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Matter-wave Optics of Dark-state Polaritons: Applications to Interferometry and Quantum Information
(2006)

The present work "Materwave Optics with Dark-state Polaritons: Applications to Interferometry and Quantum Information" deals in a broad sense with the subject of dark-states and in particular with the so-called dark-state polaritons introduced by M. Fleischhauer and M. D. Lukin. The dark-state polaritons can be regarded as a combined excitation of electromagnetic fields and spin/matter-waves. Within the framework of this thesis the special optical properties of the combined excitation are studied. On one hand a new procedure to spatially manipulate and to increase the excitation density of stored photons is described and on the other hand the properties are used to construct a new type of Sagnac Hybrid interferometer. The thesis is devided into four parts. In the introduction all notions necessary to understand the work are described, e.g.: electromagnetically induced transparency (EIT), dark-state polaritons and the Sagnac effect. The second chapter considers the method developed by A. Andre and M. D. Lukin to create stationary light pulses in specially dressed EIT-media. In a first step a set of field equations is derived and simplified by introducing a new set of normal modes. The absorption of one of the normal modes leads to the phenomenon of pulse-matching for the other mode and thereby to a diffusive spreading of its field envelope. All these considerations are based on a homogeneous field setup of the EIT preparation laser. If this restriction is dismissed one finds that a drift motion is superimposed to the diffusive spreading. By choosing a special laser configuration the drift motion can be tailored such that an effective force is created that counteracts the spreading. Moreover, the force can not only be strong enough to compensate the diffusive spreading but also to exceed this dynamics and hence to compress the field envelope of the excitation. The compression can be discribed using a Fokker-Planck equation of the Ornstein-Uhlenbeck type. The investigations show that the compression leads to an excitation of higher-order modes which decay very fast. In the last section of the chapter this exciation will be discussed in more detail and conditions will be given how the excitation of higher-order modes can be avoided or even suppressed. All results given in the chapter are supported by numerical simulatons. In the third chapter the matterwave optical properties of the dark-state polaritons will be studied. They will be used to construct a light-matterwave hybrid Sagnac interferometer. First the principle setup of such an interferometer will be sketched and the relevant equations of motion of light-matter interaction in a rotating frame will be derived. These form the basis of the following considerations of the dark-state polariton dynamics with and without the influence of external trapping potentials on the matterwave part of the polariton. It will be shown that a sensitivity enhancement compared to a passive laser gyroscope can be anticipated if the gaseous medium is initially in a superfluid quantum state in a ring-trap configuration. To achieve this enhancement a simultaneous coherence and momentum transfer is furthermore necessary. In the last part of the chapter the quantum sensitivity limit of the hybrid interferometer is derived using the one-particle density matrix equations incorporating the motion of the particles. To this end the Maxwell-Bloch equations are considered perturbatively in the rotation rate of the noninertial frame of reference and the susceptibility of the considered 3-level \(\Lambda\)-type system is derived in arbitrary order of the probe-field. This is done to determine the optimum operation point. With its help the anticipated quantum sensitivity of the light-matterwave hybrid Sagnac interferometer is calculated at the shot-noise limit and the results are compared to state-of-the-art laser and matterwave Sagnac interferometers. The last chapter of the thesis originates from a joint theoretical and experimental project with the AG Bergmann. This chapter does no longer consider the dark-state polaritons of the last two chapters but deals with the more general concept of dark states and in particular with the transient velocity selective dark states as introduced by E. Arimondo et al. In the experiment we could for the first time measure these states. The chapter starts with an introduction into the concept of velocity selective dark states as they occur in a \(\Lambda\)-configuration. Then we introduce the transient velocity selective dark-states as they occur in an particular extension of the \(\Lambda\)-system. For later use in the simulations the relevant equations of motion are derived in detail. The simulations are based on the solution of the generalized optical Bloch equations. Finally the experimental setup and procedure are explained and the theoretical and experimental results are compared.

