arXiv subjects

Stefan Schumacher

Publications and source records attributed to Stefan Schumacher.

At least 19 recordsLinked to original sources

arXiv2026

Skyrmion topology of scalar waves in real and momentum space

Generalizations of magnetic skyrmions to the context of other areas of physics, such as plasmonics, optics (including microcavity polaritons) and even water waves have become an important research topic. However, the generalization of the skyrmion number in such systems is still the subject of active research. While magnetic skyrmions textures are inherently formed by vectors (magnetic spin vectors), recent developments in other areas of physics have generalized the concept of skyrmions and skyrmionic patterns to the case in which scalar fields are used to define 3-component pseudo-spin vectors. This gives rise to a wide variety of skyrmion-like textures, depending on the detailed functional forms of the scalar fields. For example, steady-state outgoing waves in driven-dissipative polariton systems fail to have a well-defined global skyrmion number in real (configuration) space but can have one in momentum space. We classify the skyrmion integral for various scalar fields with different asymptotic behaviors in real space as well as momentum space, and in both cases give conditions for the skyrmion number not to exist, or be integer, half-integer or non-integer. Examples of physical systems to which our analysis can be applied include polariton condensates, water waves and gain-guided lasers.

physics.optics↗

arXiv2026

Quantum sampling in hybrid light-matter systems with mixed statistics

Boson sampling is one of the most prominent methods to verify quantum advantage, harnessing the computational complexity of the permanent of a network matrix. Similar quantum sampling problems utilize other expressions for the output probabilities, such as the fermion-based analog applying determinants. In this work, we study sampling setups of interacting light-matter systems, combining fermion and boson sampling. The mixed network input consists of fermionic and bosonic excitations. Sampling the output probability of the modes then yields contributions that are neither purely determinant nor permanent but general immanants. Specifically, we prove that these immanant contributions are linearly independent from determinants and permanents, rendering our mixed sampling network an ideal candidate for light-matter quantum application beyond pure fermion and boson sampling. Furthermore, quantum sampling with statistics that are neither bosonic nor fermionic results in expressions which even exceed immanants, further extending the functionality of quantum samplers.

quant-ph↗

arXiv2026

Deterministic Generation of Linear Photonic Cluster States with Semiconductor Quantum Dots: A Detailed Comparison of Different Schemes

Photonic graph states are key resource states for measurement based quantum information processing. As semiconductor quantum dots are excellent deterministic photon emitters, several protocols using them for the generation of linear cluster states have been proposed, either based on constant precession of a hole or electron spin in a weak magnetic field, or based on optical spin control, in a stronger magnetic field. We theoretically compare four such schemes, using polarization or time-bin encoding, respectively, for a range of cavity environments and spin coherence times. In particular we study how different error mechanisms affect the different schemes, using a microscopic model of the spin control, the excitation and emission dynamics, and of the phonon bath. We find the spin-precession based schemes to scale well with strong cavity enhancement and to be naturally robust against phonon-induced decoherence, while the schemes using optical spin control can perform well for lower spin coherence times and are strongly dependent on the cooperativity of the cavity induced cycling transition. Our results provide a regime map for choosing between magnetic-field-driven and optically controlled protocols depending on spin coherence time, Purcell enhancement, and suppression of unwanted decay channels.

quant-ph↗

arXiv2026

Optical vortex classification via machine learning

Optical vortices carry quantized phase information (topological charge) and are considered candidates for information processing in all-optical circuits. Accurately identifying the quantized vortex charge in a way that is most efficient is essential for data processing. Here, we demonstrate that using only intensity information machine learning algorithms are able to classify vortices into distinct phase categories using a properly trained model. Preprocessing of the original intensity data leads to an improved prediction accuracy of the trained classifier and a much shorter training time (~3 orders of magnitude faster). The learning mechanism of the algorithms is revealed by the statistical analyses based on calculation of Cohen's d. We also find that the training efficiency is associated with nonlinearity, non-Hermiticity, and the vortex shape. In some cases, the trained classifier performs well across distinct physical models. Our findings will benefit and accelerate vorticity-based binary information processing and can also be extended to other physical systems.

physics.optics↗

arXiv2026

Skyrmions in scalar fields of non-Hermitian optical microcavities: spontaneous formation, nonlinear control, and optical forces

