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Photon indistinguishability, entanglement, and antibunching are key ingredients in quantum optics and photonics. Decay cascades in quantum emitters offer a simple method to create entangled photon-pairs with negligible multi-pair generation probability. However, the degree of indistinguishability of the photons emitted in a cascade is intrinsically limited by the lifetime ratio of the involved transitions. Here we show that, for the biexciton-exciton cascade in a quantum dot, this ratio can be widely tuned by an applied electric field. Hong-Ou-Mandel interference measurements of two subsequently emitted biexciton photons show that their indistinguishability increases with increasing field, following the theoretically predicted behavior. At the same time, the emission linewidth stays close to the transform-limit, favoring applications relying on the interference among photons emitted by different sources.

High-purity multi-photon states are essential for photonic quantum computing. Among existing platforms, semiconductor quantum dots offer a promising route to scalable and deterministic multi-photon state generation. However, to fully realize their potential we require a suitable optical excitation method. Current approaches of multi-photon generation rely on active polarization-switching elements (e.g., electro-optic modulators, EOMs) to spatio-temporally demultiplex single photons. Yet, the achievable multi-photon rate is fundamentally limited by the switching speed of the EOM. Here, we introduce a fully passive demultiplexing technique that leverages a stimulated two-photon excitation process to achieve switching rates that are only limited by the quantum dot lifetime. We demonstrate this method by generating two-photon states from a single quantum dot without requiring any active switching elements. Our approach significantly reduces the cost of demultiplexing while shifting it to the excitation stage, enabling loss-free demultiplexing and effectively doubling the achievable multi-photon generation rate when combined with existing active demultiplexing techniques., Comment: 7 pages, 4 figures

Ultra-strong coupling (USC) is a light-matter interaction regime characterized by coupling strengths that substantially exceed the threshold for strong coupling. It gives rise to novel physical phenomena, such as efficient single-photon coupling and quantum gates, with applications in quantum sensing, nonlinear optics, and low-threshold lasing. Although early demonstrations in plasmonic systems have been realized, achieving USC in dielectric nanophotonic platforms, which offer lower losses and high Q-factors, remains challenging due to typically low mode overlap between the photonic field and the material resonance. Here, we demonstrate ultra-strong coupling to an epsilon-near-zero (ENZ) mode in an ultra-thin SiO$_2$ layer. Our approach leverages a dielectric dual-gradient metasurface supporting quasi-bound-states-in-the-continuum (qBIC) consisting of two tapered bars in each unit cell that generate strong out-of-plane electric fields which overlap exceptionally well with those of the ENZ mode. Using dual gradients to encode both the spectral and coupling parameter space, we track the anticrossing behaviour of this coupled system with high experimental precision, revealing a mode splitting equivalent to 19% of the ENZ mode energy; a four-to-five-fold increase compared to previous approaches. Furthermore, varying the position of the SiO$_2$ layer allows for deliberate control of the mode overlap and the coupling between the qBIC and either the ENZ mode or the transverse optical (TO) phonon can be selectively tuned. This allows us to experimentally create an USC three-resonator system, opening new possibilities for compact and scalable polaritonic devices for sensing and nonlinear optics., Comment: 20 pages, 5 figures, supplementary material

We present a general method for the implementation of quantum algorithms that optimizes both gate count and circuit depth. Our approach introduces connectivity-adapted CNOT-based building blocks called Parity Twine chains. It outperforms all known state-of-the art methods for implementing prominent quantum algorithms such as the quantum Fourier transform or the Quantum Approximate Optimization Algorithm across a wide range of quantum hardware, including linear, square-grid, hexagonal, ladder and all-to-all connected devices. For specific cases, we rigorously prove the optimality of our approach.

Active metasurfaces, compact platforms for nanoscale light manipulation, are transforming technologies like holography, quantum cryptography, and optical computing. Despite their versatility, tunability in metasurfaces has mainly relied on shifting the resonance wavelength or increasing material losses to spectrally detune or quench resonant modes, respectively. However, both methods face fundamental limitations, such as limited Q-factor and near-field enhancement control and the inability to achieve resonance on/off switching by completely coupling and decoupling the mode from the far-field. Here, we demonstrate temporal symmetry-breaking in metasurfaces via ultrafast optical pumping, marking the first experimental realization of radiative loss-driven resonance creation, annihilation, broadening, and sharpening. We introduce restored symmetry-protected bound states in the continuum as a new concept which are central to the realization of temporal symmetry-breaking. These states arise in metasurfaces with geometrically asymmetric unit cells, where the total dipole moment, composed of two antisymmetric dipoles, cancels out. Mie-resonant optical absorption within specific regions of the unit cell locally modifies the refractive index, disrupting the balance between the two dipole moments. A total dipole moment is thereby created or annihilated, and consequently, the radiative loss is tuned. This enables full control over coupling to incoming light, allowing precise adjustment of the resonance linewidth, near-field enhancement, and resonance amplitude. Our work establishes radiative loss-based active metasurfaces with potential applications ranging from high-speed optical and quantum communications to time-crystals and photonic circuits.

