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Item Open Access Optimal processes in stochastic thermodynamics(2009) Schmiedl, Tim; Seifert, Udo (Prof. Dr.)The concept of Stochastic Thermodynamics deals with the question how to define thermodynamic quantities for nonequilibrium mesoscopic systems. Here, thermal fluctuations must be considered. The main objective of this thesis is the analysis of optimization problems in the context of Stochastic Thermodynamcis. A quite natural optimization principle for nonequilibrium processes is the requirement that a defined result should be achieved with the smallest possible amount of dissipation. For a transition between two given equilibrium states in a given finite time, this is directly linked to a process schedule which leads to a minimal (mean) work. For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. Surprisingly, the optimal protocol involves jumps for overdamped Langevin dynamics and even delta-type singularities for underdamped Langevin dynamics. For purely Hamiltonian and Schrödinger dynamics in harmonic potentials, we show that the optimal protocol is highly degenerate and that even in the limit of short transition times, the optimal work is given by the adiabatic work which is substantially smaller than the work for an instantaneous jump. These optimal protocols significantly improve free energy calculations via the Jarzynski equality. Most processes in the biological cell, however, cannot be described by a nonequilibrium transition between equilibrium states. Rather, these systems are permanently driven out of equilibrium, e.g. by chemical potential differences. An important model class of such dynamics are Brownian motors which transfer either chemical or thermal energy into mechanical work leading to directed transport against a load force. It is meaningful to characterize such thermodynamic machines by their performance at maximum power output rather than at maximum efficiency. The efficiency at this maximum power then is a relevant quantity. We consider a Carnot engine on the mesoscale which can be constructed by using a Brownian particle instead of the working gas and a time-dependent trapping potential instead of the confining vessel. The efficiency at maximum power output can be calculated analytically. Surprisingly, it is given by a quite universal expression which does only depend on the viscosity (or more generally on the mobility matrices) at the two temperatures. This result is independent of the shape of the potential used to trap the particle. In contrast to heat engines, molecular motors in the biological cell are mostly driven by chemical potential differences. For two simple motor models, the efficiency of the molecular motor at maximum power shows two unexpected features: (i) Both the power output and the efficiency increase when the transition state position is moved closer to the initial motor position and (ii) for appropriate parameters, the efficiency increases when the system is driven further out of equilibrium by a higher chemical potential difference. Beyond their relevance for directed transport within the cell, molecular motors are also important for the synthesis of proteins. We study the protein production rate at a given error rate for the second stage of gene expression (translation). We find that for a given error rate equivalent to the experimentally observed value, the protein production rate is not at its theoretical maximum. We therefore conjecture that other evolutionary goals or structural reasons are responsible for the observed rate constants.Item Open Access Current induced dynamic nuclear polarization : spintronics without magnetism(2009) Kaur, Gurneet; Denninger, Gert (Prof. Dr.)The present work deals with the study of Dynamic Nuclear Polarization (DNP), especially current-induced DNP, in III-V semiconductors such as InP and GaAs. Localized electron centres in these semiconductors have extended wavefunctions and exhibit strong hyperfine coupling with the nuclei in their vicinity. These interactions not only play a critical role in electron and nuclear spin relaxation mechanisms, but also enable nuclear polarization enhancement via DNP. The doping concentration and temperature range favourable for DNP effects was determined by studying these semiconductors with varying doping concentration in a wide temperature range. Under suitable conditions, DNP enhancement by more than two orders of magnitude was observed by microwave saturation of electron spin