Topological textures of light offer powerful routes for structuring optical fields, controlling wave transport, and manipulating matter. Skyrmions, long studied as topological solitons in vector fields, have recently been extended to scalar wave systems, including acoustics, hydrodynamics, and plasmonics. However, their realization in two-dimensional scalar wave propagation with nonlinearities and in quantum fluids remains uncharted. Here, we establish such a Skyrmion framework for scalar fields in optical microcavities. With focus on exciton-polaritons, we show that nonresonant excitation without imposed phase can spontaneously generate isolated Skyrmions and self-organized Skyrmion lattices in a polariton condensate. We trace this mechanism to gain- and loss-induced phase curvature together with outward polariton flow. We further demonstrate that polariton nonlinearities provide all-optical control of these textures, enabling switching of the Skyrmion number and reconfiguration of Skyrmion moiré lattices through resonant and nonresonant excitation schemes. These results establish nonlinear non-Hermitian resonators as a versatile platform for the spontaneous generation and active control of scalar topological light fields.

physics.optics↗

arXiv2026

Universal exciton polariton logic gates in Ouroboros rings

All-optical logic gates have significantly advanced over a diverse range of photonic systems, boosted by intricate nonlinearities that facilitate the engineering of complex logic operations. Here, we demonstrate that in semiconductor microcavities, polariton condensates trapped in Ouroboros-shaped rings form specifically charged vortices, determined by the strength of nonlinearity and the excitation method. Quantized vortex phases encode binary digits that can be nonresonantly controlled by optical pulses incident directly upon the ring, enabling logic operations. By interconnecting three polariton Ouroboros rings, we realize a universal set of logic gates (AND, OR, NIMPLY) fundamental to functional polaritonic devices. The Ouroboros structures are highly customizable, providing a robust and promising platform for exploring more complex logic operations.

physics.optics↗

arXiv2026

High-quality single photons from cavity-enhanced biexciton-to-exciton transition

Resonant laser excitation of a two-level system with subsequent single-photon emission can be used to generate single photons with high indistinguishability or Hong-Ou-Mandel (HOM) visibility. However, spectral overlap between excitation laser and emitted photons generally poses significant challenges. Furthermore, emitter re-excitation intrinsically limits achievable single-photon purity. Established solutions mitigate these issues at significant cost to source efficiency and with increased source complexity. This motivates the use of few-level systems with spectral separation of excitation and emission pathways. One option is a three-level cascade. However, without targeted lifetime engineering of emitting states, the cascade naturally limits achievable photon indistinguishability. Here we study a semiconductor quantum dot with resonant and selective cavity-enhancement of biexciton-to-exciton transition. Following resonant two-photon excitation of the biexciton state, we collect the emitted single photon with the cavity. This approach circumvents emitter re-excitation and naturally introduces spectral separation of excitation laser and emitted single photon. Supported by first experimental results, we demonstrate theoretically that with selective Purcell enhancement, the observed quality quantifiers of single-photon emission (purity, equivalently $g^{(2)}(0)$, and HOM visibility $\mathcal{V}$, equivalently indistinguishability) are competitive with respect to high-quality deterministic quantum-dot single-photon sources. This is already achieved without systematic optimization or targeted system engineering, which firmly places the reported approach as a viable route to the next generation of highest-quality quantum-dot based deterministic single-photon sources.

quant-ph↗

arXiv2026

Microscopic simulations of the coupled dynamics of cavity photons, excitons, and biexcitons

The coherent interaction between quantum light and material excitations in semiconductor nanostructures is investigated using a fully quantized microscopic approach that incorporates many-body Coulomb correlations. The simulations demonstrate that the quantum dynamics is influenced by biexciton continuum states and is highly sensitive to both the frequency of the cavity mode and the strength of the light-matter coupling.

cond-mat.mes-hall↗

arXiv2026

Universal Topology of Exceptional Points in Nonlinear Non-Hermitian Systems

Exceptional points (EPs) are non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to unusual physical effects across scientific disciplines. The concept of EPs has recently been extended to nonlinear physical systems. We theoretically demonstrate a universal topology in the nonlinear parameter space for a large class of physical systems that support 2nd order EPs in the linear regime. Knowledge of this topology (called elliptic umbilic singularity in bifurcation theory) deepens our understanding of 2nd order linear EPs, which here emerge as coalescence of 4 nonlinear eigenvectors. This helps guide future experimental discovery of nonlinear EPs and their classification, establish rigorous bounds of sensitivity enhancement of EPs in nonlinear systems, and helps envision and optimize technological applications of nonlinear EPs. Our theoretical approach is general and can be extended to nonlinear perturbations of 3rd and higher-order EPs.