In this study, 27 marine bacteria were screened for production of bioactive metabolites. Two strains from the surface of the soft coral Sinularia polydactyla, collected from the Red Sea, and three strains from different habitats in the North Sea were selected as a promising candidates for isolation of antimicrobial substances. A total of 50 compounds were isolated from the selected bacterial strains. From these metabolites 25 substances were known from natural sources, 10 substances were known as synthetic chemical and herein are reported as new natural products, and 13 metabolites are new. Two substances are still under elucidation. All new compounds were chemically and biologically characterized. Pseudoalteromonas sp. T268 produced simple phenol and oxindole derivatives. Production of homogentisic acid and WZ 268S-6 from this bacteria was affected by the salinity stress. WZ 268S-6 shows antimicrobial and cytotoxic activities. Its target is still unclear. Isolation of isatin from this strain points out for the possibility of using this substance as a chemotaxonomical marker for Alteromonas-like bacteria. A large number of nitro-substituted aromatic compounds were isolated from both Salegentibacter sp. T436 and Vibrio sp. WMBA1-4. They may be derived from metabolism of phenylalanine or tyrosine. From Salegentibacter sp. T436, 24 compounds were isolated, of which four compounds are new and six compounds were known as synthetic chemicals. WZ 436S-16 (dinitro-β-styrene) is the most potent antimicrobial and cytotoxic compound. It inhibits the oxygen uptake by N. coryli and causes apoptosis in the human promyelocytic leukaemia (HL-60 cells). From Vibrio sp. WMBA1-4, 13 new alkaloids were isolated, of which four were known as synthetic products and herein are reported as new substances from natural sources. The majority of these compounds show antimicrobial and cytotoxic activities. The cytotoxic activity of WMB4S-11 against the mouse lymphocytic leukaemia (L1210 cells) is due to the inhibition in the protein biosynthesis, while the remaining cytotoxic alkaloids have no effect on the synthesis of macromolecules in this cell line. The antibacterial activity of WMB4S-2, -11, -12, -13 and the antifungal activity of WMB4S-9 are not due to the inhibition in the macromolecules biosynthesis or in the oxygen uptake by the microorganisms. The biological activity of these nitro-aromatic compounds from Salegentibacter sp. T436 and Vibrio sp. WMBA1-4 is influenced by the presence of a nitro group and its position in respect to the hydroxyl group, number of the nitro groups, and the type of substitutions on the side chain. In diaryl-maleimide derivatives, types and position of substitution on the aryl rings, on the maleimide moity, and the hydrophobicity of the aryl ring itself lead to variations in the extent of the bioactivity of these derivatives. This is the first time that vibrindole (WMB4S-14) and turbomycin B or its noncationic form (WMB4S-15), isolated from Vibrio sp., are reported as cytotoxic compounds. WMB4S-15 inhibits the biosynthesis of macromolecules in L1210 cells. The structural similarity between some of the metabolites in this study and previously reported compounds from sponges, ascidians, and bryozoan indicates that the microbial origin of these compounds must be considered.

The topic of this thesis is the coupling of an atomistic and a coarse scale region in molecular dynamics simulations with the focus on the reflection of waves at the interface between the two scales and the velocity of waves in the coarse scale region for a non-equilibrium process. First, two models from the literature for such a coupling, the concurrent coupling of length scales and the bridging scales method are investigated for a one dimensional system with harmonic interaction. It turns out that the concurrent coupling of length scales method leads to the reflection of fine scale waves at the interface, while the bridging scales method gives an approximated system that is not energy conserving. The velocity of waves in the coarse scale region is in both models not correct. To circumvent this problems, we present a coupling based on the displacement splitting of the bridging scales method together with choosing appropriate variables in orthogonal subspaces. This coupling allows the derivation of evolution equations of fine and coarse scale degrees of freedom together with a reflectionless boundary condition at the interface directly from the Lagrangian of the system. This leads to an energy conserving approximated system with a clear separation between modeling errors an errors due to the numerical solution. Possible approximations in the Lagrangian and the numerical computation of the memory integral and other numerical errors are discussed. We further present a method to choose the interpolation from coarse to atomistic scale in such a way, that the fine scale degrees of freedom in the coarse scale region can be neglected. The interpolation weights are computed by comparing the dispersion relations of the coarse scale equations and the fully atomistic system. With this new interpolation weights, the number of degrees of freedom can be drastically reduced without creating an error in the velocity of the waves in the coarse scale region. We give an alternative derivation of the new coupling with the Mori-Zwanzig projection operator formalism, and explain how the method can be extended to non-zero temperature simulations. For the comparison of the results of the approximated with the fully atomistic system, we use a local stress tensor and the energy in the atomistic region. Examples for the numerical solution of the approximated system for harmonic potentials are given in one and two dimensions.

