind sog. primitive kohlige Chondrite, eine Klasse von Meteoriten, die seit ihrer Entstehung im frühen Sonnensystem kaum verändert wurden. Sie enthalten neben frühem solarem Material präsolare Minerale, die in Sternwinden von Supernovae und roten Riesensternen kondensiert sind und die Bildung unseres Sonnensystems weitgehend unverändert überstanden haben. Strukturelle, chemische und isotopische Analysen dieser Proben besitzen demnach eine große Relevanz für eine Vielzahl astrophysikalischer Forschungsgebiete. Im Rahmen der vorliegenden Arbeit wurden Laboranalysen mittels modernster physikalischer Methoden an Bestandteilen primitiver Meteorite durchgeführt. Aufgrund der Vielfalt der zu untersuchenden Eigenschaften und der geringen Größen der analysierten Partikel zwischen wenigen Nanometern und einigen Mikrometern mussten hierbei hohe Anforderungen an Nachweiseffizienz und Ortsauflösung gestellt werden. Durch die Kombination verschiedener Methoden wurde ein neuer methodologischer Ansatz zur Analyse präsolarer Minerale (beispielsweise SiC) entwickelt. Aufgrund geringer Mengen verfügbaren Materials basiert dieses Konzept auf der parallelen nichtdestruktiven Vorcharakterisierung einer Vielzahl präsolarer Partikel im Hinblick auf ihren Gehalt diagnostischer Spurenelemente. Eine anschließende massenspektrometrische Untersuchung identifizierter Partikel mit hohen Konzentrationen interessanter Elemente ist in der Lage, Informationen zu nukleosynthetischen Bedingungen in ihren stellaren Quellen zu liefern. Weiterhin wurden Analysen meteoritischer Nanodiamanten durchgeführt, deren geringe Größen von wenigen Nanometern zu stark modifizierten Festkörpereigenschaften führen. Im Rahmen dieser Arbeit wurde eine quantitative Beschreibung von Quanteneinschluss-Effekten entwickelt, wie sie in diesen größenverteilten Halbleiter-Nanopartikeln auftreten. Die abgeleiteten Ergebnisse besitzen Relevanz für nanotechnologische Forschungen. Den Kern der vorliegenden Arbeit bilden Untersuchungen an frühen solaren Partikeln, sog. refraktären Metall Nuggets (RMN). Mit Hilfe struktureller, chemischer und isotopischer Analysen, sowie dem Vergleich der Ergebnisse mit thermodynamischen Rechnungen, konnte zum ersten Mal ein direkter Nachweis von Kondensationsprozessen im frühen solaren Nebel erbracht werden. Die analysierten RMN gehören zu den ersten Festkörperkondensaten, die im frühen Sonnensystem gebildet wurden und scheinen seit ihrer Entstehung nicht durch sekundäre Prozesse verändert worden zu sein. Weiterhin konnte erstmals die Abkühlrate des Gases des lokalen solaren Nebels, in dem die ersten Kondensationsprozesse stattfanden, zu 0.5 K/Jahr bestimmt werden, wodurch ein detaillierter Blick in die thermodynamische Geschichte des frühen Sonnensystems möglich wird. Die extrahierten Parameter haben weitreichende Auswirkungen auf die Modelle der Entstehung erster solarer Festkörper, welche die Grundbausteine der Planetenbildung darstellen.

Computer simulations of two-dimensional colloidal crystals in confinement

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two ``walls'' providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-) long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y-direction along the walls then crosses over from the logarithmic increase (characteristic for $d=2$) to a linear increase (characteristic for d=1). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising- and XY-models is made

Quantum effects and dynamics in hydrogen-bonded systems: a first-principles approach to spectroscopic experiments

