Single-Particle Orbit Tracking - Setup, Characterisation and Application
- In this thesis, the development and experimental realisation of an optical setup which records the 2-dimensional trajectories of single fluorescently labeled polystyrene beads, either 20nm or 50nm in diameter, with a high spatial and temporal resolution is introduced. Combining single molecule fluorescence techniques with a new method called single-particle orbit tracking the spatial position of the beads could be determined with an accuracy of less than 10nm at a time resolution of 4 ms. The idea is to manipulate the excitation light spatially and temporally to locate a particle. In order to do so, special optics which deflect a laser beam and guide it on a circular path were used. Subsequently, this rotating beam is projected by a microscope into the sample with the diffusing particles. Due to the spatially and periodically modulated excitation light, the emission signal of the bead is modulated with the frequency of the rotation of the laser focus. The amplitude of the modulated emission signal depends on the position of the particle within the excitation orbit. An ingeniously developed algorithm calculates the position of the particle with respect to the centre of the orbit by demodulating the emission signal and restores the particle back to the orbit centre. Applying this method successively, the trajectory of the diffusing bead can be reconstructed. Besides the experimental realisation, the characterisation of the setup in terms of the spatial and temporal accuracy as well as the experimental shortcomings that influences the measured trajectories and hence, the interpretation of the data, were also the main topics of this work. For this purpose a reference sample of 20nm sized beads in glycerol was used. The accuracies were studied mainly by computer simulations and the artifacts by experiments. The technical details of the setup and the characterisation results were published (publication P1).
The recorded trajectories were analysed with various methods, among which the commonly used mean squared displacement (MSD) yields the results with highest information. The diffusion coefficient as well as the diffusion behaviour could be quantified. With this method the obtainable accuracy in measuring the diffusion coefficient by the acquisition of single-particle trajectories was studied as a function of the length of the trajectories and as a function of the number of fitting points that were used for a linear fit to the experimentally determined MSD-curves. As expected, the relative error of the determined diffusion coefficient gets better for longer trajectories. Further, an optimal number of fitting points for the linear approximation to the MSD-curves was found, which yields the most exact values for the diffusion coefficients and which is independent of the trajectory length. For the first time, experimental results on that issue were compared with theoretical predictions, where a good agreement was found. These findings were published (publication P2). By the use of the Stokes-Einstein relation the diffusion coefficients could further be converted to particle radii. A closer examination of these radii emphasises the influence of the afore mentioned number of fitting points. For the optimal value, significantly precise radii could be determined.
Finally, an application of the new setup is presented. In cooperation with the chair of experimental physics I (group of Prof. Dr. M. Weiss) of the University of Bayreuth, the diffusion behaviour of single nanoparticles in a complex fluid was studied. Background hereto is the investigation of biochemical reactions in a biological cell, whose kinetic is given by the diffusion of the corresponding reaction partners. Due to the high crowding of the cell compartments the diffusion is hindered. The diffusion behaviour in these systems is called anomalous and more exactly subdiffusive. Several theoretical models have been developed to explain this phenomenon, but yet without experimental verifications. Here, the diffusion of 50nm sized polymer beads in the model system dextran (a highly branched biopolysaccaride) is investigated experimentally with high spatial and temporal resolution. The data were analysed in the group of the cooperation partner which yields a very good agreement with the model of “fractional Brownian motion”. These results were also published (publication P3).
Polymer Melts Investigated by Field Cycling NMR Relaxometry: From Simple Liquid to Reptation Dynamics
- The focus of this thesis is the investigation of linear polymer melts by applying Field Cycling Nuclear Magnetic Resonance (FC NMR) relaxometry. The objective is to understand their microscopic dynamics and its dependence on the molecular mass (M) of the polymer chains.