physics.optics↗

arXiv2026

Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology

Non-Hermitian systems hosting exceptional points (EPs) exhibit signal enhancement and unconventional mode dynamics. Going beyond isolated EPs, here we report on the existence of exceptional rings (ERs) in planar optical resonators with specific form of circular dichroism and TE-TM splitting. Such exceptional rings possess intriguing topologies as discussed earlier for condensed matter systems, but they remain virtually unexplored in presence of nonlinearity, for which our photonic platform is ideal. We find that when Kerr-type nonlinearity (or saturable gain) is introduced, the linear ER splits into two concentric ERs, with the larger-radius ring being a ring of third-order EPs. Transitioning from linear to nonlinear regime, we present a rigorous analysis of (spectral and band) topologies and report enhanced and adjustable perturbation response in the nonlinear regime. Whereas certain features are specific to our system, the results on non-Hermitian topologies and nonlinearity-enhanced perturbation response are generic and equally relevant to a broad class of other nonlinear non-Hermitian systems, providing a universal framework for engineering ERs and EPs in nonlinear non-Hermitian systems.

physics.optics↗

arXiv2026

Electrically tunable nonrigid moire exciton polariton supersolids at room temperature

A supersolid is a macroscopic quantum state which sustains superfluid and crystallizing structure together after breaking the U(1) symmetry and translational symmetry. On the other hand, a moire pattern can form by superimposing two periodic structures along a particular direction. Up to now, supersolids and moire states are disconnected from each other. In this work we show that exciton polariton supersolids can form moire states in a double degenerate parametric scattering process which creates two constituted supersolids with different periods in a liquid crystal microcavity. In addition, we demonstrate the nonrigidity of the moire exciton polariton supersolids by electrically tuning the wavevector and period of one supersolid component with another one being fixed. Our work finds a simple way to link moire states and supersolids, which offers to study nontrivial physics emerging from the combination of moire lattices and supersolids which can be electrically tuned at room temperature.

physics.optics↗

arXiv2025

Ultrafast Exciton-Polariton Transport and Relaxation in Halide Perovskite

Halide perovskites offer a great platform for room-temperature exciton-polaritons (EPs) due to their strong oscillator strength and large exciton binding energy, promising applications in next-generation photonic and polaritonic devices. Efficient manipulation of EP transport and relaxation is critical for device performance, yet their spatiotemporal dynamics across different in-plane momenta (k//) remain poorly understood due to limitations in experimental access. In this work, we employ energy-resolved transient reflectance microscopy (TRM) combined with the dispersion relation of EPs to achieve high-resolution imaging of EP transport at specific k//. This approach directly reveals the quasi-ballistic transport and ultrafast relaxation of EPs in different k// regions, showcasing diffusion as fast as ~490 cm2/s and a relaxation time of ~95.1 fs. Furthermore, by tuning the detuning parameter, we manipulate the ballistic transport group velocity and relaxation time of EPs across varying k//. Our results reveal key insights into the dynamics of EP transport and relaxation, providing valuable guidance for the design and optimization of polaritonic devices.

cond-mat.mtrl-sci↗

arXiv2025

Indistinguishable photons from a two-photon cascade

Decay of a four-level diamond scheme via a cascade is a potential source of entangled photon pairs. A solid-state implementation is the biexciton cascade in a semiconductor quantum dot. While high entanglement fidelities have been demonstrated, the two photons, XX and X, are temporally correlated, typically resulting in poor photon coherence. Here, we demonstrate a high two-photon interference visibility (a measure of the photon coherence) for both XX (V=94$\pm$2%) and X (V=82$\pm$6%) photons. This is achieved by Purcell-enhancing the biexciton transition in a low-noise device. We find that the photon coherence follows the well-known quantum optics result upon tuning the XX:X lifetime ratio over two orders of magnitude.

quant-ph↗

arXiv2025

Polarization- and wave-vector selective optical metasurface with near-field coupling

Metasurfaces are a powerful tool for manipulating light using small structures on the nanoscale. In most meta-surfaces, near-field couplings are treated as unfavorable perturbations. Here, we experimentally investigate a structure consisting of sinusoidally modulated silicon waveguides where near-field coupling of local resonances leads to negative coupling, i.e. a negative coupling constant. This gives rise to wave-vector dependent eigenstates of elliptical, linear and circular polarizations. In particular, fully circular polarization states are not only present at a single point in momentum-space (k-space), but along a line. This circular polarization line, as well as a linear polarization line, emanates from a polarization degeneracy at the Dirac point. We experimentally validate the existence of these eigenstates and demonstrate the energy-, polarization- and wave-vector-dependence of this metasurface. By tuning the incident k-vector, certain polarization-energy eigenstates are strongly reflected allowing for uses in angle-tunable polarization filters and light sources.

physics.optics↗

arXiv2025

Non-Hermitian trapping of Dirac exciton-polariton condensates in a perovskite metasurface