Computer simulations have become an important tool in physics. Especially systems in the solid state have been investigated extensively with the help of modern computational methods. This thesis focuses on the simulation of hydrogen-bonded systems, using quantum chemical methods combined with molecular dynamics (MD) simulations. MD simulations are carried out for investigating the energetics and structure of a system under conditions that include physical parameters such as temperature and pressure. Ab initio quantum chemical methods have proven to be capable of predicting spectroscopic quantities. The combination of these two features still represents a methodological challenge. Furthermore, conventional MD simulations consider the nuclei as classical particles. Not only motional effects, but also the quantum nature of the nuclei are expected to influence the properties of a molecular system. This work aims at a more realistic description of properties that are accessible via NMR experiments. With the help of the path integral formalism the quantum nature of the nuclei has been incorporated and its influence on the NMR parameters explored. The effect on both the NMR chemical shift and the Nuclear Quadrupole Coupling Constants (NQCC) is presented for intra- and intermolecular hydrogen bonds. The second part of this thesis presents the computation of electric field gradients within the Gaussian and Augmented Plane Waves (GAPW) framework, that allows for all-electron calculations in periodic systems. This recent development improves the accuracy of many calculations compared to the pseudopotential approximation, which treats the core electrons as part of an effective potential. In combination with MD simulations of water, the NMR longitudinal relaxation times for 17O and 2H have been obtained. The results show a considerable agreement with the experiment. Finally, an implementation of the calculation of the stress tensor into the quantum chemical program suite CP2K is presented. This enables MD simulations under constant pressure conditions, which is demonstrated with a series of liquid water simulations, that sheds light on the influence of the exchange-correlation functional used on the density of the simulated liquid.

Quantum dot-dye hybrid systems for energy transfer applications

In this thesis, we focus on the preparation of energy transfer-based quantum dot (QD)-dye hybrid systems. Two kinds of QD-dye hybrid systems have been successfully synthesized: QD-silica-dye and QD-dye hybrid systems.rn rnIn the QD-silica-dye hybrid system, multishell CdSe/CdS/ZnS QDs were adsorbed onto monodisperse Stöber silica particles with an outer silica shell of thickness 2 - 24 nm containing organic dye molecules (Texas Red). The thickness of this dye layer has a strong effect on the total sensitized acceptor emission, which is explained by the increase in the number of dye molecules homogeneously distributed within the silica shell, in combination with an enhanced surface adsorption of QDs with increasing dye amount. Our conclusions were underlined by comparison of the experimental results with Monte-Carlo simulations, and by control experiments confirming attractive interactions between QDs and Texas Red freely dissolved in solution. rnrnNew QD-dye hybrid system consisting of multishell QDs and organic perylene dyes have been synthesized. We developed a versatile approach to assemble extraordinarily stable QD-dye hybrids, which uses dicarboxylate anchors to bind rylene dyes to QD. This system yields a good basis to study the energy transfer between QD and dye because of its simple and compact design: there is no third kind of molecule linking QD and dye; no spacer; and the affinity of the functional group to the QD surface is strong. The FRET signal was measured for these complexes as a function of both dye to QD ratio and center-to-center distance between QD and dye by controlling number of covered ZnS layers. Data showed that fluorescence resonance energy transfer (FRET) was the dominant mechanism of the energy transfer in our QD-dye hybrid system. FRET efficiency can be controlled by not only adjusting the number of dyes on the QD surface or the QD to dye distance, but also properly choosing different dye and QD components. Due to the strong stability, our QD-dye complexes can also be easily transferred into water. Our approach can apply to not only dye molecules but also other organic molecules. As an example, the QDs have been complexed with calixarene molecules and the QD-calixarene complexes also have potential for QD-based energy transfer study. rn

Superfluid and antiferromagnetic phases in ultracold fermionic quantum gases

In this thesis several models are treated, which are relevant for ultracold fermionic quantum gases loaded onto optical lattices. In particular, imbalanced superfluid Fermi mixtures, which are considered as the best way to realize Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states experimentally, and antiferromagnetic states, whose experimental realization is one of the next major goals, are examined analytically and numerically with the use of appropriate versions of the Hubbard model.rnrnThe usual Bardeen-Cooper-Schrieffer (BCS) superconductor is known to break down in a magnetic field with a strength exceeding the size of the superfluid gap. A spatially inhomogeneous spin-imbalanced superconductor with a complex order parameter known as FFLO-state is predicted to occur in translationally invariant systems. Since in ultracold quantum gases the experimental setups have a limited size and a trapping potential, we analyze the realistic situation of a non-translationally invariant finite sized Hubbard model for this purpose. We first argue analytically, why the order parameter should be real in a system with continuous coordinates, and map our statements onto the Hubbard model with discrete coordinates defined on a lattice. The relevant Hubbard model is then treated numerically within mean field theory. We show that the numerical results agree with our analytically derived statements and we simulate various experimentally relevant systems in this thesis.rnrnAnalogous calculations are presented for the situation at repulsive interaction strength where the N'eel state is expected to be realized experimentally in the near future. We map our analytical results obtained for the attractive model onto corresponding results for the repulsive model. We obtain a spatially invariant unit vector defining the direction of the order parameter as a consequence of the trapping potential, which is affirmed by our mean field numerical results for the repulsive case. Furthermore, we observe domain wall formation, antiferromagnetically induced density shifts, and we show the relevant role of spin-imbalance for antiferromagnetic states.rnrnSince the first step for understanding the physics of the examined models was the application of a mean field approximation, we analyze the effect of including the second order terms of the weak coupling perturbation expansion for the repulsive model. We show that our results survive the influence of quantum fluctuations and show that the renormalization factors for order parameters and critical temperatures lead to a weaker influence of the fluctuations on the results in finite sized systems than on the results in the thermodynamical limit. Furthermore, in the context of second order theory we address the question whether results obtained in the dynamical mean field theory (DMFT), which is meanwhile a frequently used method for describing trapped systems, survive the effect of the non-local Feynman diagrams neglected in DMFT.