With the commercial availability of FC NMR relaxometers, the method gained attraction for studying dynamics of soft condensed matter due to its ability to detect both the structural or alpha-relaxation (identified with the segmental dynamics) and slower collective dynamics. In the case of polymer melts the latter is described most often by the Rouse model for non-entangled chains and the Doi/Edwards tube-reptation model for entangled polymers. Since 2004 a commercial relaxometer by Stelar has been operated in the Rössler group. Its capability to rapidly switch between different magnetic fields allows to measure the spin-lattice relaxation time in the proton frequency range from 10 kHz to 20 MHz. In previous works by the Rössler group the pioneering works by Kimmich and co-workers have been extended in order to combine the results of a broad temperature range: Frequency-temperature superposition is applied to construct master curves in the susceptibility representation. The key benefits are: the susceptibility is scaled by time constant of segmental dynamics and an "isofrictional" representation is achieved; the accessible frequency range is significantly increased; the time constants are provided and compared with those obtained by other techniques; the regimes of glassy and polymer dynamics can be easily distinguished; finally, the dipolar correlation function is obtained directly by Fourier transform.
In this thesis by employing the above approach, the dipolar correlation function of polybutadienes (PB) melts is presented and comprises - depending on M - glassy, Rouse and entanglement dynamics. The latter two relaxation regimes can be described by different power-laws, which are compared to the predictions of the tube-reptation model. A good agreement is found for the Rouse regime (I). For the constrained Rouse regime (II) at long times, a highly protracted crossover to completely established reptation dynamics is discovered. That is, the exponent depends on M and reaches 0.32 only at M=441000, which is in accord with Double Quantum (DQ) 1H NMR results by Saalwächter and co-workers and very close to 0.25 predicted for regime II of the tube-reptation model. This is only achieved by additional relaxation experiments in cooperation with the Fujara group at TU Darmstadt, since their home-built FC NMR relaxometer is equipped with an active stray field compensation, which allows to reach extremely low frequencies down to 200 Hz. Consequently, the frequency range is extended by two decades toward lower frequencies with respect to the commercial spectrometer and the obtained correlation function stretches over 10 decades in time and 8 in amplitude for molecular masses up to 220 Me. This establishes FC 1H NMR also at long times as competitive with DQ 1H NMR.
The analyses of the dipolar correlation function appear to support the applicability of the tube-reptation model. However, intramolecular and intermolecular relaxation contributions have to be discriminated and up to now the dominance of the first has been assumed implicitly. Therefore, isotopic blends of high-M protonated and deuterated PB are investigated, which allows to decompose the 1H master curves into intramolecular and intermolecular relaxation contributions. They reflect reorientational and translational dynamics, respectively. It is demonstrated that at long times or low frequencies the intermolecular contribution dominates. Consequently, the reorientational correlation function obtained from the intramolecular part exhibits a faster decay with the long-time exponent 0.49. This is ascertained by the FC 2H NMR relaxation of completely deuterated PB, which detects reorientational dynamics only. The observed exponent is significantly larger than 0.25 of regime II of the tube reptation model. Concomitantly, the segmental mean square displacement is attained from the intermolecular part following an approach by Kimmich and Fatkullin. The predicted power-laws of the tube-reptation model for the Rouse and constrained Rouse regimes are identified for the first time by FC NMR: a transition between the power-laws t^ 0.49 and t^0.19 is revealed, respectively. Thus, NMR relaxometry is designated as a method comparable to neutron scattering to study subdiffusion in polymer melts. In conclusion, the power-law predictions of the tube-reptation model are disclosed by the segmental mean square displacement, yet not by the reorientational correlation function. Thus, the simple tube-reptation model does not completely describe the microscopic dynamics of polymer melts.
Experimental classification of divertor detachment
- Avoiding damage of the divertor material by keeping the power load below a certain threshold is a major challenge for the operation of
future fusion devices such as ITER. For Tungsten, the foreseen ITER divertor target material, the
power load must be kept below 5 MW m^2 in continuous operation. This can in ITER only be achieved with the plasma
being detached or partially detached from the divertor.