transitions in InP. Additionally, we report the first experimental observation of electric-current induced DNP in InP. This is consistent with model predictions in zinc-blende semiconductors with strong spin-orbit effects. This provides a promising possibility to generate spin polarization by means of electric current and hence is an important step towards an "all electric spintronic device". Analogous to the spin Hall effect, the "spin Gunn effect" was proposed theoretically in III-V semiconductors recently. A small spin polarization is expected to grow and lead to spin polarized domains within the Gunn regime. If demonstrated experimentally, the spin Gunn effect can open a wide range of possibilities in the field of spintronics. We investigated the possible existence of spin Gunn effect in InP and GaAs by means of pulsed NMR measurements. From our measurements we conclude that the electron spin polarization and the resulting DNP effects appear to be much smaller than the theoretical predictions.Item Open Access Resonant X-ray scattering studies of ruthenium oxides and ruthenocuprates(2009) Bohnenbuck, Britta; Keimer, Bernhard (Prof. Dr.)The magnetic and orbital properties of the ruthenium oxides Ca3Ru2O7 and Mn doped Sr3Ru2O7 and the ruthenocuprate RuSr2GdCu2O8 were investigated using resonant and high-energy x-ray diffraction. Bilayered Ca3Ru2O7 is a paramagnetic metal at high temperatures and orders antiferromagnetically at T_N=56K. A second phase transition to a less conductive state is observed at T_MI=48K. This transition is accompanied by abrupt structural changes and a reorientation of the magnetic moment. In addition, there is experimental evidence for the existence of orbital order below T_MI. Our resonant x-ray diffraction studies at the Ru L-absorption edges were focused on the investigation of the magnetic reflections (001) and (110). The observation of a magnetic signal at these reciprocal space positions is in full agreement with an A-type antiferromagnetic structure, consisting of ferromagnetic bilayers coupled antiferromagnetically along the c-axis. Based on the azimuthal angle dependence of the signals, the direction of the magnetic moment was determined to lie along the b-axis below T_MI and along the $a$-axis between T_MI and T_N. The origin of the reorientation of the magnetic moment at T_MI is not yet completely understood. However, it might result from the strong spin-orbit coupling which presumably causes an unquenched orbital magnetization. The latter might then induce additional terms in the spin Hamiltonian that are responsible for the reorientation of the magnetic moment. Although various experiments have given indirect evidence of orbital order below T_MI, we did not detect any orbital signal within the experimental sensitivity. This indicates that the orbital ordering parameter is significantly weaker than in the single layered counterpart Ca2RuO4, which is presumably due to residual charge or orbital fluctuations in the insulating state. RuSr2GdCu2O8 exhibits long range magnetic order and superconductivity within a broad coexistence range. Only limited information about the magnetic structure has been available so far, as most studies were performed on powder samples due to the small size of available crystals. In this situation, resonant x-ray diffraction at the Ru L-absorption edges has turned out to be the ideal tool for the investigation of RuSr2GdCu2O8 since it is sensitive to magnetism, but does not depend on a large crystal mass. Our single crystal studies of the magnetic reflections (1/2 1/2 1/2) and (1/2 1/2 3/2) indicate a G-type antiferromagnetic structure, characterized by a doubling of the unit cell along all three crystallographic directions. From the azimuthal angle dependence of the magnetic signal, we deduced a magnetic moment direction along a low symmetry axis with substantial components parallel and perpendicular to the RuO2 planes. These findings are consistent with previous neutron powder diffraction results and magnetization data. A symmetry analysis in conjunction with a recent crystallographic study revealed that the experimentally observed G-type antiferromagnetic structure needs to be accompanied by an additional ferromagnetic in-plane component, which alternates between neighboring RuO2 layers. This ferromagnetic mode corresponds exactly to the one deduced from nuclear and ferromagnetic resonance experiments. Therefore, our resonant x-ray diffraction data reconcile a variety of apparently contradictory