Bottle microresonators for applications in quantum optics and all-optical signal processing

This thesis reports on the experimental realization, characterization and application of a novel microresonator design. The so-called “bottle microresonator” sustains whispering-gallery modes in which light fields are confined near the surface of the micron-sized silica structure by continuous total internal reflection. While whispering-gallery mode resonators in general exhibit outstanding properties in terms of both temporal and spatial confinement of light fields, their monolithic design makes tuning of their resonance frequency difficult. This impedes their use, e.g., in cavity quantum electrodynamics (CQED) experiments, which investigate the interaction of single quantum mechanical emitters of predetermined resonance frequency with a cavity mode. In contrast, the highly prolate shape of the bottle microresonators gives rise to a customizable mode structure, enabling full tunability. The thesis is organized as follows: In chapter I, I give a brief overview of different types of optical microresonators. Important quantities, such as the quality factor Q and the mode volume V, which characterize the temporal and spatial confinement of the light field are introduced. In chapter II, a wave equation calculation of the modes of a bottle microresonator is presented. The intensity distribution of different bottle modes is derived and their mode volume is calculated. A brief description of light propagation in ultra-thin optical fibers, which are used to couple light into and out of bottle modes, is given as well. The chapter concludes with a presentation of the fabrication techniques of both structures. Chapter III presents experimental results on highly efficient, nearly lossless coupling of light into bottle modes as well as their spatial and spectral characterization. Ultra-high intrinsic quality factors exceeding 360 million as well as full tunability are demonstrated. In chapter IV, the bottle microresonator in add-drop configuration, i.e., with two ultra-thin fibers coupled to one bottle mode, is discussed. The highly efficient, nearly lossless coupling characteristics of each fiber combined with the resonator's high intrinsic quality factor, enable resonant power transfers between both fibers with efficiencies exceeding 90%. Moreover, the favorable ratio of absorption and the nonlinear refractive index of silica yields optical Kerr bistability at record low powers on the order of 50 µW. Combined with the add-drop configuration, this allows one to route optical signals between the outputs of both ultra-thin fibers, simply by varying the input power, thereby enabling applications in all-optical signal processing. Finally, in chapter V, I discuss the potential of the bottle microresonator for CQED experiments with single atoms. Its Q/V-ratio, which determines the ratio of the atom-cavity coupling rate to the dissipative rates of the subsystems, aligns with the values obtained for state-of-the-art CQED microresonators. In combination with its full tunability and the possibility of highly efficient light transfer to and from the bottle mode, this makes the bottle microresonator a unique tool for quantum optics applications.

