08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access 3D direct laser writing of highly absorptive photoresist for miniature optical apertures(2022) Schmid, Michael D.; Toulouse, Andrea; Thiele, Simon; Mangold, Simon; Herkommer, Alois; Giessen, HaraldThe importance of 3D direct laser writing as an enabling technology increased rapidly in recent years. Complex micro-optics and optical devices with various functionalities are now feasible. Different possibilities to increase the optical performance are demonstrated, for example, multi-lens objectives, a combination of different photoresists, or diffractive optical elements. It is still challenging to create fitting apertures for these micro optics. In this work, a novel and simple way to create 3D-printed opaque structures with a highly absorptive photoresist is introduced, which can be used to fabricate microscopic apertures increasing the contrast of 3D-printed micro optics and enabling new optical designs. Both hybrid printing by combining clear and opaque resists, as well as printing transparent optical elements and their surrounding opaque apertures solely from a single black resist by using different printing thicknesses are demonstrated.Item Open Access 3D printed micro-optics for quantum technology: Optimised coupling of single quantum dot emission into a single-mode fibre(2021) Sartison, Marc; Weber, Ksenia; Thiele, Simon; Bremer, Lucas; Fischbach, Sarah; Herzog, Thomas; Kolatschek, Sascha; Jetter, Michael; Reitzenstein, Stephan; Herkommer, Alois; Michler, Peter; Portalupi, Simone Luca; Giessen, HaraldItem Open Access 3D printed stacked diffractive microlenses(2019) Thiele, Simon; Pruss, Christof; Herkommer, Alois; Giessen, HaraldItem Open Access 3D stimulated Raman spectral imaging of water dynamics associated with pectin-glycocalyceal entanglement(2023) Floess, Moritz; Steinle, Tobias; Werner, Florian; Wang, Yunshan; Wagner, Willi Linus; Steinle, Verena; Liu, Betty; Zheng, Yifan; Chen, Zi; Ackermann, Maximilian; Mentzer, Steven J.; Giessen, HaraldItem Open Access 3D-printed miniature spectrometer for the visible range with a 100 × 100 μm2 footprint(2021) Toulouse, Andrea; Drozella, Johannes; Thiele, Simon; Giessen, Harald; Herkommer, AloisItem Open Access Absorbing state phase transition with Clifford circuits(2024) Makki, Nastasia; Lang, Nicolai; Büchler, Hans PeterItem Open Access Adaptive piecewise Poly-Sinc methods for ordinary differential equations(2022) Khalil, Omar; El-Sharkawy, Hany; Youssef, Maha; Baumann, GerdWe propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. Our work extends the adaptive piecewise Poly-Sinc method to function approximation, for which we derived an a priori error estimate for our adaptive method and showed its exponential convergence in the number of iterations. In this work, we show the exponential convergence in the number of iterations of the a priori error estimate obtained from the piecewise collocation method, provided that a good estimate of the exact solution of the ordinary differential equation at the Sinc points exists. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on regular and stiff ordinary differential equations.Item Open Access Addressing single nuclear spins quantum memories by a central electron spin(2022) Vorobyov, Vadim; Javadzade, Javid; Joliffe, Matthew; Kaiser, Florian; Wrachtrup, JörgNuclei surrounding single electron spins are valuable resources for quantum technology. For application in this area, one is often interested in weakly coupled nuclei with coupling strength on the order of a few 10-100 kHz. In this paper, we compare methods to address single nuclear spins with this type of hyperfine coupling to a single electron spin. To achieve the required spectral resolution, we specifically focus on two methods, namely dynamical decoupling and correlation spectroscopy. We demonstrate spectroscopy of two single nuclear spins and present a method to derive components of their hyperfine coupling tensor from those measurements.Item Open Access Algebraic conditions for conformal superintegrability in arbitrary dimension(2024) Kress, Jonathan; Schöbel, Konrad; Vollmer, AndreasWe consider second order (maximally) conformally superintegrable systems and explain how the definition of such a system on a (pseudo-)Riemannian manifold gives rise to a conformally invariant interpretation of superintegrability. Conformal equivalence in this context is a natural extension of the classical (linear) Stäckel transform, originating from the Maupertuis-Jacobi principle. We extend our recently developed algebraic geometric approach for the classification of second order superintegrable systems in arbitrarily high dimension to conformally superintegrable systems, which are presented via conformal scale choices of second order superintegrable systems defined within a conformal geometry. For superintegrable systems on constant curvature spaces, we find that the conformal scales of Stäckel equivalent systems arise from eigenfunctions of the Laplacian and that their equivalence is characterised by a conformal density of weight two. Our approach yields an algebraic equation that governs the classification under conformal equivalence for a prolific class of second order conformally superintegrable systems. This class contains all non-degenerate examples known to date, and is given by a simple algebraic constraint of degree two on a general harmonic cubic form. In this way the yet unsolved classification problem is put into the reach of algebraic geometry and geometric invariant theory. In particular, no obstruction exists in dimension three, and thus the known classification of conformally superintegrable systems is reobtained in the guise of an unrestricted univariate sextic. In higher dimensions, the obstruction is new and has never been revealed by traditional approaches.Item Open Access Alignment-free difference