Universität Stuttgart
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Item Open Access Fractional calculus for distributions(2024) Hilfer, Rudolf; Kleiner, TillmannFractional derivatives and integrals for measures and distributions are reviewed. The focus is on domains and co-domains for translation invariant fractional operators. Fractional derivatives and integrals interpreted as -convolution operators with power law kernels are found to have the largest domains of definition. As a result, extending domains from functions to distributions via convolution operators contributes to far reaching unifications of many previously existing definitions of fractional integrals and derivatives. Weyl fractional operators are thereby extended to distributions using the method of adjoints. In addition, discretized fractional calculus and fractional calculus of periodic distributions can both be formulated and understood in terms of -convolution.Item Open Access Physics-informed transformers for electronic quantum states(2025) Sobral, João Augusto; Perle, Michael; Scheurer, Mathias S.Neural-network-based variational quantum states, particularly autoregressive models, are powerful tools for describing complex many-body wave functions. However, their performance depends on the computational basis chosen and they often lack physical interpretability. We propose a modified variational Monte-Carlo framework which leverages prior physical information to construct a complete computational many-body basis containing a reference state that serves as a rough approximation to the true ground state. A Transformer is used to parametrize and autoregressively sample corrections to this reference state, giving rise to a more interpretable and computationally efficient representation of the ground state. We demonstrate this approach in a fermionic model featuring a metal-insulator transition by employing Hartree-Fock and a strong-coupling limit to define physics-informed bases. We also show that the Transformer’s hidden representation captures the natural energetic order of the different basis states. This work paves the way for more efficient and interpretable neural quantum-state representations.Item Open Access Charge regulation and swelling of weak polyelectrolyte nanogels in divalent salt solutions(2026) Beyer, David; Holm, ChristianWe use computer simulations to investigate the behavior of a weak polyelectrolyte nanogel in a solution containing divalent salt. In our simulations, we systematically vary the bulk pH value and the bulk concentration of divalent salt, allowing us to study the influence of charge regulation and divalent ions on the ionization behavior, ion partitioning, and nanogel swelling. With regard to the ionization behavior, we observe that, with an increasing concentration of divalent salt, the suppression of ionization becomes weaker. Moreover, we find that the strongly non‐uniform ionization profile observed in the absence of divalent counterions becomes increasingly uniform as the concentration of divalent salt is increased. We also study the partitioning of monovalent and divalent counterions between the nanogel and the bulk solution; our analysis shows that the uptake of divalent ions may be enhanced by up to tenfold as compared to the mean‐field prediction. Finally, we consider the influence of divalent ions on the pH‐dependent swelling behavior of the nanogel. Here, we observe a two‐stage swelling driven by charge regulation and ion partitioning. Overall, our results highlight the complex interplay of ionization equilibria, valency effects, and ion partitioning in weak polyelectrolyte systems.Item Open Access Nanoscale mapping of magnetic auto-oscillations with a single spin sensor(2025) Hache, Toni; Anshu, Anshu; Shalomayeva, Tetyana; Richter, Gunther; Stöhr, Rainer; Kern, Klaus; Wrachtrup, Jörg; Singha, AparajitaSpin Hall nano-oscillators convert DC to magnetic auto-oscillations in the microwave regime. Current research on these devices is dedicated to creating next-generation energy-efficient hardware for communication technologies. Despite intensive research on magnetic auto-oscillations within the past decade, the nanoscale mapping of those dynamics remained a challenge. We image the distribution of free-running magnetic auto-oscillations by driving the electron spin resonance transition of a single spin quantum sensor, enabling fast acquisition (100 ms/pixel). With quantitative magnetometry, we experimentally demonstrate for the first time that the auto-oscillation spots are localized at magnetic field minima acting as local potential wells for confining spin-waves. By comparing the magnitudes of the magnetic stray field at these spots, we decipher the different frequencies of the auto-oscillation modes. The insights gained regarding the interaction between auto-oscillation modes and spin-wave potential wells enable advanced engineering of real devices.Item Open Access Direct electron beam patterning of electro-optically active PEDOT:PSS(2024) Doshi, Siddharth; Ludescher, Dominik; Karst, Julian; Floess, Moritz; Carlström, Johan; Li, Bohan; Mintz Hemed, Nofar; Duh, Yi-Shiou; Melosh, Nicholas A.; Hentschel, Mario; Brongersma, Mark; Giessen, HaraldThe optical and electronic tunability of the conductive polymer poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) has enabled emerging applications as diverse as bioelectronics, flexible electronics, and micro- and nano-photonics. High-resolution spatial patterning of PEDOT:PSS opens up opportunities for novel active devices in a range of fields. However, typical