Traffic flow on road networks has been a continuous source of challenging mathematical problems. Mathematical modelling can provide an understanding of dynamics of traffic flow and hence helpful in organizing the flow through the network. In this dissertation macroscopic models for the traffic flow in road networks are presented. The primary interest is the extension of the existing macroscopic road network models based on partial differential equations (PDE model). In order to overcome the difficulty of high computational costs of PDE model an ODE model has been introduced. In addition, steady state traffic flow model named as RSA model on road networks has been dicsussed. To obtain the optimal flow through the network cost functionals and corresponding optimal control problems are defined. The solution of these optimization problems provides an information of shortest path through the network subject to road conditions. The resulting constrained optimization problem is solved approximately by solving unconstrained problem invovling exact penalty functions and the penalty parameter. A good estimate of the threshold of the penalty parameter is defined. A well defined algorithm for solving a nonlinear, nonconvex equality and bound constrained optimization problem is introduced. The numerical results on the convergence history of the algorithm support the theoretical results. In addition to this, bottleneck situations in the traffic flow have been treated using a domain decomposition method (DDM). In particular this method could be used to solve the scalar conservation laws with the discontinuous flux functions corresponding to other physical problems too. This method is effective even when the flux function presents more than one discontinuity within the same spatial domain. It is found in the numerical results that the DDM is superior to other schemes and demonstrates good shock resolution.

Biological Soil Crusts (BSCs), composed of lichens, mosses, green algae, microfungi and cyanobacteria are an ecological important part of the perennial landcover of many arid and semiarid regions (Belnap et al. 2001a), (Büdel 2002). In many arid and hyperarid areas BSCs form the only perennial "vegetation cover" largely due to their extensive resistance to drought (Lange et al. 1975). For the Central Namib Desert (Namibia), BSCs consisting of extraordinary vast lichen communities were recently mapped and classified into six morphological classes for a coastal area of 350 km x 60 km. Embedded into the project "BIOTA" (www.biota-africa.org) financed by the German Federal Ministry of Education and Research the study was undertaken in the framework of the PhD thesis by Christoph Schultz. Some of these lichen communities grouped together in so called "lichen fields" have already been studied concerning their ecology and diversity in the past (Lange et al. 1994), (Loris & Schieferstein 1992), (Loris et al. 2004), (Ullmann & Büdel 2001a), (Wessels 1989). Multispectral LANDSAT 7 ETM+ and LANDSAT 5 TM satellite imagery was utilized for an unitemporal supervised classification as well as for the establishment of a monitoring based on a combined retrospective supervised classification and change detection approach (Bock 2003), (Weiers et al. 2003). Results comprise the analysis of the mapped distribution of lichen communities for the Central Namib Desert as of 2003 as well as reconstructed distributions for the years 2000, 1999, 1992 and 1991 derived from retrospective supervised classification. This allows a first monitoring of the disturbance, destruction and recovery of the lichen communities in these arid environments including the analysis of the major abiotic processes involved. Further analysis of these abiotic processes is key for understanding the influence of Namib lichen communities on overall aeolian and water induced erosion rates, nutrient cycles, water balance and pedogenic processes (Belnap & Gillette 1998), (Belnap et al. 2001b), (Belnap 2001c), (Evans & Lange 2001), (McKenna Neumann & Maxwell 1999). In order to aid the understanding of these processes SRTM digital elevation model data as well as climate data sets were used as reference. Good correlation between geomorphological form elements as well as hydrological drainage system and the disturbance patterns derived from individual post classification change comparisons between the timeframes could be observed. Conjoined with the climate data sets sporadic foehn-like windstorms as well as extraordinary precipitation events were identified to largely affect the distribution patterns of lichen communities. Therefore the analysis and monitoring of the diversity, distribution and spatiotemporal change of Central Namib BSCs with the means of Remote Sensing and GIS applications proof to be important tools to create further understanding of desertification and degradation processes in these arid regions.