Divertor detachment is characterized by a strong reduction of the ion flux to the target. With a reduction of the temperature,
achieved by increasing the main plasma density or by seeding additional impurities, volumetric processes such as charge exchange collisions
and recombination become dominant. These processes lead to a strong reduction of the ion flux and plasma pressure in front of the divertor target.
Although the single physical mechanisms leading to detachment seem to be understood, it was not yet possible to theoretically
simulate detachment correctly with respect to experimental observations. This means that some understanding of this process is still missing.
In the detached regime,
the region of high electron density is retracted from the target and a knowledge of the electron density distribution in the divertor
volume is necessary to understand the detachment process. In this context, a diagnostic determining the electron density in the
divertor volume, based on the spectroscopic measurement of the
Stark broadening of the Balmer lines, has been installed at ASDEX Upgrade. Initial problems with reflected stray-radiation have been
solved and first measurements were successfully compared for consistency with other diagnostics.
The detachment process was then investigated with an extensive set of density ramp discharges with different heating powers,
fuelling species and magnetic field directions. The density measurements in the divertor volume were combined with all other available
divertor diagnostics and a consistent picture of the detachment process was obtained. It was found that detachment is not a continuous
but undergoes three different states. During one of these states radiative fluctuations close to the X-point and high densities far away
from the separatrix occur. This is a situation which is not described by present day theoretical models.
Furthermore, it was shown that the conditions of both the inner and outer divertor are
strongly coupled and that the inner divertor even influences the outer divertor. This effect was not shown yet, neither experimentally
nor by theoretical simulations.
It was further discovered how additional puffing of nitrogen into the divertor, which removes power via radiation, changes the
detached divertor conditions and may even change the confined plasma conditions. The effect of an additional magnetic perturbation
field on the detachment process has also been investigated. Finally, an unstable situation was found, during which the divertor plasma
oscillates between two detachment states back and forth.
Secondary relaxation processes in neat and binary glass formers studied by 2H NMR spectroscopy
- The present study employs various solid state 2H NMR techniques to elucidate glassy dynamics in plastic crystals and binary mixtures of glass forming substances. We focus on the Johari-Goldstein beta-process, which not only plays a key role for the understanding of glassy dynamics in neat systems, but also in binary mixtures thereof.
The first part is devoted to the plastic crystalline (PC) phase of cyanocyclohexane. A 2D 2H NMR assessment regarding the alpha-process demonstrated that dynamics is not governed by the symmetry of the lattice, rather molecular reorientation in cyanocyclohexane can be modelled via the same distribution of small and large angular jumps as reported for many structural glass formers. Although the stimulated echo technique yields a strong temperature dependence of the latter fractions, it was shown that this effect can be rationalized via the time-window of the experiment and the inherent decoupling of jump-times within the distribution of angles. This analysis also holds in case of previously studied structural glass formers and questions the arise of a dynamical crossover at temperatures somewhat above Tg.
The beta-process of cyanocyclohexane below Tg is well described by models developed for the structural glass former toluene, where the C-2H bond is confined to the base circle of a cone, i.e. also the secondary relaxation is not significantly affected by the translational symmetry of the PC phase. As alpha- and beta-process do not merge in cyanocyclohexane, pronounced effects were observed at high temperatures: for the first time an additional minimum in the spin-lattice relaxation T1 reflecting the beta-process was found. Furthermore the solid-echo spectra at T>Tg exhibit an articulate and characteristic deviation from a Pake pattern over a broad temperature range. These fast motion limit line-shape effects allow for a direct determination of the spatial restriction: a model based on a Gaussian distribution of cone opening angles proved adequate for a detailed modelling of the spectral evolution. T1 was modelled by means of the spectral density from dielectric spectroscopy, the results in terms of the relaxation strength 1-S are in agreement with the line shape analysis. Hence the pronounced NMR effects naturally arise due to the non-merging beta-process in cyanocyclohexane and are in full agreement with an extension of previous models for the beta-process in structural glass formers at T<Tg. Furthermore the present study emphasizes the important role of the beta-process for glassy dynamics, as it demonstrates that a substantial fraction of correlation is lost via the beta-process at high temperatures in the absence of merging.