Interacting quantum-dissipative tunnelling systems

Die Untersuchung von dissipativen Quantensystemen erm¨oglicht es, Quantenph¨anomene auch auf makroskopischen L¨angenskalen zu beobachten. Das in dieser Dissertation gew¨ahlte mikroskopische Modell erlaubt es, den bisher nur ph¨anomenologisch zug¨anglichen Effekt der Quantendissipation mathematisch und physikalisch herzuleiten und zu untersuchen. Bei dem betrachteten mikroskopischen Modell handelt es sich um eine 1-dimensionale Kette von harmonischen Freiheitsgraden, die sowohl untereinander als auch an r anharmonische Freiheitsgrade gekoppelt sind. Die F¨alle einer, respektive zwei anharmonischer Bindungen werden in dieser Arbeit explizit betrachtet. Hierf¨ur wird eine analytische Trennung der harmonischen von den anharmonischen Freiheitsgraden auf zwei verschiedenen Wegen durchgef¨uhrt. Das anharmonische Potential wird als symmetrisches Doppelmuldenpotential gew¨ahlt, welches mit Hilfe der Wick Rotation die Berechnung der ¨Uberg¨ange zwischen beiden Minima erlaubt. Das Eliminieren der harmonischen Freiheitsgrade erfolgt mit Hilfe des wohlbekannten Feynman-Vernon Pfadintegral-Formalismus [21]. In dieser Arbeit wird zuerst die Positionsabh¨angigkeit einer anharmonischen Bindung im Tunnelverhalten untersucht. F¨ur den Fall einer fernab von den R¨andern lokalisierten anharmonischen Bindung wird ein Ohmsches dissipatives Tunneln gefunden, was bei der Temperatur T = 0 zu einem Phasen¨ubergang in Abh¨angigkeit einer kritischen Kopplungskonstanten Ccrit f¨uhrt. Dieser Phasen¨ubergang wurde bereits in rein ph¨anomenologisches Modellen mit Ohmscher Dissipation durch das Abbilden des Systems auf das Ising-Modell [26] erkl¨art. Wenn die anharmonische Bindung jedoch an einem der R¨ander der makroskopisch grossen Kette liegt, tritt nach einer vom Abstand der beiden anharmonischen Bindungen abh¨angigen Zeit tD ein ¨Ubergang von Ohmscher zu super- Ohmscher Dissipation auf, welche im Kern KM(τ ) klar sichtbar ist. F¨ur zwei anharmonische Bindungen spielt deren indirekteWechselwirkung eine entscheidende Rolle. Es wird gezeigt, dass der Abstand D beider Bindungen und die Wahl des Anfangs- und Endzustandes die Dissipation bestimmt. Unter der Annahme, dass beide anharmonischen Bindung gleichzeitig tunneln, wird eine Tunnelwahrscheinlichkeit p(t) analog zu [14], jedoch f¨ur zwei anharmonische Bindungen, berechnet. Als Resultat erhalten wir entweder Ohmsche Dissipation f¨ur den Fall, dass beide anharmonischen Bindungen ihre Gesamtl¨ange ¨andern, oder super-Ohmsche Dissipation, wenn beide anharmonischen Bindungen durch das Tunneln ihre Gesamtl¨ange nicht ¨andern.

The g-factor of the electron bound in 28 Si 13+ : the most stringent test of bound-state quantum electrodynamics

This thesis describes the ultra-precise determination of the g-factor of the electron bound to hydrogenlike 28Si13+. The experiment is based on the simultaneous determination of the cyclotron- and Larmor frequency of a single ion, which is stored in a triple Penning-trap setup. The continuous Stern-Gerlach effect is used to couple the spin of the bound electron to the motional frequencies of the ion via a magnetic bottle, which allows the non-destructive determination of the spin state. To this end, a highly sensitive, cryogenic detection system was developed, which allowed the direct, non-destructive detection of the eigenfrequencies with the required precision.rnThe development of a novel, phase sensitive detection technique finally allowed the determination of the g-factor with a relative accuracy of 40 ppt, which was previously inconceivable. The comparison of the hereby determined value with the value predicted by quantumelectrodynamics (QED) allows the verification of the validity of this fundamental theory under the extreme conditions of the strong binding potential of a highly charged ion. The exact agreement of theory and experiment is an impressive demonstration of the exactness of QED. The experimental possibilities created in this work will allow in the near future not only further tests of theory, but also the determination of the mass of the electron with a precision that exceeds the current literature value by more than an order of magnitude.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Computer simulations of two-dimensional colloidal crystals under confinement and shear