The validity of formulas w.r.t. a specification over first-order logic with a semantics based on all models is semi-decidable. Therefore, we may implement a proof procedure which finds a proof for every valid formula fully automatically. But this semantics often lacks intuition: Some pathological models such as the trivial model may produce unexpected results w.r.t. validity. Instead, we may consider just a class of special models, for instance, the class of all data models. Proofs are then performed using induction. But, inductive validity is not semi-decidable -- even for first-order logic. This theoretical drawback manifests itself in practical limitations: There are theorems that cannot be proved by induction directly but only generalizations can be proved. For their definition, we may have to extend the specification. Therefore, we cannot expect to prove interesting theorems fully automatically. Instead, we have to support user-interaction in a suitable way. In this thesis, we aim at developing techniques that enhance automatic proof control of (inductive) theorem provers and that enable user-interaction in a suitable way. We integrate our new proof techniques into the inductive theorem prover QuodLibet and validate them with various case studies. Essentially, we introduce the following three proof techniques: -We integrate a decision procedure for linear arithmetic into QuodLibet in a close way by defining new inference rules that perform the elementary steps of the decision procedure. This allows us to implement well-known heuristics for automatic proof control. Furthermore, we are able to provide special purpose tactics that support the manual speculation of lemmas if a proof attempt gets stuck. The integration improves the ability of the theorem prover to prove theorems automatically as well as its efficiency. Our approach is competitive with other approaches regarding efficiency; it provides advantages regarding the speculation of lemmas. -The automatic proof control searches for a proof by applying inference rules. The search space is not only infinite, but grows dramatically with the depth of the search. In contrast to this, checking and analyzing performed proofs is very efficient. As the search space also has a high redundancy, it is reasonable to reuse subproofs found during proof search. We define new notions for the contribution of proof steps to a proof. These notions enable the derivation of pruned proofs and the identification of superfluous subformulas in theorems. A proof may be reused in two ways: upward propagation prunes a proof by eliminating superfluous proof steps; sideward reuse closes an open proof obligation by replaying an already found proof. -For interactive theorem provers, it is essential not only to prove automatically as many lemmas as possible but also to restrict proof search in such a way that the proof process stops within a reasonable amount of time. We introduce different markings in the goals to be proved and the lemmas to be applied to restrict proof search in a flexible way: With a forbidden marking, we can simulate well-known approaches for applying conditional lemmas. A mandatory marking provides a new heuristics which is inspired by local contribution of proof steps. With obligatory and generous markings, we can fine-tune the degree of efficiency and extent of proof search manually. With an elaborate case study, we show the benefits of the different techniques, in particular the synergetic effect of their combination.

This thesis discusses methods for the classification of finite projective planes via exhaustive search. In the main part the author classifies all projective planes of order 16 admitting a large quasiregular group of collineations. This is done by a complete search using the computer algebra system GAP. Computational methods for the construction of relative difference sets are discussed. These methods are implemented in a GAP-package, which is available separately. As another result --found in cooperation with U. Dempwolff-- the projective planes defined by planar monomials are classified. Furthermore the full automorphism group of the non-translation planes defined by planar monomials are classified.

The new international capital standard for credit institutions (“Basel II”) allows banks to use internal rating systems in order to determine the risk weights that are relevant for the calculation of capital charge. Therefore, it is necessary to develop a system that enfolds the main practices and methods existing in the context of credit rating. The aim of this thesis is to give a suggestion of setting up a credit rating system, where the main techniques used in practice are analyzed, presenting some alternatives and considering the problems that can arise from a statistical point of view. Finally, we will set up some guidelines on how to accomplish the challenge of credit scoring. The judgement of the quality of a credit with respect to the probability of default is called credit rating. A method based on a multi-dimensional criterion seems to be natural, due to the numerous effects that can influence this rating. However, owing to governmental rules, the tendency is that typically one-dimensional criteria will be required in the future as a measure for the credit worthiness or for the quality of a credit. The problem as described above can be resolved via transformation of a multi-dimensional data set into a one-dimensional one while keeping some monotonicity properties and also keeping the loss of information (due to the loss of dimensionality) at a minimum level.