The second part addresses the dynamics of the glass former toluene in binary mixtures. Below Tg of neat toluene a pronounced concentration dependence of the beta-process was observed in mixtures of toluene and a polychlorinated biphenyl (PCB54). Whereas the distribution of correlation times remains unaltered, the relaxation strength of the process significantly decreases below a threshold toluene concentration of x=0.7. Stimulated echo experiments demonstrated that this attenuation arises from a fraction of toluene molecules, 1-fb, which do no longer exhibit a beta-process. This finding is in accordance with bi-exponential magnetization curves observed around Tg of the mixture. Hence the "islands of mobility" concept for the beta-process, refuted in the case of neat glass formers, was introduced in binary mixtures thereof.
A model was developed that links the fraction 1-fb to toluene molecules in a local PCB54 rich environment, which only exhibit the alpha-process of the latter, whereas the remainder of molecules reorient on a faster time scale (alpha'-process) and show a beta-process. This bimodal approach with two distinct toluene sub-ensembles was shown to explain the observed behaviour in virtually all NMR experiments, whereas an adaptation via a single broad distribution for the toluene motion was infeasible. The relative weight of the fractions is a function of concentration and temperature, as 2D NMR spectra demonstrated that exchange between the sub-ensembles exists. 2D NMR experiments furthermore show that toluene molecules in the mixtures reorient via the same mechanism as in the neat system - both sub-ensembles are governed by typical glassy dynamics.
To widen the validity of the present study, previous results from other binary mixtures containing toluene were reassessed: all features regarding the beta-process were recovered and its concentration dependence below Tg in diverse mixtures was successfully described within a simple lattice model. This dependence of the beta-process on the local toluene concentration provides strong arguments for a cooperativeness of the process, in contrast to the general perception.
Organization of Paramagnetic and Nonmagnetic Colloidal Particles in Ferrofluid
- In this thesis, I have studied magnetic dipolar interactions between paramagnetic and nonmagnetic colloidal particles immersed in a magnetic fluid under the influence of an external time dependent magnetic field. These interactions play an important role in colloidal self-assembly. As a result, of these interactions different forms of anisotropic superstructures evolve in 2-Dimension and 3-Dimension during the self-assembly process. The time dependent external magnetic field is an important controlling parameter for the self-assembly process. The interactions leads to a specific equilibrium positions of the paramagnetic and nonmagnetic particles with specific orientations of the magnetic moments. Three different colloidal systems immersed in ferrofluid with external time dependent magnetic field have been investigated. In each of them the effect of inter dipolar interactions on the particles is discussed. Three systems are arranged and discussed in three separate chapters. In chapter 3, an attempt has been made to study the diffusion of particles in a colloidal flower system and compare the diffusion of the petals of the flower with other single file diffusion in 1-dimension. Beside the long-range interactions, in chapter 4, we have studied the strength of the systems and order of phase transition taking place due to core size effects of self-assembled flower shaped magnetic colloidal clusters and diamagnetic clusters in a precessing magnetic field. In chapter 5, different anisotropic assemblies and colloidal phases are studies as a function of the composition mixture of paramagnetic and diamagnetic particles in an external time dependent magnetic field.