In this thesis we are presenting a broadly based computer simulation study of two-dimensional colloidal crystals under different external conditions. In order to fully understand the phenomena which occur when the system is being compressed or when the walls are being sheared, it proved necessary to study also the basic motion of the particles and the diffusion processes which occur in the case without these external forces. In the first part of this thesis we investigate the structural transition in the number of rows which occurs when the crystal is being compressed by placing the structured walls closer together. Previous attempts to locate this transition were impeded by huge hysteresis effects. We were able to determine the transition point with higher precision by applying both the Schmid-Schilling thermodynamic integration method and the phase switch Monte Carlo method in order to determine the free energies. These simulations showed not only that the phase switch method can successfully be applied to systems with a few thousand particles and a soft crystalline structure with a superimposed pattern of defects, but also that this method is way more efficient than a thermodynamic integration when free energy differences are to be calculated. Additionally, the phase switch method enabled us to distinguish between several energetically very similar structures and to determine which one of them was actually stable. Another aspect considered in the first result chapter of this thesis is the ensemble inequivalence which can be observed when the structural transition is studied in the NpT and in the NVT ensemble. The second part of this work deals with the basic motion occurring in colloidal crystals confined by structured walls. Several cases are compared where the walls are placed in different positions, thereby introducing an incommensurability into the crystalline structure. Also the movement of the solitons, which are created in the course of the structural transition, is investigated. Furthermore, we will present results showing that not only the well-known mechanism of vacancies and interstitial particles leads to diffusion in our model system, but that also cooperative ring rotation phenomena occur. In this part and the following we applied Langevin dynamics simulations. In the last chapter of this work we will present results on the effect of shear on the colloidal crystal. The shear was implemented by moving the walls with constant velocity. We have observed shear banding and, depending on the shear velocity, that the inner part of the crystal breaks into several domains with different orientations. At very high shear velocities holes are created in the structure, which originate close to the walls, but also diffuse into the inner part of the crystal.

Thermal excitations of optical nanofibers measured with a fiber-integrated Fabry-Pérot cavity

Efficient coupling of light to quantum emitters, such as atoms, molecules or quantum dots, is one of the great challenges in current research. The interaction can be strongly enhanced by coupling the emitter to the eva-nescent field of subwavelength dielectric waveguides that offer strong lateral confinement of the guided light. In this context subwavelength diameter optical nanofibers as part of a tapered optical fiber (TOF) have proven to be powerful tool which also provide an efficient transfer of the light from the interaction region to an optical bus, that is to say, from the nanofiber to an optical fiber. rnAnother approach towards enhancing light–matter interaction is to employ an optical resonator in which the light is circulating and thus passes the emitters many times. Here, both approaches are combined by experi-mentally realizing a microresonator with an integrated nanofiber waist. This is achieved by building a fiber-integrated Fabry-Pérot type resonator from two fiber Bragg grating mirrors with a stop-band near the cesium D2-line wavelength. The characteristics of this resonator fulfill the requirements of nonlinear optics, optical sensing, and cavity quantum electrodynamics in the strong-coupling regime. Together with its advantageous features, such as a constant high coupling strength over a large volume, tunability, high transmission outside the mirror stop band, and a monolithic design, this resonator is a promising tool for experiments with nanofiber-coupled atomic ensembles in the strong-coupling regime. rnThe resonator's high sensitivity to the optical properties of the nanofiber provides a probe for changes of phys-ical parameters that affect the guided optical mode, e.g., the temperature via the thermo-optic effect of silica. Utilizing this detection scheme, the thermalization dynamics due to far-field heat radiation of a nanofiber is studied over a large temperature range. This investigation provides, for the first time, a measurement of the total radiated power of an object with a diameter smaller than all absorption lengths in the thermal spectrum at the level of a single object of deterministic shape and material. The results show excellent agreement with an ab initio thermodynamic model that considers heat radiation as a volumetric effect and that takes the emitter shape and size relative to the emission wavelength into account. Modeling and investigating the thermalization of microscopic objects with arbitrary shape from first principles is of fundamental interest and has important applications, such as heat management in nano-devices or radiative forcing of aerosols in Earth's climate system. rnUsing a similar method, the effect of the TOF's mechanical modes on the polarization and phase of the fiber-guided light is studied. The measurement results show that in typical TOFs these quantities exhibit high-frequency thermal fluctuations. They originate from high-Q torsional oscillations that couple to the nanofiber-guided light via the strain-optic effect. An ab-initio opto-mechanical model of the TOF is developed that provides an accurate quantitative prediction for the mode spectrum and the mechanically induced polarization and phase fluctuations. These high-frequency fluctuations may limit the ultimate ideality of fiber-coupling into photonic structures. Furthermore, first estimations show that they may currently limit the storage time of nanofiber-based atom traps. The model, on the other hand, provides a method to design TOFs with tailored mechanical properties in order to meet experimental requirements. rn