Uncoupling protein1 (UCP1) in brown adipose tissue was discovered earlier as the main uncoupling source of respiration. We describe the basic facts and a modest contribution of our group to the area of research on mitochondrial uncoupling proteins. After defining the terms uncoupling, leak, proton-mediated uncoupling, we discuss the assumption that due to its low abundance, uncoupling protein 2 (UCP2) can provide only mild uncoupling, i.e. can decrease the proton motive force by several mV only. A fatty acid cycling mechanism is described as a plausible explanation for the protonophoretic function of all uncoupling proteins together with our experiments supporting it. A speculation for the phylogenesis of all uncoupling proteins can be deduced by estimated UCP2 content in several tissues, and details of its activation are explained on the basis of our experiments. In the present study a solubilization and refolding method for UCP2 from inclusion bodies was developed and characterized. As it was known and also demonstrated from previous experiments on UCP1 that fatty acids are substrates, we used the same procedure to study the function of UCP2. Utilizing spin-labelled fatty acids (SLFA) for our experiments we demonstrated the binding of fatty acids to UCP2, and the competition of other natural fatty acids like oleic acid, palmitic acid, arachidonic acid and eicosatrienoic acid to the preformed complex emphasizes the presence of a fatty acid binding site for mitochondrial UCP2. The findings were observed by EPR spectroscopy where the highly immobilized spectra with presence of spin-labelled fatty acid eventually end up as free spin label spectra with a particular concentration of the natural fatty acid added to the UCP2 bound with spin-labelled fatty acid. This fits in significantly with the earlier findings of UCP1 and also leads to assumption of functional explanation about the physiological relevance between the uncoupling proteins functions. The present study, in which representative and sensitive parameters for EPR spectroscopy were established, at the same time describes the concentration effects of fatty acids upon the protein bound with spin-labelled fatty acids which are much of importance in comparison to physiological levels, being in the micromolar range (µM) as compared with milli molar (mM) as for UCP1 previously. In appropriate examples, different fatty acids are used and compared with competitors like alkylsulfonates also emphasizing the function of the protein. And the studies with the effect of nucleotides inhibition demonstrate that there exists a putative binding site for fatty acids. Much significance lies in demonstration with the spin-labelled-ATP studies where competition of ATP to the protein bound to spin-labelled ATP explains about the inhibition effect of nucleotides on the UCP2. So the present study applies different methods for the functional characterization of UCP2. The studies of natural fatty acids and alkylsulfonates with UCP2 bound to spin-labelled fatty acid, and study of nucleotide inhibition on UCP2 are closely related and give the much awaited answer to the question of functional similarities between UCP1 and UCP2. This supports the discussion of many groups which predict the functional similarity between these two proteins based upon sequence homology. Also many attempts have been reported in literature to explain the physiological functional relevance where by this present study can also be added to as we now suppose from the present conclusions of our experiments.

This work deals with the mathematical modeling and numerical simulation of the dynamics of a curved inertial viscous Newtonian fiber, which is practically applicable to the description of centrifugal spinning processes of glass wool. Neglecting surface tension and temperature dependence, the fiber flow is modeled as a three-dimensional free boundary value problem via instationary incompressible Navier-Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the fiber center-line with the inner viscous transport. The physically reasonable form of the one-dimensional fiber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms. For the numerical simulation of the derived model a finite volume code is developed. The results of the numerical scheme for high Reynolds numbers are validated by comparing them with the analytical solution of the inviscid problem. Moreover, the influence of parameters, like viscosity and rotation on the fiber dynamics are investigated. Finally, an application based on industrial data is performed.