Active and Passive Transport at Interfaces
- In this thesis we studied different forms of transport at interfaces. Four different interfacial transport mechanisms have been investigated. In each of them one physical aspect of active and passive transport is discussed. The four systems are arranged and discussed in four separate chapters. In chapter 3 and 4 we study the effect of static or hydrodynamic interactions on the cross over from individual diffusion towards collective diffusion. In chapter 3 the diffusion of circular domains on a giant unilamellar vesicle is measured. By tracking the motion of hydrodynamic interacting domains on a curved membrane we determined whether it is possible to extract rheological properties of the bilayer membrane. A similar two dimensional system interacting via static dipole interactions is studied in chapter 4. A mixture of paramagnetic and nonmagnetic colloidal particles immersed into a diluted ferrofluid is self assembled into colloidal flowers. In this experiment the effect of static interactions on the modes of diffusion of the petals of the colloidal flower is investigated in a one dimensional system. The results are compared with the single file diffusion of a hard core interacting one dimensional system. In chapter 5, the effect of actively directing particles with fluctuating active forces in a symmetry broken environment is studied. We address the question how to competing symmetry breaking effects decide on the direction of motion. The system consists of paramagnetic colloidal particles placed into an aqueous solution above the liquid-solid interface of a magnetic garnet film. An external modulated field supplies the fluctuations and the symmetry is broken by tilting the external field with respect to the magnetic film and/or by a magnetic symmetry broken pattern of the magnetic film. The direction of motion of the paramagnetic colloids is measured and we give a theoretical explanation of why which symmetry breaking wins. The fluidization of a two dimensional solid to a two dimensional liquid via the yielding of the monolayer is studied in chapter 6. The monolayer is locally yielded with thermo capillary interactions by focusing a laser onto it. We investigate the yielding as a function of the chemical nature of the monolayer and determine the thermodynamic requirements necessary for thermo capillary yielding.
Dynamics and statistics of hydrodynamically interacting particles in laminar flows
- The subject of this thesis is the investigation of the dynamics and statistics of hydrodynamically interacting particles in low Reynolds number flows, which is discussed in three interrelated themes. The first theme focuses on polymer fractionation. With our basic model we explore the possibility to sort dumbbells with respect to their size using a two dimensional periodic potential. It turns out that the purely diffusive behavior of a dumbbell in this structured landscape is dominated by the ratio of two characteristic length scales, namely the wavelength of the potential l and the size of the dumbbell b. We explain why the diffusion constant in the potential plane shows a pronounced local maximum around l/b equal 3/2. Furthermore, the influence of the spring rigidity and the hydrodynamic interaction on the diffusive motion are examined as well as the dumbbell statistics. If the dumbbell is driven by an external flow through the periodic landscape two different kinds of motion occur: transport along a potential valley and a stair-like motion oblique to the trenches. In the latter case, the dumbbell jumps regularly to a neighboring valley which results in an effective deflection. The onset of the oblique movement as well as the deflection angle beta depend on the hydrodynamic interaction, on the ratio l/b, and on the Brownian motion of the beads. Especially the significant dependence of beta on l/b enables particle sorting. The results are published. The second theme deals with the Brownian dynamics in shear flows. Here, we investigate the correlations of particle fluctuations in order to characterize the direct interplay between thermal motion, hydrodynamic interactions, and non-uniform flows.With respect to the experimental implementation the particles are caught by harmonic potentials. First, we consider one trapped Brownian bead in linear shear and Poiseuille flows. The correlation functions of the particle’s position and velocity fluctuations are calculated analytically. The main result is the occurrence of shear-induced cross-correlations between orthogonal fluctuations in the shear plane which are asymmetric in time. Moreover, the positional probability distribution, P(r), of a single bead in both types of flow is determined. In Poiseuille flow, where no analytical solutions can be obtained, we use perturbation expansions to derive formulas for P(r) that are valuable for the analysis of experimental data. In the case of a linear shear flow, a connection between the static correlations and the distribution functions is derived which allows a consistency check between independent measurements. Considering a system with several Brownian particles it is obvious that hydrodynamic