New enhancement strategies for plasmon-enhanced fluorescence biosensors

This thesis investigates metallic nanostructures exhibiting surface plasmon resonance for the amplification of fluorescence signal in sandwich immunoassays. In this approach, an analyte is captured by an antibody immobilized on a plasmonic structure and detected by a subsequently bound fluorophore labeled detection antibody. The highly confined field of surface plasmons originates from collective charge oscillations which are associated with high electromagnetic field enhancements at the metal surface and allow for greatly increased fluorescence signal from the attached fluorophores. This feature allows for improving the signal-to-noise ratio in fluorescence measurements and thus advancing the sensitivity of the sensor platform. In particular, the thesis presents two plasmonic nanostructures that amplify fluorescence signal in devices that rely on epifluorescence geometry, in which the fluorophore absorbs and emits light from the same direction perpendicular to the substrate surface.rnThe first is a crossed relief gold grating that supports propagating surface plasmon polaritons (SPPs) and second, gold nanoparticles embedded in refractive index symmetric environment exhibiting collective localized surface plasmons (cLSPs). Finite-difference time-domain simulations are performed in order to design structures for the optimum amplification of established Cy5 and Alexa Fluor 647 fluorophore labels with the absorption and emission wavelengths in the red region of spectrum. The design takes into account combined effect of surface plasmon-enhanced excitation rate, directional surface plasmon-driven emission and modified quantum yield for characteristic distances in immunoassays. Homebuilt optical instruments are developed for the experimental observation of the surface plasmon mode spectrum, measurements of the angular distribution of surface plasmon-coupled fluorescence light and a setup mimicking commercial fluorescence reading systems in epifluorescence geometry.rnCrossed relief grating structures are prepared by interference lithography and multiple copies are made by UV nanoimprint lithography. The fabricated crossed diffraction gratings were utilized for sandwich immunoassay-based detection of the clinically relevant inflammation marker interleukin 6 (IL-6). The enhancement factor of the crossed grating reached EF=100 when compared to a flat gold substrate. This result is comparable to the highest reported enhancements to date, for fluorophores with relatively high intrinsic quantum yield. The measured enhancement factor excellently agrees with the predictions of the simulations and the mechanisms of the enhancement are explained in detail. Main contributions were the high electric field intensity enhancement (30-fold increase) and the directional fluorescence emission at (4-fold increase) compared to a flat gold substrate.rnCollective localized surface plasmons (cLSPs) hold potential for even stronger fluorescence enhancement of EF=1000, due to higher electric field intensity confinement. cLSPs are established by diffractive coupling of the localized surface plasmon resonance (LSPR) of metallic nanoparticles and result in a narrow resonance. Due to the narrow resonance, it is hard to overlap the cLSPs mode with the absorption and emission bands of the used fluorophore, simultaneously. Therefore, a novel two resonance structure that supports SPP and cLSP modes was proposed. It consists of a 2D array of cylindrical gold nanoparticles above a low refractive index polymer and a silver film. A structure that supports the proposed SPP and cLSP modes was prepared by employing laser interference lithography and the measured mode spectrum was compared to simulation results.rn

How different is water crystallization from polymer crystallization under confinement?