results on the magnetic structure of RuSr2GdCu2O8 and thus resolve a big controversy in the experimental literature. Bilayered Sr3Ru2O7 has attracted a lot of interest in the past years due to the observation of the quantum critical behavior which is related to a metamagnetic transition. In the ground state, the material is a paramagnetic metal and shows Fermi liquid behavior below 10K. Upon substituting Mn for Ru, an insulating antiferromagnetic state is induced; its transition temperature varies with the Mn concentration. Using resonant x-ray diffraction at the Ru L-absorption edges, we investigated the antiferromagnetic structure of 10 Mn substituted Sr3Ru2O7. Our studies of the superstructure reflections (1/4 1/4 0) and (3/4 3/4 0) indicate that the magnetic order is essentially two dimensional and that the magnetic moments are aligned along the c-axis. In combination with a previous neutron powder diffraction study, which was carried out on 5% Mn substituted Sr3Ru2O7, our results suggest an up-up-down-down spin arrangement in the RuO2 planes, which is independent of the Mn concentration. This implies that an antiferromagnetic instability is already present in the parent compound Sr3Ru2O7. Interestingly, the anisotropic resistivity behavior, observed in the nematic phase of Sr3Ru2O7, could be explained assuming the same up-up-down-down spin arrangement as in Mn substituted Sr3Ru2O7. If the two phases are in fact identical, has to be checked by a detailed single crystal neutron diffraction study including a complete structure refinement.Item Open Access Spectroscopic study of CaMnO3/CaRuO3 superlattices and YTiO3 single crystals(2009) Yordanov, Petar; Keimer, Bernhard (Prof. Dr.)The first two sections of Chapter 1 give a general overview of the research topics and experimental methods discussed in the thesis. Further on, in Chapter 2, some of the most important characteristics and mechanisms underlying the physics of transition metal oxides are presented. As the experimental part of the thesis includes studies on manganites and titanates, these two classes of compounds are exemplified in the exposition of Chapter 2. Several recent works in the emerging research field of transition metal oxide interfaces and superlattices are also discussed along with a brief introduction in x-ray spectroscopic methods with synchrotron radiation. Chapter 3 introduces the principles of optical spectroscopy and the simplest models for dielectric function, i.e., Lorentz oscillator and Drude dielectric function. The following Chapter 4 introduces two of the experimental techniques in optical spectroscopy, reflectance and spectroscopic ellipsometry. Further on, we describe the design of a new home-built apparatus for near-normal reflectance with high magnetic fields. Several critical technical details and findings during the assembling process are also discussed. Chapter 5 represents a comprehensive experimental spectroscopic study of a prototypical superlattice system made from an antiferromagnetic insulator CaMnO3 and a paramagnetic metal CaRuO3. The resulting interface ferromagnetic state was closely investigated by means of optical spectroscopy as well as by soft x-ray scattering and absorption methods. This study led us to the conclusion that magnetic bound states, i.e. magnetic polarons, have to be considered in the description of this SL system. Chapter 6 describes a polarized far infrared reflectance study with high magnetic field on the ferromagnetic Mott insulator YTiO3, single crystals. All 25 infrared-active phonon modes were observed. The temperature and magnetic-field dependence of the phonon modes revealed a weak spin-phonon coupling in YTiO3 and largely extended temperature range (up to TM ~ 80 - 100K), for the field-induced effects on the oscillator parameters. This later observation, uncovered short-range magnetic order state which remains even at temperatures as high as three times the temperature of the actual ferromagnetic transition of Tc ~ 30K. While a quantitative theoretical description of these data is thus far not available, they point to a complex interplay between spin, orbital, and lattice degrees of freedom due to the near-degeneracy of the Ti t2g orbitals in YTiO3.Item Open Access In-situ-Röntgenbeugungsuntersuchungen zur Stabilität zweidimensionaler Legierungsfilme(2009) Becker, Moritz; Dosch, Helmut (Prof. Dr.)Diese Arbeit untersucht das Phasenverhalten ultradünner, im Volumen nicht mischbarer Fe-Ag Legierungsfilme auf Ru(0001)- und