We consider the selective sensing of planar waves in the presence of noise. We present different methods to control the sensitivity of a quantum sensor network, which allow one to decouple it from arbitrarily selected waves while retaining sensitivity to the signal. Comparing these methods with classical (non-entangled) sensor networks we demonstrate two advantages. First, entanglement increases precision by enabling the Heisenberg scaling. Second, entanglement enables the elimination of correlated noise processes corresponding to waves with different propagation directions, by exploiting decoherence-free subspaces. We then provide a theoretical and numerical analysis of the advantage offered by entangled quantum sensor networks, which is not specific to waves and can be of general interest. We demonstrate an exponential advantage in the regime where the number of sensor locations is comparable to the number of noise sources. Finally, we outline a generalization to other waveforms, e.g., spherical harmonics and general time-dependent fields.

Metasurfaces offer a powerful platform for effective light manipulation, which is crucial for advanced optical technologies. While designs of polarization-independent structures have reduced the need for polarized illumination, they are often limited by either low Q factors or low resonance modulation. Here, we design and experimentally demonstrate a metasurface with polarization-independent quasi-bound state in the continuum (quasi-BIC), where the unit cell consists of four silicon squares arranged in a two-dimensional array and the resonance properties can be controlled by adjusting the edge length difference between different squares. Our metasurface experimentally achieves a Q factor of approximately 100 and a resonance modulation of around 50%. This work addresses a common limitation in previous designs, which either achieved high Q factors exceeding 200 with a resonance modulation of less than 10%, leading to challenging signal-to-noise ratio requirements, or achieved strong resonance modulation with Q factors of only around 10, limiting light confinement and fine-tuning capabilities. In contrast, our metasurface ensures that the polarization-independent signal is sharp and distinct within the system, reducing the demands on signal-to-noise ratio and improving robustness. Experiments show the consistent performance across different polarization angles. This work contributes to the development of versatile optical devices, enhancing the potential for the practical application of BIC-based designs in areas such as optical filtering and sensing.

We review $H^{1}$-well-posedness for initial value problems of ordinary differential equations with state-dependent right-hand side. We streamline known approaches to infer existence and uniqueness of solutions for small times given a Lipschitz-continuous prehistory. The paramount feature is a reduction of the differential equation to a fixed point problem that admits a unique solution appealing to the contraction mapping principle. The use of exponentially weighted Sobolev spaces in this endeavor proves to be as powerful as for ordinary differential equations without delay. Our result includes a blow-up criterium for global existence of solutions. The discussion of well-posedness is concluded by new results covering continuous dependence on initial prehistories and on the right-hand sides.

We present an application of recent well-posedness results in the theory of delay differential equations for ordinary differential equations arXiv:2308.04730 to a generalized population model for stem cell maturation. The weak approach using Sobolev-spaces we take allows for a larger class of initial prehistories and makes checking the requirements for well-posedness of such a model considerably easier compared to previous approaches. In fact the present approach is a possible means to guarantee that the solution manifold is not empty, which is a necessary requirement for a $C^{1}$-approach to work.

Photonic metasurfaces offer exceptional control over light at the nanoscale, facilitating applications spanning from biosensing, and nonlinear optics to photocatalysis. Many metasurfaces, especially resonant ones, rely on periodicity for the collective mode to form, which makes them subject to the influences of finite size effects, defects, and edge effects, all of which have considerable negative impact at the application level. These aspects are especially important for quasi-bound state in the continuum (BIC) metasurfaces, for which the collective mode is highly sensitive to perturbations due to high quality factors and strong near-field enhancement. Here, we quantitatively investigate the mode formation in quasi-BIC metasurfaces on the individual resonator level using scattering scanning near-field optical microscopy (s-SNOM) in combination with a new image processing technique. We find that the quasi-BIC mode is formed at a minimum size of 10 x 10-unit cells much smaller than expected from far-field measurements. Furthermore, we show that the coupling direction of the resonators, defects and edge states have pronounced influence on the quasi-BIC mode. This study serves as a link between the far-field and near-field responses of metasurfaces, offering crucial insights for optimizing spatial footprint and active area, holding promise for augmenting applications such as catalysis and biospectroscopy., Comment: 30 pages, 6 figures, 8 supplementary figures