lithographic processes require tedious indirect patterning and dry etch processes, while solution-processing methods such as ink-jet printing have limited spatial resolution. Here, we report a method for direct write nano-patterning of commercially available PEDOT:PSS through electron-beam induced solubility modulation. The written structures are water stable and maintain the conductivity as well as electrochemical and optical properties of PEDOT:PSS, highlighting the broad utility of our method. We demonstrate the potential of our strategy by preparing prototypical nano-wire structures with feature sizes down to 250 nm, an order of magnitude finer than previously reported direct write methods, opening the possibility of writing chip-scale microelectronic and optical devices. We finally use the high-resolution writing capabilities to fabricate electrically-switchable optical diffraction gratings. We show active switching in this archetypal system with >95 % contrast at CMOS-compatible voltages of +2 V and -3 V, offering a route towards highly-miniaturized dynamic optoelectronic devices.Item Open Access Electronic and structural instabilities in the putative excitonic insulator Ta2NiSe5(2025) Zhang, Yuanshan; Takagi, Hidenori (Prof. Dr.)Item Open Access Rigorous compilation for near-term quantum computers(2024) Brandhofer, Sebastian; Polian, Ilia (Prof.)Quantum computing promises an exponential speedup for computational problems in material sciences, cryptography and drug design that are infeasible to resolve by traditional classical systems. As quantum computing technology matures, larger and more complex quantum states can be prepared on a quantum computer, enabling the resolution of larger problem instances, e.g. breaking larger cryptographic keys or modelling larger molecules accurately for the exploration of novel drugs. Near-term quantum computers, however, are characterized by large error rates, a relatively low number of qubits and a low connectivity between qubits. These characteristics impose strict requirements on the structure of quantum computations that must be incorporated by compilation methods targeting near-term quantum computers in order to ensure compatibility and yield highly accurate results. Rigorous compilation methods have been explored for addressing these requirements as they exactly explore the solution space and thus yield a quantum computation that is optimal with respect to the incorporated requirements. However, previous rigorous compilation methods demonstrate limited applicability and typically focus on one aspect of the imposed requirements, i.e. reducing the duration or the number of swap gates in a quantum computation. In this work, opportunities for improving near-term quantum computations through compilation are explored first. These compilation opportunities are included in rigorous compilation methods to investigate each aspect of the imposed requirements, i.e. the number of qubits, connectivity of qubits, duration and incurred errors. The developed rigorous compilation methods are then evaluated with respect to their ability to enable quantum computations that are otherwise not accessible with near-term quantum technology. Experimental results demonstrate the ability of the developed rigorous compilation methods to extend the computational reach of near-term quantum computers by generating quantum computations with a reduced requirement on the number and connectivity of qubits as well as reducing the duration and incurred errors of performed quantum computations. Furthermore, the developed rigorous compilation methods extend their applicability to quantum circuit partitioning, qubit reuse and the translation between quantum computations generated for distinct quantum technologies. Specifically, a developed rigorous compilation method exploiting the structure of a quantum computation to reuse qubits at runtime yielded a reduction in the required number of qubits of up to 5x and result error by up to 33%. The developed quantum circuit partitioning method optimally distributes a quantum computation to distinct separate partitions, reducing the required number of qubits by 40% and the cost of partitioning by 41% on average. Furthermore, a rigorous compilation method was developed for quantum computers based on neutral atoms that combines swap gate insertions and topology changes to reduce the impact of limited qubit connectivity on the quantum computation duration by up to 58% and on the result fidelity by up to 29%. Finally, the developed quantum circuit adaptation method enables to translate between distinct quantum technologies while considering heterogeneous computational primitives with distinct characteristics to reduce the idle time of qubits by up to 87% and the result fidelity by up to 40%.Item Open Access Thermal diffusion and trapping of vacancies for the formation of optical centers in diamond(2024) Santonocito, Santo; Wrachtrup, Jörg (Prof. Dr.)Since its introduction, quantum physics has revolutionized our understanding of the fundamental laws governing the universe. Originally employed to address problems unsolvable by classical mechanics, quantum physics has gradually found a wide variety of applications in modern life, many of which are based on the principle of quantum coherence, such as lasers. Despite these advancements, understanding the behavior of complex quantum systems remains an enduring challenge, primarily due to the exponential growth in complexity as the number of system components increases. This difficulty is largely attributed to the limited