frequency light source tunable from 5 to 20 µm by mixing two independently tunable OPOs(2020) Mörz, Florian; Steinle, Tobias; Linnenbank, Heiko; Steinmann, Andy; Giessen, HaraldTunable mid-infrared ultrashort lasers have become an essential tool in vibrational spectroscopy in recent years. They enabled and pushed a variety of spectroscopic applications due to their high brilliance, beam quality, low noise, and accessible wavelength range up to 20 µm. Many state-of-the-art devices apply difference frequency generation (DFG) to reach the mid-infrared spectral region. Here, birefringent phase-matching is typically employed, resulting in a significant crystal rotation during wavelength tuning. This causes a beam offset, which needs to be compensated to maintain stable beam pointing. This is crucial for any application. In this work, we present a DFG concept, which avoids crystal rotation and eliminates beam pointing variations over a broad wavelength range. It is based on two independently tunable input beams, provided by synchronously pumped parametric seeding units. We compare our concept to the more common DFG approach of mixing the signal and idler beams from a single optical parametric amplifier (OPA) or oscillator (OPO). In comparison, our concept enhances the photon efficiency of wavelengths exceeding 11 µm more than a factor of 10 and we still achieve milliwatts of output power up to 20 µm. This concept enhances DFG setups for beam-pointing-sensitive spectroscopic applications and can enable research at the border between the mid- and far-IR range due to its highly efficient performance.Item Open Access Analysis of target data-dependent greedy kernel algorithms : convergence rates for f-, f· P- and f/P-greedy(2022) Wenzel, Tizian; Santin, Gabriele; Haasdonk, BernardData-dependent greedy algorithms in kernel spaces are known to provide fast converging interpolants, while being extremely easy to implement and efficient to run. Despite this experimental evidence, no detailed theory has yet been presented. This situation is unsatisfactory, especially when compared to the case of the data-independent P-greedy algorithm, for which optimal convergence rates are available, despite its performances being usually inferior to the ones of target data-dependent algorithms. In this work, we fill this gap by first defining a new scale of greedy algorithms for interpolation that comprises all the existing ones in a unique analysis, where the degree of dependency of the selection criterion on the functional data is quantified by a real parameter. We then prove new convergence rates where this degree is taken into account, and we show that, possibly up to a logarithmic factor, target data-dependent selection strategies provide faster convergence. In particular, for the first time we obtain convergence rates for target data adaptive interpolation that are faster than the ones given by uniform points, without the need of any special assumption on the target function. These results are made possible by refining an earlier analysis of greedy algorithms in general Hilbert spaces. The rates are confirmed by a number of numerical examples.Item Open Access Analysis of the acoustlc transients in the pulse response of the linear electro-optic effect(1976) Veeser, Hermann; Bogner, Udo; Eisenmenger, WolfgangThe pulse response of the linear electro-optic effect is investigated with high temporal and spatial resolution in KDP, KD*P, and biaxial LiCOOH · H2O. Experimental results, which are explained theoretically, show that the piezo-optic transients induced by the piezoelectric effect, are generated by stress release waves. Starting from the surfaces, these excite by reflection, diffraction, and superposition, due to the finite crystal dimensions, normal vibration modes too. It is shown that the direct electro-optic effect can be measured for all crystal classes at the beginning of the pulse response. The pulse method also yields static electro-optic, piezo-optic, and elastic constants. The values of r63, r63, p66 and c66 measured in KDP, agree well with those of other authors. Measurement of the direct electro-optic effect of LiCOOH · H2O in some directions yields values within 1 to 4 × 10-12 m/V.Item Open Access Analysis of the fine structure of the D‐exciton shell in cuprous oxide(2021) Heckötter, Julian; Rommel, Patric; Main, Jörg; Aßmann, Marc; Bayer, ManfredThe exciton states in cuprous oxide show a pronounced fine structure splitting associated with the crystal environment and the resulting electronic band structure. High‐resolution spectroscopy reveals an especially pronounced splitting of the yellow D excitons with one state pushed above any other state with the same principal quantum number. This large splitting offset is related to a strong mixing of these D states with the 1S exciton of the green series, as suggested by previously published calculations. Here, a detailed comparison of this theory with experimental data is given, which leads to a complete reassignment of the experimentally observed D exciton lines. The origin of different amounts of green admixture to D‐envelope states is deduced by analyzing the different terms of the Hamiltonian. The yellow-green mixing leads to level repulsion and induces an exchange interaction splitting to D‐envelope states, from which one of them becomes the highest state within each multiplet. Furthermore, the assignment of D exciton states according to their total angular momentum F is given and corrects an earlier description given in a former study.Item Open Access Analysis of the phonon spectrum emitted by superconducting Al-tunneling junctions at high quasiparticle injection rates(1981) Welte, Michael; Eisenmenger, WolfgangThe phonon spectrum emitted by superconducting Al-tunneling junctions is analyzed by experiments, in which two junctions of different energy gaps are used as phonon generator