The (dual) Cauchy identity has an easy algebraic proof utilising a commutation relation between the up and (dual) down operators. By using Fomin's growth diagrams, a bijective proof of the commutation relation can be "bijectivised" to obtain RSK like correspondences. In this paper we give a concise overview of this machinery and extend it to Littlewood type identities by introducing a new family of relations between these operators, called projection identities. Thereby we obtain infinite families of bijections for the Littlewood identities generalising the classical ones. We believe that this approach will be useful for finding bijective proofs for Littlewood type identities in other settings such as for Macdonald polynomials and their specialisations, alternating sign matrices or vertex models., Comment: 29 pages

We introduce a probabilistic generalization of the dual Robinson--Schensted--Knuth correspondence, called $qt$RSK${}^*$, depending on two parameters $q$ and $t$. This correspondence extends the $q$RS$t$ correspondence, recently introduced by the authors, and allows the first tableaux-theoretic proof of the dual Cauchy identity for Macdonald polynomials. By specializing $q$ and $t$, one recovers the row and column insertion version of the classical dual RSK correspondence as well as of $q$- and $t$-deformations thereof which are connected to $q$-Whittaker and Hall--Littlewood polynomials. When restricting to Jack polynomials and $\{0,1\}$-matrices corresponding to words, we prove that the insertion tableaux obtained by $qt$RSK${}^*$ are invariant under swapping letters in the input word. Our approach is based on Fomin's growth diagrams and the notion of probabilistic bijections., Comment: 65 pages

The research communities studying visualization and sonification for data display and analysis share exceptionally similar goals, essentially making data of any kind interpretable to humans. One community does so by using visual representations of data, and the other community employs auditory (non-speech) representations of data. While the two communities have a lot in common, they developed mostly in parallel over the course of the last few decades. With this STAR, we discuss a collection of work that bridges the borders of the two communities, hence a collection of work that aims to integrate the two techniques into one form of audiovisual display, which we argue to be "more than the sum of the two." We introduce and motivate a classification system applicable to such audiovisual displays and categorize a corpus of 57 academic publications that appeared between 2011 and 2023 in categories such as reading level, dataset type, or evaluation system, to mention a few. The corpus also enables a meta-analysis of the field, including regularly occurring design patterns such as type of visualization and sonification techniques, or the use of visual and auditory channels, showing an overall diverse field with different designs. An analysis of a co-author network of the field shows individual teams without many interconnections. The body of work covered in this STAR also relates to three adjacent topics: audiovisual monitoring, accessibility, and audiovisual data art. These three topics are discussed individually in addition to the systematically conducted part of this research. The findings of this report may be used by researchers from both fields to understand the potentials and challenges of such integrated designs while hopefully inspiring them to collaborate with experts from the respective other field., Comment: 30 pages, 9 figures, accepted for EuroVis 2024 conference

We study the statistical resilience of the anti-concentration properties of Rademacher polynomials in face of adversarial deterministic noise taking the form of sign-flips. Given a multilinear polynomial $f:\mathbb{R}^n \to \mathbb{R}$ and a Rademacher vector $\boldsymbol{\xi} \in \{\pm 1\}^n$ (with independent entries), our results provide probabilistic lower bound estimations on the number of sign-flips that $\boldsymbol{\xi}$ can sustain without ``inflating" the atom probability $\sup_{x \in \mathbb{R} } \mathbb{P}\{f(\boldsymbol{\xi}) = x\}$ otherwise resulting in an adversarially biased distribution. Special emphasis is put on bilinear and quadratic forms, for which strengthened estimates are attained. From a computational perspective, our results in this venue are instance-bound in such a way that allows for an efficient computation of the statistical resilience guarantees from the quadratic polynomial itself directly. All of our probabilistic lower bound resilience guarantees are asymptotically tight. On route, we provide a short proof for a new small-ball probability estimate fitting Rademacher multilinear polynomials $f: \mathbb{R}^n \to \mathbb{R}$ removeing a polylog-factor from the classical Meka-Nguyen-Vu bound provided the coefficients are independent of $n$ (dimension-free, hereafter). This removal was conjectured to be possible by Meka-Nguyen-Vu regardless of our assumption. Bilinear Rademacher forms with dimension-free coefficients arise naturally in Combinatorics and specifically in the dense case of the edge-statistics conjecture posed by Alon, Hefetz, Krivelevich, and Tyomkyn. This case of the conjecture was resolved by Kwan and Sauermann. Replacing the appeal to the Meka-Nguyen-Vu classical bound in the work of Kwan, Sudakov, and Tran with our shortly proved result attains an additional proof of the dense case of the edge-statistics conjecture., Comment: Numerous changes from the last version: 1. An oversight in the proof fixed. 2. Added treatment of high degree polynomials 3. New results added