Ir(111)-Substraten mit oberflächensensitiver Röntgenbeugung (SXRD). Die Experimente wurden an den Synchrotronstrahlungsquellen Ångstrømquelle Karlsruhe (ANKA) und Swiss Light Source (SLS) mit einer im Rahmen dieser Arbeit entworfenen, transportablen UHV-Kammer durchgeführt, die in-situ Probenpräparation und zeitaufgelöste oberflächensensitive Röntgenbeugungsexperimente ermöglicht. Ein grundlegendes Verständnis von Legierungen ist ohne die detaillierte Kenntnis der atomaren Wechselwirkungspotentiale nicht möglich. Wäre diese Kenntnis erlangt, würde sich die Möglichkeit eröffnen, eine gewünschte Legierung am Rechner zu entwickeln, das heißt die benötigte Materialzusammensetzung a-priori aus den gewünschten Legierungseigenschaften zu ermitteln. Die atomaren Wechselwirkungen - üblicherweise unterteilt in chemische und spannungsinduzierte Wechselwirkungen - bestimmen, im Wettstreit mit der Entropie, die atomare Konfiguration der Legierung. Eisen und Silber dienen als Modellsystem einer im Volumen phasenseparierenden Legierung. Die stark ausgeprägte Entmischung reicht bei allen Mischungsverhältnissen bis in die flüssige Phase und deutet damit darauf, dass nicht nur die spannungsinduzierten sondern auch die chemischen Wechselwirkungen die Phasentrennung begünstigen. Die Beschränkung einer solchen binären Mischung auf einen ultradünnen Film auf einem Substrat wird die Energie der Verspannungen im Film verändern und zusätzliche chemische Wechselwirkungen zwischen Filmmaterialien und Substrat einbringen. In einem einfachen Modell wird die Spannungsenergie im Film minimiert, wenn die Gitterkonstante des Substrats zwischen denen der reinen Filmmaterialien liegt, wie bei Fe-Ag auf Ru(0001) und Ir(111). Das heißt, während Spannungen im Volumen stets entmischend wirken, können sie im Film die Legierungsbildung begünstigen, wobei sogenannte spannungsstabilisierte Oberflächenlegierungen entstehen. Im Rahmen dieser Arbeit wurde das Phasenverhalten von Submonolagen-Filmen aus Eisen und Silber auf Ru(0001)- und Ir(111)-Substraten mit zunehmender Temperatur und Zeit für drei Mischungsverhältnisse (eisenreich, ausgeglichen und silberreich) untersucht. Die abgeschiedenen reinen Eisen- und Silberphasen lassen sich dabei in einem SXRD-Experiment deutlich von möglichen Legierungsphasen, über die, den verschiedenen atomaren Konfigurationen zuzuordnenden Streubilder, unterscheiden. Der Anteil der Phasenabscheidung in die reinen Eisen- und Silberphasen lässt sich über die integrierte Intensität der Reflexe der reinen Silberphase bestimmen. Auf der Ru(0001)-Oberfläche konnte bereits bei Raumtemperatur eine Entmischung der ultradünnen Fe-Ag Filme beobachtet werden, wobei die Phasentrennung im Zeitrahmen der Experimente noch nicht vollständig abgelaufen ist. Nach dem Anlassen der Proben bis 670 K, das heißt bis knapp unter der Desorptionstemperatur von Silber, zeigen die Filme eine vollständige Phasenseparation. Auf der Ir(111)-Oberfläche konnte bei Raumtemperatur bei keinem Mischungsverhältnis eine Phasentrennung im Zeitrahmen der Experimente beobachtet werden. Der Prozess der Phasenseparation in den Fe-Ag Filmen läuft damit auf der Ir(111)-Oberfläche deutlich langsamer als auf der Ru(0001)-Oberfläche ab. Anlassen der Filme mit eisenreichem und ausgeglichenem Mischungsverhältnis auf 670 K führt erneut zu vollständiger Entmischung. Die silberreiche Mischung zeigt dagegen eine unvollständige Phasenseparation. Zusätzlich sind diffuse Streusignale um die Crystal Truncation Rods des Ir(111)-Substrats zu beobachten, die schwache, aber langreichweitige 2 dimensionale Korrelationen im Film aufzeigen. Eine wahrscheinliche Interpretation ist eine Tröpfchenphase mit Eisenclustern in einer Silbermatrix. Diese Beobachtung zeigt, dass die diffuse Röntgenstreuung sich ausgezeichnet eignet, Korrelationen in binären 2 dimensionalen Mischungen zu untersuchen und dabei wertvolle Beiträge zur Bestimmung atomarer Wechselwirkungspotentiale zu geben.Item Open Access Einzelmolekülspektroskopie in lebenden Zellen : Untersuchung und Anwendung alternativer Fluoreszenzmarkierungen mit verbesserten photophysikalischen Eigenschaften(2009) Neugart, Felix; Wrachtrup, Jörg (Prof. Dr.)Die Methoden der Einzelmolekülspektroskopie werden seit Mitte der 90er Jahre in ansteigendem Maße für Untersuchungen in Modellsystemen in der Biochemie und Molekularbiologie angewandt. Die Anwendung dieser Methoden auf biologische Fragestellungen zu Untersuchungen in lebenden Zellen stellt dagegen ein noch junges und noch kaum verbreitetes Fachgebiet