Ziel der vorliegenden Dissertation war es, Einblicke in das Kristallisationsverhalten weicher Materie („soft matter“), wie verschiedener Polymere oder Wasser, unter räumlicher Einschränkung („confinement“) zu erlangen. Dabei sollte untersucht werden, wie, weshalb und wann die Kristallisation in nanoporösen Strukturen eintritt. Desweiteren ist Kristallisation weicher Materie in nanoporösen Strukturen nicht nur aus Aspekten der Grundlagenforschung von großem Interesse, sondern es ergeben sich zahlreiche praktische Anwendungen. Durch die gezielte Steuerung der Kristallinität von Polymeren könnten somit Materialien mit verschiendenen mechanischen und optischen Eigenschaften erhalten werden. Desweiteren wurde auch räumlich eingeschränktes Wasser untersucht. Dieses spielt eine wichtige Rolle in der Molekularbiologie, z.B. für das globuläre Protein, und als Wolkenkondensationskeime in der Atmosphärenchemie und Physik. Auch im interstellaren Raum ist eingeschränktes Wasser in Form von Eispartikeln anzutreffen. Die Kristallisation von eingeschränktem Wasser zu verstehen und zu beeinflussen ist letztlich auch für die Haltbarkeit von Baumaterialien wie etwa Zement von großem Interesse.rnUm dies zu untersuchen wird Wasser in der Regel stark abgekühlt und das Kristallisationsverhalten in Abhängigkeit des Volumens untersucht. Dabei wurde beobachtet, dass Mikro- bzw. Nanometer große Volumina erst ab -38 °C bzw. -70 °C kristallisieren. Wasser unterliegt dabei in der Regel dem Prozess der homogenen Nukleation. In der Regel gefriert Wasser aber bei höheren Temperaturen, da durch Verunreinigungen eine vorzeitige, heterogene Nukleation eintritt.rnDie vorliegende Arbeit untersucht die sachdienlichen Phasendiagramme von kristallisierbaren Polymeren und Wasser unter räumlich eingeschränkten Bedingungen. Selbst ausgerichtetes Aluminiumoxid (AAO) mit Porengrößen im Bereich von 25 bis 400 nm wurden als räumliche Einschränkung sowohl für Polymere als auch für Wasser gewählt. Die AAO Nanoporen sind zylindrisch und parallel ausgerichtet. Außerdem besitzen sie eine gleichmäßige Porenlänge und einen gleichmäßigen Durchmesser. Daher eignen sie sich als Modelsystem um Kristallisationsprozesse unter wohldefinierter räumlicher Einschränkung zu untersuchen.rnEs wurden verschiedene halbkristalline Polymere verwendet, darunter Poly(ethylenoxid), Poly(ɛ-Caprolacton) und Diblockcopolymere aus PEO-b-PCL. Der Einfluss der Porengröße auf die Nukleation wurde aus verschiedenen Gesichtspunkten untersucht: (i) Einfluss auf den Nukleationmechanismus (heterogene gegenüber homogener Nukleation), (ii) Kristallorientierung und Kristallinitätsgrad und (iii) Zusammenhang zwischen Kristallisationstemperatur bei homogener Kristallisation und Glasübergangstemperatur.rnEs konnte gezeigt werden, dass die Kristallisation von Polymeren in Bulk durch heterogene Nukleation induziert wird und das die Kristallisation in kleinen Poren hauptsächlich über homogene Nukleation mit reduzierter und einstellbarer Kristallinität verläuft und eine hohe Kristallorientierung aufweist. Durch die AAOs konnte außerdem die kritische Keimgröße für die Kristallisation der Polymere abgeschätzt werden. Schließlich wurde der Einfluss der Polydispersität, von Oligomeren und anderen Zusatzstoffen auf den Nukleationsmechanismus untersucht.rn4rnDie Nukleation von Eis wurde in den selben AAOs untersucht und ein direkter Zusammenhang zwischen dem Nukleationstyp (heterogen bzw. homogen) und der gebildeten Eisphase konnte beobachtet werden. In größeren Poren verlief die Nukleation heterogen, wohingegen sie in kleineren Poren homogen verlief. Außerdem wurde eine Phasenumwandlung des Eises beobachtet. In den größeren Poren wurde hexagonales Eis nachgewiesen und unter einer Porengröße von 35 nm trat hauptsächlich kubisches Eis auf. Nennenswerter Weise handelte es sich bei dem kubischem Eis nicht um eine metastabile sondern eine stabile Phase. Abschließend wird ein Phasendiagramm für räumlich eingeschränktes Wasser vorgeschlagen. Dieses Phasendiagramm kann für technische Anwendungen von Bedeutung sein, so z.B. für Baumaterial wie Zement. Als weiteres Beispiel könnten AAOs, die die heterogene Nukleation unterdrücken (Porendurchmesser ≤ 35 nm) als Filter für Reinstwasser zum Einsatz kommen.rnNun zur Anfangs gestellten Frage: Wie unterschiedlich sind Wasser und Polymerkristallisation voneinander unter räumlicher Einschränkung? Durch Vergleich der beiden Phasendiagramme kommen wir zu dem Schluss, dass beide nicht fundamental verschieden sind. Dies ist zunächst verwunderlich, da Wasser ein kleines Molekül ist und wesentlich kleiner als die kleinste Porengröße ist. Wasser verfügt allerdings über starke Wasserstoffbrückenbindungen und verhält sich daher wie ein Polymer. Daher auch der Name „Polywasser“.