interactions influence the correlations. In order to investigate this effect, we calculate the positional correlation functions for a setup of two trapped Brownian beads which are exposed to a linear shear flow. As expected, the one-particle correlations change compared to the single particle case described above. They depend on the distance between the two beads. In addition, we find inter-particle correlations between orthogonal positional fluctuations of different particles. The structure of these new cross-correlations depends significantly on the relative orientation of the two beads in the shear flow. They can have zero, one, or two local extrema as a function of time. In collaboration with Prof. Wagner from Saarbrücken some of our predictions are already confirmed by experiments, where polystyrene beads are caught by optical traps and simultaneously exposed to linear shear flows in a special microfluidic device. The results are published and further investigations are in progress.The third theme concentrates on the rheology of colloidal suspensions. Our deterministic model system consists of Hookean dumbbells suspended in a confined Newtonian fluid under constant shear. We perform a numerical study using fluid particle dynamics simulations, where the effective viscosity of the suspension, eta, and the dumbbell statistics are determined. The investigations on the tumbling motion of a single dumbbell reveals that eta is influenced by three different contributions: the volume fraction occupied by the dumbbell, the hydrodynamic interaction between the beads, and elastic correlation effects. For a suspension of independent spheres we observe in our simulations that the viscosity, as a function of the volume fraction Phi, differs from the prediction of Einstein, Batchelor and Green if Phi becomes larger than 8%. Replacing the beads by dumbbells leads to an increase of eta , which depends significantly on the length of the springs connecting the two beads. The distribution function for the orientation angle of the dumbbells indicates the complex motion of the individual objects in the suspension, which may lead to the so-called elastic turbulence, as experimentally discovered by Groisman and Steinberg.
Holographic Investigation of Azobenzene-Containing Low-Molecular-Weight Compounds
- In the present thesis, holographic volume and surface relief gratings in azobenzene-containing low-molecular-weight compounds are investigated to obtain a broader understanding of this new class of material. Azobenzene chromophores undergo light-induced trans-cis-trans isomerization cycles leading to a reorientation of the long axis of the chromophores. If linearly polarized light is incident on the sample, these isomerizations result in a reorientation of this axis perpendicular to the light polarization. A holographic light grating, which can be formed by the interference of two coherent laser beams, leads to the inscription of a refractive-index modulation in the material. The azobenzene-containing low-molecular-weight compounds studied in this thesis consist of different building blocks: the core unit, the azobenzene chromophores with substituents, and the spacer and the linkage group between chromophore and core unit. These components can be used in a modular-design principle to synthesize a large library of low-molecular-weight compounds. Surprisingly, some of the investigated low-molecular-weight compounds form also a liquid-crystalline phase besides the amorphous phase as evidenced by polarized microscopy. If these liquid-crystalline compounds are prepared as solid films, however, they are quenched to an amorphous state. Upon reorientation of the azobenzene chromophores by illumination with a holographic light grating, a phase transition from the amorphous to an ordered state can be induced. This phase change in the latent liquid-crystalline low-molecular-weight compounds is very interesting for applications. The latent liquid-crystalline low-molecular-weight compounds show a post-development of the refractive-index modulation after the writing process. The holographic gratings are even stable at temperatures higher than the glass transition temperature, which further proves the light-induced formation of an ordered domain. In contrast to their polymeric counterparts, molecular materials are expected to show a faster response to light because of the absence of polymer chain entanglements. Therefore, molecular glasses can be used as blending material for photo-addressable polymers to improve the photo-sensitivity of the blend as compared to the pure polymer. The influence of the core and the substituent was investigated in low-molecular-weight compounds which do not form liquid-crystalline phases. An azobenzene-containing diblock copolymer for holographic data storage consists of an inert majority block and a minority block containing the covalently bound photo-sensitive azobenzene chromophores. Blending a few weight percent of the optimized molecular glass to the diblock copolymer leads to an increase of sensitivity with increasing content of the molecular glass, mainly because the writing time to the maximum of the