dar. Die Herausforderungen, Einzelmolekülspektroskopiemethoden, die in Modellsystemen etabliert wurden, auf die Bedingungen in lebenden Zellen zu übertragen, liegen in einem verminderten Signal-Rausch-Verhältnis und in der Notwendigkeit, bestimmte Moleküle in ihrer zellulären Umgebung hoch spezifisch zu markieren. Um eine größere Verbreitung dieser Methoden zur direkten Untersuchung biologischer Fragestellungen in lebenden Zellen zu erreichen, sind Verbesserungen vor allem der photophysikalischen Eigenschaften der Fluoreszenzmarkierungen gegenüber den bisher verbreiteten Markierungen notwendig. In dieser Arbeit wurde das Ziel verfolgt, Konzepte zu alternativen Fluoreszenzmarkierungen im Hinblick auf verbesserte photophysikalische Eigenschaften zu untersuchen und anzuwenden. Zum einen wurden an fluoreszierenden Nanodiamanten mit NV-Zentren eine Reihe von Experimenten durchgeführt mit dem Ziel, diese als Fluoreszenzmarkierung zur Anwendung in lebenden Zellen zu etablieren. Zum Anderen wurde die bislang wenig verbreitete Markierungsmethode der Tags (ACP-Tag) genutzt, um die Vorteile einer genspezifischen Markierung von autofluoreszierenden Proteinen und die photophysikalischen Eigenschaften von synthetischen Farbstoffen zu kombinieren. Das gegenüber autofluoreszierenden Proteinen erhöhte Signal-Rausch-Verhältnis führte hierbei zu Resultaten, die bei der Verwendung von autofluoreszierenden Proteinen nicht zu erreichen gewesen wären. Die Anwendung der in dieser Arbeit vorgestellten Methoden der Einzelmolekülspektroskopie ermöglicht es, zellbiologische Fragestellungen zu beantworten, die mit bisher etablierten zellbiologischen Methoden nicht untersucht werden konnten. In den letzten Jahren wurden solche Methoden bereits in kommerzielle Systeme eingeführt bzw. sie stehen in der Entwicklung. So ist in den kommenden Jahren eine weitere Verbreitung der Methoden der Einzelmolekülspektroskopie insbesondere unter Biologen und Medizinern zu erwarten.Item Open Access The role of MHD instabilities in the improved H-mode scenario(2009) Flaws, Asher; Stroth, Ulrich (Prof.)Recently a regime of tokamak operation has been discovered, dubbed the improved H-mode scenario, which simultaneously achieves increased energy confinement and stability with respect to standard H-mode discharges. It has been suggested that magnetohydrodynamic (MHD) instabilities play some role in establishing this regime. In this thesis MHD instabilities were identified, characterised, and catalogued into a database of improved H-mode discharges in order to statistically examine their behaviour. The onset conditions of MHD instabilities were compared to existing models based on previous H-mode studies. Slight differences were found, most notably a reduced $\beta_N$ onset threshold for the frequently interrupted regime for neoclassical tearing modes (NTM). This reduced threshold is due to the relatively low magnetic shear of the improved H-mode regime. This study also provided a first-time estimate for the seed island size of spontaneous onset NTMs, a phenomenon characteristic of the improved H-mode scenario. Energy confinement investigations found that, although the NTM impact on confinement follows the same model applicable to other operating regimes, the improved H-mode regime acts to mitigate the impact of NTMs by limiting the saturated island sizes for NTMs with toroidal mode number $n \geqslant 2$. Surprisingly, although a significant loss in energy confinement is observed during the sawtooth envelope, it has been found that discharges containing fishbones and low frequency sawteeth achieve higher energy confinement than those without. This suggests that fishbone and sawtooth reconnection may indeed play a role in establishing the high confinement regime. It was found that the time evolution of the central magnetic shear consistently locks in the presence of sawtooth and fishbone reconnection. Presumably this is due to the periodic redistribution of the central plasma current, an effect which is believed to help establish and maintain the characteristic current profile required for improved H-mode operation. A similar effect was proposed for the NTM instability whereby the magnetic island drives an additional toroidal current which flattens the central current density profile. However, it was found that the NTM impact on the toroidal current density could be accounted for purely in terms of the $3$ conventional current contributions, namely: ohmic, bootstrap, and auxiliary heating current drive, without