and detector. The energy gap of the Al-films is varied by the evaporation conditions. The experiments show clearly that the phonon spectrum and the quasiparticle distributions in the generator are strongly nonthermal and depend markedly on the primary tunneling injection. At high injection rates also significant consequences of gap reductions and instabilities are observed.Item Open Access An approach to quantum physics teaching through analog experiments(2022) Aehle, Stefan; Scheiger, Philipp; Cartarius, HolgerWith quantum physics being a particularly difficult subject to teach because of its contextual distance from everyday life, the need for multiperspective teaching material arises. Quantum physics education aims at exploring these methods but often lacks physical models and haptic components. In this paper, we provide two analog models and corresponding teaching concepts that present analogies to quantum phenomena for implementation in secondary school and university classrooms: While the first model focuses on the polarization of single photons and the deduction of reasoning tools for elementary comprehension of quantum theory, the second model investigates analog Hardy experiments as an alternative to Bell’s theorem. We show how working with physical models to compare classical and quantum perspectives has proven helpful for novice learners to grasp the abstract nature of quantum experiments and discuss our findings as an addition to existing quantum physics teaching concepts.Item Open Access Approximation of a two‐dimensional Gross-Pitaevskii equation with a periodic potential in the tight‐binding limit(2024) Gilg, Steffen; Schneider, GuidoThe Gross-Pitaevskii (GP) equation is a model for the description of the dynamics of Bose-Einstein condensates. Here, we consider the GP equation in a two‐dimensional setting with an external periodic potential in the x‐direction and a harmonic oscillator potential in the y‐direction in the so‐called tight‐binding limit. We prove error estimates which show that in this limit the original system can be approximated by a discrete nonlinear Schrödinger equation. The paper is a first attempt to generalize the results from [19] obtained in the one‐dimensional setting to higher space dimensions and more general interaction potentials. Such a generalization is a non‐trivial task due to the oscillations in the external periodic potential which become singular in the tight‐binding limit and cause some irregularity of the solutions which are harder to handle in higher space dimensions. To overcome these difficulties, we work in anisotropic Sobolev spaces. Moreover, additional non‐resonance conditions have to be satisfied in the two‐dimensional case.Item Open Access An approximation of solutions to heat equations defined by generalized measure theoretic Laplacians(2020) Ehnes, Tim; Hambly, BenWe consider the heat equation defined by a generalized measure theoretic Laplacian on [0, 1]. This equation describes heat diffusion in a bar such that the mass distribution of the bar is given by a non-atomic Borel probabiliy measure μ, where we do not assume the existence of a strictly positive mass density. We show that weak measure convergence implies convergence of the corresponding generalized Laplacians in the strong resolvent sense. We prove that strong semigroup convergence with respect to the uniform norm follows, which implies uniform convergence of solutions to the corresponding heat equations. This provides, for example, an interpretation for the mathematical model of heat diffusion on a bar with gaps in that the solution to the corresponding heat equation behaves approximately like the heat flow on a bar with sufficiently small mass on these gaps.Item Open Access Arrays of individually controllable optical tweezers based on 3D-printed microlens arrays(2020) Schäffner, Dominik; Preuschoff, Tilman; Ristok, Simon; Brozio, Lukas; Schlosser, Malte; Giessen, Harald; Birkl, GerhardItem Open Access Assignment of fundamental vibrations and estimation of electron-molecular vibration coupling constants for bis(ethylenedioxy)tetrathiafulvalene (BEDO)(1993) Pokhodnia, Konstantin I.; Kozlov, Mikhail E.; Onischenko, V. G.; Schweitzer, Dieter; Moldenhauer, Jörg; Zamboni, RobertoThe 1.r. absorption and Raman spectra of BEDO are investigated. All fundamental vibrations are assigned using correlations between the obtained data and those for a well-known compound BEDT-TTF (ET). Comparative normal coordinate analysts has been done. The results are used for calculation of electron-intramolecular vibration coupling constants of BEDO based superconducting charge-transfer complexes. Comparison of these values with the constants obtained earlier for ET shows that BEDO is a perspective donor for searching new superconductors on its basis.Item Open Access An atomic‐scale vector network analyzer(2024) Baumann, Susanne; McMurtrie, Gregory; Hänze, Max; Betz, Nicolaj; Arnhold, Lukas; Malavolti, Luigi; Loth, SebastianElectronic devices have been ever‐shrinking toward atomic dimensions and have reached operation frequencies in the GHz range, thereby outperforming most conventional test equipment, such as vector network analyzers (VNA). Here the capabilities of a VNA on the atomic scale in a scanning tunneling microscope are implemented. Nonlinearities present in the voltage‐current characteristic of atoms and nanostructures for phase‐resolved microwave spectroscopy with unprecedented spatial resolution at GHz frequencies are exploited. The amplitude and phase response up to 9.3 GHz is determined, which permits accurate de‐embedding of the transmission line and application of distortion‐corrected waveforms in the tunnel junction itself. This enables quantitative characterization of the complex‐valued admittance of individual magnetic iron atoms which show a lowpass response with a magnetic‐field‐tunable cutoff frequency.