computational power of classical computers. As Richard Feynman famously remarked, ”Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly, it’s a wonderful problem, because it doesn’t look easy”, highlighting the intrinsic link between the complexity of quantum phenomena and the need for computational paradigms that can inherently handle such complexity. Contrary to Gordon Moore’s 1965 prediction, recent years have seen a slowdown in the reduction of transistor size as physical limits have been approached, thereby obstructing further advances in classical computational power. Ongoing research into alternative methods to enhance computational performance has thus shifted focus towards quantum computers. Proposed initially in 1988 by Y. Yamamoto and K. Igeta, quantum computers are based on qubits as units of information. Unlike classical bits that exist strictly as either 0 or 1, qubits are quantum systems that can exist in any arbitrary superposition of two distinct states (|0⟩ and |1⟩). This property enables quantum computers to perform computational tasks through the temporal evolution of these systems via logical operations (defined as gates), potentially offering exponential speed-ups for problems intractable with classical computation. Over the years, advancements in the production and control of various quantum systems have led to the exploration of applications such as nanoscale quantum sensing. Among several types of quantum technologies, including single photons and trapped ions, devices based on spin impurities in solid-state systems have been demonstrated exceptionally effective for both quantum computing and quantum sensing. These impurities meet the DiVincenzo criteria for quantum systems, featuring spins that not only define discrete, individually addressable energy levels but also allow for initialization, coherent manipulation, and measurement. Furthermore, these systems are sensitive to physical quantities like electric and magnetic fields due to Stark and Zeeman interactions, respectively. Among the various spin impurities, the negatively charged nitrogen-vacancy (NV) center in diamond is extensively studied. This atomic-scale spin system is composed of a nitrogen atom located in a neighboring lattice site of a vacancy and surrounded by carbon atoms. Recent advances in material engineering have enabled the controlled synthesis of diamond crystals with a high degree of purity, allowing NV centers to function as wellisolated spin systems. The NV center is characterized by triplet spin energy configuration, including a spin-selective relaxation via inter system crossing, that enables to initialize, manipulate, and optically read out the ground state spin. Moreover, the energy levels of the NV center are sensitive to variations in magnetic fields, electric fields, temperature, and strain, making this center a versatile sensor for various physical phenomena. Its atomic size and spin properties render the NV suitable for quantum sensing applications. Unlike other competing sensing technologies that require high-energy systems, the NV center can operate under standard temperature and pressure conditions. Furthermore, the chemically inert nature of diamond renders NV-based devices biocompatible, allowing for their placement within a few nanometers from the field sources and, thus, enabling imaging of magnetic field at nanometer scale. The most common technique for creating single NV centers in diamond involves ion implantation followed by thermal annealing. This method allows the creation of NVs at various depths within diamond with nanometer precision. Despite its spatial resolution, low-energy implantation, necessary for near-surface NV positioning (relevant for sensing applications), results in a low yield of NVs even when the concentration of vacancies induced by implantation is significantly higher than that of atomic nitrogen included within the diamond lattice. This inefficiency is related to the tendency of vacancy to aggregate into di-vacancies (V2) or multi-vacancy complexes (Vn) in ion-damaged areas rather than getting trapped at nitrogen lattice site and forming NV centers. Although a higher implantation dose could potentially increase the yield, it would also result in greater lattice damage, which would reduce the spin coherence time (T2) of the NV, compromising its sensitivity as a quantum sensor. In addition to the challenges associated with low formation efficiency, the proximity of NV centers to the diamond surface (less than 10 nm) introduces further complications. Surface-induced noise and electronic defects can degrade spin coherence and destabilize the NV charge state, significantly impacting the performance and reliability of these shallow defects. Addressing these issues, while simultaneously maximizing NV concentration and preserving T2 and signal contrast, remains a critical challenge in the field of quantum sensing. Recent advancements in material processing and NV creation strategies have provided promising solutions. Co-implantation of nitrogen and helium ions, with precise optimization of implantation energies (below 10 keV) and fluences, has been shown to minimize lattice damage and enhance the efficiency of NV formation. Helium co-implantation, in particular, facilitates the introduction of vacancies at controlled depths, improving the nitrogen-to-NV conversion efficiency. This technique has proven particularly effective for generating shallow NV centers with narrow linewidths in optically detected magnetic resonance (ODMR) measurements, a key requirement for quantum sensing