Massless Dirac particles avoid trapping due to their exceptional tunneling properties manifested in the so-called Klein paradox. This conclusion stems from the conservative treatment, but so far, it has not been extended to a non-Hermitian framework. Recently, driven-dissipative bosonic condensation of Dirac exciton-polaritons was demonstrated in metasurface waveguides. Here, we report an experimental observation of spatial binding and energy quantization of Dirac exciton-polaritons in a halide perovskite metasurface. A combination of spatially profiled nonresonant optical excitation and exciton-polariton interaction forms an effective non-Hermitian complex potential responsible for the observed effect. In the case of tightly focused pump spots spanning from 9 to 17~$μ$m, several bound states simultaneously achieve macroscopic occupation, constituting a multi-mode bosonic condensation of exciton-polaritons. Our theoretical analysis based on the driven-dissipative extension of the Dirac equation reveals that the non-Hermitian character of the effective trap allows for confinement even in the case of the gapless Dirac-like photonic dispersion, both above and below the energy of the dispersion crossing.

cond-mat.mes-hall↗

arXiv2025

Topological edge states in curved zigzag superlattices in nonlinear exciton-polaritons

Zigzag chains allow for the formation of topological edge states. Several distinct chain architectures have been developed for this purpose. Here, we report a zigzag superlattice, containing two staggered sub-lattices, that supports multiple edge states, including higher-order modes. In such lattices, the intra- and intercell coupling is imbalanced by the tunneling effect of the eigenstates or deformation of the higher-order modes. We demonstrate that by arranging the zigzag superlattice into a curved shape, some of the edge states transition into bulk states as the curvature of the lattice increases, while some bulk states become more localized towards edge states. The reason is that a curved superlattice strengthens the intra-lattice coupling of the inner sub-lattice due to the separation reduction of the potential wells. %which, on the one hand, hinders the tunneling of the eigenstate to the outer sub-lattice and hence weakens the edge states formed in the inner sub-lattice. On the other hand, it can isolate more edge states formed in the outer sub-lattice, because of the induced more intensive deformation of the higher-order modes in the inner sub-lattice. We also show that some bulk states at larger curvatures can be transformed into edge states by a repulsive nonlinearity, which also enables the coexistence of different edge states. As a specific and ideal platform for realizing such topological superlattices we explore exciton-polaritons in semiconductor microcavities with their strong nonlinearity and possibility for optical excitation and control. Our work introduces an additional dimension for the design of complex topological lattices and functional photonic devices.

physics.optics↗

arXiv2025

Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm

The time-dependent one-dimensional nonlinear Schrödinger equation (NLSE) is solved numerically by a hybrid pseudospectral-variational quantum algorithm that connects a pseudospectral step for the Hamiltonian term with a variational step for the nonlinear term. The Hamiltonian term is treated as an integrating factor by forward and backward Fourier transformations, which are here carried out classically. This split allows us to avoid higher-order time integration schemes, to apply a first-order explicit time stepping for the remaining nonlinear NLSE term in a variational algorithm block, and thus to avoid numerical instabilities. We demonstrate that the analytical solution is reproduced with a small root mean square error for a long time interval over which a nonlinear soliton propagates significantly forward in space while keeping its shape. We analyze the accuracy of the quantum algorithm and compare it with classical approaches. Furthermore, we investigate the influence of algorithm parameters on the accuracy of the results, including the temporal step width and the depth of the quantum circuit.

quant-ph↗

arXiv2025

Microscopic approach to the quantized light-matter interaction in semiconductor nanostructures: Complex coupled dynamics of excitons, biexcitons, and photons

We present a microscopic and fully quantized model to investigate the interaction between semiconductor nanostructures and quantum light fields including the many-body Coloumb interaction between photoexcited electrons and holes. Our approach describes the coupled dynamics of the quantum light field and single and double electron-hole pairs, i.e., excitons and biexcitons, and exactly accounts for Coulomb many-body correlations and carrier band dispersions. Using a simplified yet exact approach, we study a one-dimensional two-band system interacting with a single-mode, two-photon quantum state within a Tavis$\unicode{x2013}$Cummings framework. By employing an exact coherent factorization scheme, the computational complexity is reduced significantly enabling numerical simulations. We also derive a simplified model which includes only the bound $1s$-exciton and biexciton states for comparison. Our simulations reveal distinct single- and two-photon Rabi oscillations, corresponding to photon-exciton and exciton-biexciton transitions. We demonstrate, in particular, that biexciton continuum states significantly modify the dynamics in a way that cannot be captured by simplified models which consider only bound states. Our findings emphasize the importance of a comprehensive microscopic modeling in order to accurately describe quantum optical phenomena of interacting electronic many-body systems.

cond-mat.mes-hall↗