Universität Stuttgart
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Item Open Access Noise-induced quantum synchronization with entangled oscillations(2025) Tao, Ziyu; Schmolke, Finn; Hu, Chang-Kang; Huang, Wenhui; Zhou, Yuxuan; Zhang, Jiawei; Chu, Ji; Zhang, Libo; Sun, Xuandong; Guo, Zechen; Niu, Jingjing; Weng, Wenle; Liu, Song; Zhong, Youpeng; Tan, Dian; Yu, Dapeng; Lutz, EricRandom fluctuations can lead to cooperative effects in complex systems. We here report the observation of noise-induced quantum synchronization in a chain of superconducting transmon qubits with nearest-neighbor interactions. The application of Gaussian white noise to a single site leads to synchronous oscillations in the entire chain. We show that the two synchronized end qubits are entangled, with nonzero concurrence, and that they belong to a class of generalized Bell states known as maximally entangled mixed states, whose entanglement cannot be increased by any global unitary. We further demonstrate the stability against frequency detuning of both synchronization and entanglement by determining the corresponding generalized Arnold tongue diagrams. Our results highlight the constructive influence of noise in a quantum many-body system, and initiate the exploration of collective synchronization effects with stronger than classical correlations.Item Open Access Fundamental limits on nonequilibrium sensing(2025) Dechant, Andreas; Lutz, EricThe performance of equilibrium sensors is restricted by the laws of equilibrium thermodynamics. Here, we investigate the physical limits on nonequilibrium sensing in bipartite systems with both reciprocal and nonreciprocal couplings. We show that one of the subsystems, acting as a Maxwell demon, can significantly suppress the fluctuations of the other subsystem relative to its response to an external perturbation. The importance of nonreciprocal interactions for such negative violations of the fluctuation-dissipation relation to occur is identified. We further demonstrate that these violations can considerably improve the signal-to-noise ratio above its corresponding equilibrium value, allowing the subsystem to operate as an enhanced sensor. In addition, we find that the nonequilibrium signal-to-noise ratio of linear systems may be arbitrarily large at low frequencies after proper parameter optimization, even at a fixed overall amount of dissipation. These results indicate that highly accurate nonreciprocal sensors can be designed at a finite energetic cost.Item Open Access Nonequilibrium thermodynamics of quantum coherence beyond linear response(2024) Rodrigues, Franklin L. S.; Lutz, EricQuantum thermodynamics allows for the interconversion of quantum coherence and mechanical work. Quantum coherence is thus a potential physical resource for quantum machines. However, formulating a general nonequilibrium thermodynamics of quantum coherence has turned out to be challenging. In particular, precise conditions under which coherence is beneficial to or, on the contrary, detrimental for work extraction from a system have remained elusive. We here develop a generic dynamic-Bayesian-network approach to the far-from-equilibrium thermodynamics of coherence. We concretely derive generalized fluctuation relations and a maximum-work theorem that fully account for quantum coherence at all times, for both closed and open dynamics. We obtain criteria for successful coherence-to-work conversion, and identify a nonequilibrium regime where maximum work extraction is increased by quantum coherence for fast processes beyond linear response.Item Open Access Wave functions and oscillator strengths in a two-band model for Rydberg excitons in cuprous oxide quantum wells(2024) Kühner, LeonRydberg physics is the study of systems involving highly excited states of atoms or molecules, known as Rydberg states. In these states, one or more electrons are far from the nucleus, giving the atom exaggerated properties such as large size, long lifetimes, and strong interactions with external fields and nearby particles. These unique features make Rydberg systems a valuable tool for exploring a range of phenomena in atomic physics, quantum optics, and condensed matter physics. They are particularly important for applications in quantum technologies, such as quantum simulation and computation and sensing. Another candidate for Rydberg physics are excitons. When an electron is excited from the valence band to the conduction band the electron in the conduction band and the positively charged hole in the valance band can form hydrogen-like states. Excitons in cuprous oxide, though with relatively low principal quantum numbers, have already been detected in the 1950s by Gross and Hayashi. In 2014 it was possible to measure exciton states with a principal quantum number up to n=25, since then the exciton Rydberg physics has attracted large attention. These states have radii in the range of microns. Rydberg excitons show a large variety of phenomena which do not occur in atomic physics, for example the structure of the valence band leads to a breaking of the spherical symmetry, the spin-orbit coupling leads to the occurrence of a green and yellow exciton series, and central-cell corrections have effects on even parity states. Other effects occur when Rydberg excitons are confined in quantum wells. Such effects have been experimentally observed in GaAs. Thin layers in cuprous oxide have already been produced. Therefore, the observation of excitons in cuprous oxide quantum wells is expected soon. Excitons in quantum wells allow one to investigate the dimensional crossover from three-dimensional systems with weak confinement to two-dimensional systems with strong confinement. For this system the energy spectra have already been