applications. In parallel, high-temperature annealing protocols, typically at temperatures exceeding 1200◦C, have been employed to mitigate the formation of vacancy complexes and restore lattice integrity, further enhancing NV coherence times. Furthermore, surface treatments, such as hydrogen and oxygen termination prior to implantation, have shown promise in addressing surface-induced noise. These treatments not only enhance the nitrogen-to-NV conversion efficiency but also improve the stability of shallow NV centers by reducing charge-state conversion to neutral NV configurations. Additionally, pre-doping diamond substrates with nitrogen prior to ion implantation has emerged as a powerful method to enhance NV yield. Molecular dynamics simulations suggest that nitrogen concentrations of approximately 1000 ppm optimize vacancy diffusion and NV formation, achieving yields up to 10%. These techniques, combined with advancements in chemical vapor deposition (CVD) diamond growth, allow for controlled nitrogen incorporation and defect alignment along specific crystallographic orientations, critical for achieving reproducible quantum performance. In addition to quantum sensing, the domain of quantum information processing has also gathered increasing attention. Although NV centers meet the DiVincenzo necessary criteria for quantum applications, they lack some optical properties ideal for quantum information processing, such as a high Debye-Waller factor and minimal spectral diffusion. In contrast, color centers in diamond based on group-IV elements are considered suitable candidates. These centers not only exhibit higher optical performances than NV centers but also show inherent compatibility with nanostructures usually employed for enhancing optical properties. Like NVs, these group-IV color centers can be precisely engineered through ion implantation followed by annealing. However, since nitrogen is intrinsically present within the diamond lattice, the formation of unwanted NV centers is inevitable. Developing methods to suppress the formation of unwanted NVs is crucial for advancing the application of group-IV color centers in quantum information processing. This thesis primarily examines the formation of color centers in diamond, achieved through the trapping of diffusing vacancies. Specifically, it explores the use of irradiation and annealing techniques designed to generate vacancies and promote their diffusion within the diamond lattice. A critical aspect of this study involves identifying the inherent limitations associated with these techniques and understanding the underlying reasons of these constraints. The aim is to develop novel methodologies that can overcome these limitations. One such innovative method has been applied for the synthesis of tin-vacancy (SnV) centers in diamond. These developments are crucial for improving the production of color centers in diamond, thereby broadening their utility in quantum technology applications. Impurity centers in diamond lattice. The present work starts with an overview of diamond as host material for color centers employed for quantum applications, focusing particularly on the NV. The discussion includes description of the chemical vapor deposition (CVD) and high temperature high pressure (HPHT) growth techniques of diamond, pivotal in synthesizing substrates with controlled level of the impurities. This control is significant as the presence of any paramagnetic impurities within the lattice can compromise the spin properties of targeted color centers. The chapter further focuses on the NV center physical properties, providing a basic introduction of the associated spin manipulation techniques. Moreover, detailed attention is given to the methods employed to create NV centers, with a specific focus on ion implantation followed by annealing, and on the limitations associated with these technique. Vacancy diffusion and defect formation in a crystalline solid. The second chapter addresses the diffusion of vacancies and their trapping by defects within the diamond lattice. Here, a novel model of vacancy diffusion based on probabilistic atomic jumps in crystal lattice, is developed to investigate the limit in the NV formation due to trapping of diffusing vacancies induced by irradiation. The NV formation within the model is considered as competing mechanism of vacancy trapping between nitrogen atoms, divacancies (V2) and multi-vacancies complexes (Vn). A critical parameter of the described model is the so-defined capture cross-section, which, quantifying the probability for a vacancy to be trapped by a specific defect, can be related to the formation energy of the corresponding defect. The model, developed for different vacancies distributions scenarios, has been validated through Monte Carlo simulations. The efficiency of NV formation by irradiation techniques: estimates by the model and the experimental validation. The third chapter starts with the description of the so-called ”Scanning Protocol” developed to collect profiles of NV centers within the diamond bulk with a nanometric precision. In this protocol, photoluminesce (PL) confocal scans of fixed area have been collected at different depth with a step 0.1 µm. Within each scan, the position and the fluorescence intensity of NV centers have been evaluated by employing a 2-D Gaussian fit. An additional 1-D Gaussian fit of the NV PL intensity as function of depth result in the localization of the NV in the diamond bulk. NV depth distributions by helium implantation followed by annealing have been collected for