requiring an additional current source.Item Open Access Strukturentstehung in Driftwellenturbulenz toroidaler Plasmen(2009) Manz, Peter; Stroth, Ulrich (Prof. Dr.)In Fusionsplasmen ist die Turbulenz und der damit inhergehende turbulente Transport für den größten Anteil der Teilchen- und Energieverluste verantwortlich. Durch die annähernd freie Bewegung der Ladungsträger parallel zum Magnetfeld kann die Turbulenz in magnetisierten Plasmen, rotierenden Flüssigkeiten im geophysikalischen Kontext entsprechend, als zweidimensional betrachtet werden. In zweidimensionaler Turbulenz bilden sich durch Wirbelvermischung größere Wirbelstrukturen aus. Es wird davon ausgegangen, dass die Wirbel untereinander wechselwirken und sich gegenseitig durchmischen und so schrittweise immer größere Wirbel bilden. Da dieser Prozess stufenweise abläuft wird dieser als Kaskade bezeichnet. Große Wirbelsysteme können für die Fusionsforschung von entscheidender Bedeutung sein, da sie nicht gleichmäßige radiale elektrische Felder aufbauen können, die eine Schlüsselgröße von internen Transport-Barrieren sind. Die nichtlineare Wechselwirkung zwischen Wirbeln verschiedener Skalen wird im Detail untersucht. Die Untersuchung erlaubt Rückschlüsse auf den Entstehungsmechanismus von großskaligen Wirbelstrukturen in magnetisierten Plasmen.Item Open Access Decoherence and relaxation of a pair of interacting spins coupled to independent environments(2009) Nägele, Peter; Weiß, Ulrich (Prof. Dr.)In this thesis, a scheme for calculating the dynamics of two coupled dissipative spins is developed, where each of the spins is coupled to its own boson bath. We derive analytic path sum results both in the Markov-regime and in the one-boson exchange regime. The analysis is also performed with the Bloch-Redfield method. It is shown that the two different approaches lead to identical results for the dynamics. This is not obvious a priori because both methods are based on different procedures. The path sum method gives detailed insight into the internal dynamics of two coupled spins because we consider every path sequence that contributes to the time evolution. While most studies of coupled spins are restricted to one type of coupling, e.g., Ising type, we will generalize here to linear combinations of possible couplings. Especially interesting is the occurrence of a frustration of decoherence, if the spins are interacting via a linear combination of longitudinal and transverse coupling and, when in addition, some of the eigenfrequencies become degenerate. Our analysis shows that degenerate but mutual exclusive ground states lead to increased coherence times. Maximization of coherence is one of the crucial goals of quantum state engineering. Another topic of interest is the impact of non-linear quantum environments, formed by surrounding dissipative spins. A distribution of bistable background charges is known to be responsible for $1/f$ noise in solid state devices, like the superconducting quantum interference devices. Since $1/f$ noise is seemingly the dominating source of decoherence at very low temperature, there is a profound theoretical interest in modeling it. Therefore, we analyze two interacting spins, where one of them is coupled to a boson bath and thereby represents a resonant non-linear quantum environment. We study the crossover from a non-linear to a linear bath and study the corresponding time scale for the relevant bath correlations. Interestingly, for large and increasing temperature we find a decreasing decoherence for the central spin.Item Open Access Three-dimensional optical metamaterials(2009) Liu, Na; Giessen, Harald (Prof. Dr.)Metamamaterials have attracted a lot of attention due to their fascinating properties. Many proactical applications have been suggested such as negative refraction, perfect lens, and invisibility cloak. In order to create real materials, we need three-dimensional structures. These structures pose some challenges in fabrication as well as with regards to understanding their optical properties, especially the relevant coupling mechanisms between neighboring elements and layers. In this thesis, we are going to present the advantages and problems associated with different fabrication methods. We will discuss coupling between the elements, taking electric and magnetic dipoles as well as higher order multipoles into account. Longitudinal and transverse interactions as well as their interplay will be examined.
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