computed and effects like overlapping Rydberg series and resonances have been discussed. The theoretical calculations have so far been restricted to the computation of eigenenergies in a hydrogen-like model ignoring the impact of the valence band. The aim of this thesis is to study the effects of Rydberg excitons which rely on the wave functions. Such effects are the behavior of wave functions from weak to strong confinement and the quenching behavior in these regions that are visualized in this thesis. Numerically the wave functions are expanded in a B-spline basis. Also resonances above the first scattering threshold as well as bound states in the continuum above this threshold are visualized. Further, wave functions that undergo an avoided crossing are investigated. Another aspect is the influence of electrostatic effects for exciton states in quantum wells. These lead to the appearance of surface excitons, which can be seen in the visualization of these states. Oscillator strengths are investigated and rely on the behavior of the wave function. In our system the oscillator strengths are no longer translational invariant. Ultimately, this work provides a comprehensive exploration of Rydberg exciton wave functions, which could be instrumental in advancing the use of these systems in emerging quantum applications.Item Open Access Item Open Access Excitons in cuprous oxide quantum wells : computation of spectra in consideration of the valence band structure(2025) Scheuler, NiklasIn finite-sized crystals, quantum confinement causes excitons to exhibit properties that differ significantly from those in bulk systems. Recent studies on excitons in bulk cuprous oxide have demonstrated that an accurate description requires accounting for the material's complex valence-band structure. By contrast, existing work on excitons in quantum wells has largely relied on simplified hydrogen-like models that neglect these band-structure effects. The aim of this thesis is to bridge this gap. Using the Luttinger-Kohn model, we derive the complete Hamiltonian for excitons in cuprous oxide quantum wells, fully incorporating the band structure. The symmetry properties of the resulting system are analyzed. Numerical results obtained from diagonalizing the Hamiltonian using B-spline basis functions reveal energy shifts and the lifting of degeneracies arising from the coupling terms of the complex valence band. Furthermore, we compute relative oscillator strengths of excitonic transitions induced by circularly polarized light.Item Open Access Lösung der Schrödingergleichung für Systeme mit Delta-Potentialen unter besonderer Berücksichtigung des dreidimensionalen harmonischen Oszillators(2025) Hartung, Fiona SophieExzitonen wurden erstmals 1930 eingeführt als die Anregungsquanten von Elektronen in Halbleitern. Zwischen dem Elektron und dem dazugehörigen Loch besteht eine Coulomb-Interaktion, die zu wasserstoffartigen Zustandsserien führt. Das 1S Exziton in Cu2O ist aufgrund seines kleinen Radius eine Mischung aus einem Frenkel und einem Wannier Exziton, weshalb Korrekturen vorgenommen werden müssen, um diesen Zustand korrekt zu beschreiben, die sogenannten Central-Cell-Corrections. Ein Teil dieser Korrekturen kann über ein attraktives Delta-Potential modelliert werden. Da dreidimensionale Delta-Potentiale jedoch aufgrund ihrer Divergenz am Ursprung nicht exakt lösbar sind, sondern nur über Regularisierungen einzelne gebundene Zustände ermittelt werden können, stellt sich die Frage, welchen Einfluss ein attraktives Delta-Potential auf ein bekanntes System hat. In dieser Bachelorarbeit soll daher betrachtet werden, wie sich ein attraktives Delta-Potential auf das bekannte System des dreidimensionalen harmonischen Oszillators auswirkt. Dazu wird dieser zunächst vorgestellt und gelöst und anschließend wird die Auswirkung des Delta-Potentials mittels Störungstheorie auf das System betrachtet. Außerdem wird das gestörte System über die Eigenzustände des ungestörten System als Matrix dargestellt, aus welcher sich durch Diagonalisierung die Energieeigenwerte und Wellenfunktionen des gestörten Systems bestimmen lassen. Hierbei wird die Auswirkung verschiedener Parameter wie der Stärke des Delta-Potentials, die Größe der verwendeten Matrix oder die Skalierung der Koordinaten auf das System untersucht.Item Open Access Electrostatic all-passive force clamping of charged nanoparticles(2025) Tuna, Yazgan; Al-Hiyasat, Amer; Kashkanova, Anna D.; Dechant, Andreas; Lutz, Eric; Sandoghdar, VahidIn the past decades, many techniques have been explored for trapping microscopic and nanoscopic objects, but the investigation of nano-objects under arbitrary forces and conditions remains nontrivial. One fundamental case concerns the motion of a particle under a constant force, known as force clamping . Here, we employ metallic nanoribbons embedded in a glass substrate in a capacitor configuration to generate a constant electric field on a charged nanoparticle in a water-filled glass nanochannel. We estimate the force fields from Brownian trajectories over several micrometers and confirm the constant behavior of the forces both numerically and experimentally. Furthermore, we manipulate the diffusion and relaxation times of the nanoparticles by tuning the charge density on the electrode. Our highly compact and controllable setting allows for the trapping and force-clamping of charged nanoparticles in a solution, providing a platform for investigating nanoscopic diffusion phenomena.Item Open Access Quantum kernel methods and applications to differential equations(2024) Flórez Ablan, RobertoQuantum computers have the potential to surpass classical computers in specific tasks, promising advantages in many fields. Machine Learning (ML), a domain with significant