refractive-index modulation decreased. The increase of the sensitivity is much larger than the observed rise of the refractive-index modulation due to the higher concentration of azobenzene chromophores. It was demonstrated that the shorter writing times are not caused by thermal effects, the molecules of the molecular glass in the inert block, or by changes of the free volume or the morphology, but that they are due to the azobenzene chromophores of the molecular glass in the minority block. They reorient faster than the chromophores attached to the polymer backbone and, thereby create free volume. Additionally, they can assist the reorientation of the azobenzene chromophores bound to the polymer by cooperative effects, i.e. dipolar and steric interactions. Both effects result in shorter writing time and higher sensitivity of the system. In a blend containing two weight percent of the molecular glass, the inscribed gratings are still long-term stable and the sensitivity increases by a factor of 1.7 as compared to the pure diblock copolymer. Upon illumination of an azobenzene-containing material with a holographic light grating, besides the volume grating, also a surface relief grating can develop. Surface modulations with heights of up to 600 nm were achieved in molecular glasses. It was found that the build-up of the surface relief grating depends on the electrical susceptibility of the material at the optical frequency of the laser and the polarization of the laser beams. These experimental findings are in agreement with the gradient force model. According to this theory, the macroscopic material transport results from the forces on the polarized material in the electrical field gradient caused by the holographic light grating. For many applications it is important that the holographically produced surface relief gratings can be transferred to polymer surfaces. Replica molding can be used to easily copy the surface modulations to e.g. polycarbonate.
Modulation of Incommensurately Modulated Structures Studied by the Maximum Entropy Method
- In this thesis, modulated properties of incommensurately modulated crystals are studied by the Maximum Entropy Method (MEM). This was done exemplarily on the compounds Rubidium tetrachlorozincate and Chromium pyrophosphate. To do so, the MEM derived (3+1)-dimensional superspace electron density was analysed to receive information on atomic positions and their modulation, and structure refinement by the method of least-squares and interpretation of the difference-Fourier maps were performed to better describe the atomic displacement parameters (ADPs) and to improve the applied structural models. All the MEM calculations are done by the computer program BayMEM. The analysis of this MEM reconstructed density map is done by the computer program EDMA. Our results suggest that the modulation of harmonic ADPs, anharmonic ADPs and its modulation form an intrinsic part of incommensurately modulated structures. We have shown that with a data set of certain resolution and satellite reflections of higher order, the inclusion of modulation of harmonic ADPs, the anharmonic ADPs and the modulation of anharmonic ADPs can significantly improve the fit of the structure model to the diffraction data. Such model then better represents the true nature of the structure under investigation.
Bogoliubov Excitations of Inhomogeneous Bose-Einstein Condensates
- In this thesis, different aspects of interacting ultracold bosons in presence of inhomogeneous external potentials are studied. The first part deals with repulsively interacting Bose-Einstein condensates in speckle disorder potentials. In the Bogoliubov approach, the many-body problem is split into the Gross-Pitaevskii condensate (mean-field) and the Bogoliubov excitations, which are bosonic quasiparticles. The disorder potential causes an imprint in the condensate, which makes the Hamiltonian for the Bogoliubov excitations inhomogeneous. The inhomogeneous Bogoliubov Hamiltonian is the starting point for a diagrammatic perturbation theory that leads to the renormalized Bogoliubov dispersion relation. From this effective dispersion relation, physical quantities are derived, e.g. the mean free path and disorder corrections to the speed of sound and the density of states. The analytical results are supported by a numerical integration of the Gross-Pitaevskii equation and by an exact diagonalization of the disordered Bogoliubov problem. In the second part, Bloch oscillations of Bose-Einstein condensates in presence of time-dependent interactions are considered. In general, the interaction leads to dephasing and destroys the Bloch oscillation. Feshbach resonances allow the atom-atom interaction to be manipulated as function of time. In particular, modulations around zero are considered. Different modulations lead to very different behavior: either the wave packet evolves periodically with time or it decays rapidly. The former is explained by a periodic time-reversal argument. The decay in the other cases can be described by a dynamical instability with respect to small perturbations, which are similar to the Bogoliubov excitations in the first part.