different annealing temperatures. A fit of these distributions through the model developed in chapter 2, provides an activation energy for vacancies diffusion in diamond of 1.7 eV. This value has subsequently been used into the model to evaluate the capture cross section ratio between NV and V2 in a range of 0.1 to 0.5. This result demonstrates the tendency of vacancies to preferentially aggregate rather than being trapped by nitrogen, defining the limit (low formation yield) in the NV formation (as for other color center in diamond) by ion implantation or electron irradiation followed by annealing. The ability of the model developed in chapter 2 to predict NV center concentrations resulting from the aforementioned techniques enables the formulation of strategies aimed at enhancing the formation of NV centers associated with these techniques. This enhancement can be achieved while preserving the spin properties of the NV centers. Furthermore, the model probabilistic approach holds promise for wider applications in the engineering of additional vacancy-related defects in diamond. This extends the model utility significantly within the realm of quantum engineering. Planar p-n junction structures on diamond for controlling the vacancy diffusion. The final chapter explores an advanced engineering technique to control vacancy diffusion at thermal annealing. Specifically, vacancies created by ion implantation within the depletion region of a diamond p+ junction get charged, and their long-range diffusion has been proved to be suppressed due to repulsive forces from ionized donors in the depleted region of the n-doped substrate. This mechanism is demonstrated to reduce the formation of NV centers by limiting vacancy trapping at nitrogen sites in the diamond bulk. The effectiveness of this technique is verified through the fabrication of p+-n junctions in high purity single-crystal diamond substrates. Indeed, C and He implantations (tuned to create vacancies as described above) across such junction, followed by annealing at 1200◦ resulted in a strong reduction of NVs compared to not doped areas subjected to the same implantation and annealing procedure. The method described has been successfully applied to the implantation of tin to produce SnV centers in diamond. This approach resulted in both an enhanced yield of SnV centers and a reduction of unwanted NVs along the implantation paths of the Sn atoms. The utility of this method extends beyond the creation of SnV centers; it is also applicable to the formation of other color centers in diamond. By providing control over vacancy diffusion within semiconductor materials, this technique possesses substantial potential for a variety of applications in the field of quantum technologies.Item Open Access Exploring the growth of refractory metal and sapphire films by thermal laser epitaxy(2024) Majer, Lena N.; Mannhart, Jochen (Prof. Dr.)Item Open Access Overview: the Janus-nature of molecular CO2 in charge adjustment at wet surfaces(2026) Vogel, Peter; Qaisrani, Muhammad Nawaz; Rasenat, Mattis; Lützenkirchen, Johannes; Sulpizi, Marialore; Beyer, David; Holm, Christian; Palberg, ThomasMolecular CO2 readily dissolves in aqueous electrolyte solutions and partially dissociating to form carbonic acid. The decharging effects of the dissociation products mediated by the ensuing pH-shift and the additional salinity are well established. However, the effects of dissolved molecular CO2 have not been studied systematically. We summarize recent and novel investigations on the role of CO2 regarding charge control at surfaces submersed in aqueous electrolytes. In our electrokinetic and conductometric measurements on representative surfaces, we took special care to control and monitor the electrolyte composition in situ. We discriminate the effects of molecular and dissociated CO2via control experiments using HCl. Depending on the surface under investigation and the charging mechanisms involved, we find that molecular CO2 assists either charging, de-charging and/or recharging. This contrasting charge regulating behaviour reveals the Janus nature of dissolved molecular CO2 with respect to charge control at wet surfaces. In our complementary molecular dynamics simulations, Q4 silica and 9% ionized Q3 silica surfaces are studied as hydrophobic/hydrophilic, respectively charged/uncharged, analogues, as well as uncharged Q3 silica and molecularly rough Isoleucin-coated quartz surfaces. In all cases, we find that the charge-neutral CO2 molecule physisorbs in a thin diffusive layer close to the surface, which leads to pronounced re-structuring of the electric double layer. Based on this result, we suggest to interpret the experimentally observed Janus nature of molecular CO2 in terms of a local decrease of the dielectric permittivity. This in turn leads to a local strengthening of electrostatic interactions dominating the double layer structure next to charged surfaces. Specifically, we propose that CO2 induces a dielectric charge regulation for weakly acidic surface groups, assists the incorporation of OH− into the H-bond network at smooth inert surfaces, and induces significant ion-correlations promoting co-ion binding. Overall, we demonstrate that molecular CO2 allows for a controlled charge-adjustment in opposing directions. We anticipate that our findings on the one hand provide substantial challenges for analytical or numerical modelling as well as for controlled experimental work, but on the other hand bear important practical implications for applications ranging from desalination to bio-membranes.