societal impact, is a key area of interest for exploring the applications of quantum computing. Here, we investigate two research directions aimed at understanding how current quantum computers can be used to solve ML problems. First, we study Quantum Kernels (QKs). By calculating inner products between quantum states, QKs can be used to define similarity measures between points. QKs are a promising approach to Quantum Machine Learning (QML) but, in general, they have not been shown to outperform classical ML methods. A key reason for this is that QKs suffer from the exponential concentration problem. As the number of qubits increases, the kernel matrices become similar to the identity matrix, preventing generalization. One strategy to alleviate the exponential concentration problem is to rescale the data points that enter the quantum model. This technique is known as bandwidth tuning and has been shown to allow generalization in QKs. However, it has been numerically demonstrated that using this method results in QKs that cannot provide a quantum advantage over classical methods. In this thesis, we propose an explanation for this phenomenon. We show that due to the size of the rescaling factors, the QKs become similar to polynomial and RBF kernels, which are classically tractable. Second, we implemented a Differential Equation (DE) solver based on variational quantum methods. A Quantum Neural Network (QNN) or QK, is used to represent an ansatz for the solution of a DE. The DE information is included into a loss function, which is minimized using a classical optimizer. In the case of a QK, the optimized parameters are the coefficients of a linear combination of QKs evaluated at the data points. In the case of a QNN, the optimized parameters are the phases of the quantum gates. The QNN implementation was included into the open-source QML python library sQUlearn. A preliminary hyperparameter study was conducted for QKs. Based on our limited investigation, we conclude that QKs leveraging the fidelity between quantum states, known as Fidelity Quantum Kernels (FQKs), demonstrate superior performance compared to those employing a semi-classical approach, referred to as Projected Quantum Kernels (PQKs).Item Open Access Classical and semiclassical approaches to excitons in cuprous oxide(2024) Ertl, Jan; Main, Jörg (Prof. Dr.)When an electron is excited from the valence into the conduction band it leaves behind a positively charged hole in the valence band to which it can couple through the Coulomb interaction. Bound states of electrons and holes, the excitons, are the solid state analogue of the hydrogen atom. As such they follow a Rydberg series. T. Kazimierczuk et al. [Nature 514, 343 (2014)] were able to show the existence of Rydberg excitons in cuprous oxide up to principle quantum number n=25. These states then have extensions in the µm range and thus lie in a region where the correspondence principle is applicable and quantum mechanics turns into classical mechanics. A more precise study of experimental spectra reveals significant deviations from a purely hydrogen-like behavior. These deviations can be traced to the complex valence band structure of cuprous oxide which inherits the cubic symmetry of the system. A theoretical description of the band structure introduces new degrees of freedom, i.e., a quasispin I=1 describing the three-fold degenerate valence band. Due to the coupling of quasispin and hole spin the valence band splits resulting in a yellow exciton series and two green exciton series with light and heavy holes. In this thesis we provide a semiclassical interpretation for excitons in cuprous oxide beyond the hydrogen-like model. To this end we introduce an adiabatic approach diagonalizing the band structure part of the Hamiltonian in a basis for quasi- and hole spin. This leads to a description via energy surfaces in momentum space, which correspond to the different exciton series. Classical dynamics can be calculated by choosing the energy surface of the series under interest and integrating Hamilton's equations of motion. Due to the energy surfaces the symmetry is drastically reduced compared to the hydrogen-like problem now allowing for the existence of fully three-dimensional orbits as well as the possibility of chaotic dynamics. For the yellow exciton series we find mostly regular phase space regions with quasi-periodic motion on near-integrable tori and small chaotic phase space regions. To demonstrate the existence of classical exciton orbits in the quantum spectra we show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. An analysis of the energy dependence reveals that the dynamics deviations' from a purely hydrogen-like behavior increase with decreasing energy. Starting from the full Hamiltonian we develop a spherical model from which we are able to derive the quantum defects of the yellow exciton series using a semiclassical torus quantization. A comparison with quantum mechanical calculations show good agreement with our semiclassical results, thus allowing to identify individual quantum states by a corresponding classical exciton orbit in analogy to Bohr's atomic model. Finally, we provide a comparison of yellow exciton series with the two distinct green exciton series. The phase space is analyzed by application of Poincaré surfaces of section and Lagrangian descriptors. In addition, we investigate the Lyapunov stability of individual orbits. The analysis reveals the existence of a classically chaotic exciton dynamics for both yellow and green excitons, however, the chaotic regions are more pronounced for the green than for the yellow excitons. Excitons in cuprous oxide thus provide an example of a two-particle system with chaos even without the application of external fields.