Enhancing and controlling light-matter interactions is crucial in nanotechnology and material science, propelling research on green energy, laser technology, and quantum cryptography. Central to enhanced light-matter coupling are two parameters: the spectral overlap between an optical cavity mode and the material's spectral features (e.g., excitonic or molecular absorption lines), and the quality factor of the cavity. Controlling both parameters simultaneously is vital, especially in complex systems requiring extensive data to uncover the numerous effects at play. However, so far, photonic approaches have focused solely on sampling a limited set of data points within this 2D parameter space. Here we introduce a nanophotonic approach that can simultaneously and continuously encode the spectral and quality factor parameter space of light-matter interactions within a compact spatial area. Our novel dual-gradient metasurface design is composed of a 2D array of smoothly varying subwavelength nanoresonators, each supporting a unique mode. This results in 27,500 distinct modes within one array and a resonance density approaching the theoretical upper limit for metasurfaces. By applying our dual-gradient to surface-enhanced molecular sensing, we demonstrate the importance of coupling tailoring and unveil an additional coupling-based dimension of spectroscopic data. Our metasurface design paves the way for generalized light-matter coupling metasurfaces, leading to advancements in the field of photocatalysis, chemical sensing, and entangled photon generation., Comment: 5 figures, 5 supplementary notes, 14 supplementary figures

Metasurfaces have unlocked significant advancements across photonics, yet their efficient active control remains challenging. The active materials required often lack continuous tunability, exhibit inadequate refractive index (RI) changes, or suffer from high losses. These aspects pose an inherent limitation for resonance-shifting based switching: when RI changes are small, the resulting shift is also minor. Conversely, high RI changes typically come with high intrinsic losses necessitating broad modes because narrow ones cannot tolerate such losses. Therefore, larger spectral shifts are required to effectively detune the modes. This paper introduces a novel active metasurface approach that converts the constraint of high intrinsic losses into a beneficial feature. This is achieved by controlling the losses in a hybrid vanadium dioxide (VO$_{2}$) - silicon metasurface, supporting symmetry-protected bound states in the continuum (BICs) within the infrared spectrum. By leveraging the temperature-controlled losses in VO$_{2}$ and combining them with the inherent far-field-coupling tunability of BICs, we gain unprecedented precision in independently controlling both the radiative and nonradiative losses of the resonant system. Our dual-control mechanism allows us to optimize our metasurfaces and we experimentally demonstrate quality factors above 200, a maximum reflectance amplitude of 90%, a relative switching contrast of 78%, and continuous tuning from under- to over-coupling within the infrared spectral range. This study provides a foundation for experimentally and technologically simple, fine-tunable, active metasurfaces for applications ranging from molecular sensors to filters and optical modulators., Comment: 25 pages, 4 figures, 4 supplementary figures

We study Ramsey properties of randomly perturbed $3$-uniform hypergraphs. For~$t\geq 2$, write $\tilde K^{(3)}_t$ to denote the $3$-uniform {\it expanded} clique hypergraph obtained from the complete graph $K_t$ by expanding each of the edges of the latter with a new additional vertex. For an even integer $t\geq 4$, let~$M$ denote the asymmetric maximal density of the pair $(\tilde K^{(3)}_t,\tilde K^{(3)}_{t/2})$. We prove that adding a set~$F$ of random hyperedges satisfying $|F|\gg n^{3-1/M}$ to a given $n$-vertex $3$-uniform hypergraph~$H$ with non-vanishing edge density asymptotically almost surely results in a perturbed hypergraph enjoying the Ramsey property for $\tilde K^{(3)}_t$ and two colours. We conjecture that this result is asymptotically best possible with respect to the size of $F$ whenever $t\geq 6$ is even. The key tools of our proof are a new variant of the hypergraph regularity lemma accompanied with a \emph{tuple lemma} providing appropriate control over joint link graphs. Our variant combines the so called strong and the weak hypergraph regularity lemmata., Comment: 47 pages, 1 figure. In this version two proofs are provided for the tuple lemma; a short one employing the hypergraph counting lemma and longer one avoids the counting lemma

Solid-state quantum emitters embedded in circular Bragg resonators are attractive due to their ability to emit quantum states of light with high brightness and low multi-photon probability. As for any emitter-microcavity system, fabrication imperfections limit the spatial and spectral overlap of the emitter with the cavity mode, thus limiting their coupling strength. Here, we show that an initial spectral mismatch can be corrected after device fabrication by repeated wet chemical etching steps. We demonstrate ~16 nm wavelength tuning for optical modes in AlGaAs resonators on oxide, leading to a 4-fold Purcell enhancement of the emission of single embedded GaAs quantum dots. Numerical calculations reproduce the observations and suggest that the achievable performance of the resonator is only marginally affected in the explored tuning range. We expect the method to be applicable also to circular Bragg resonators based on other material platforms, thus increasing the device yield of cavity-enhanced solid-state quantum emitters.

Visualization onboarding supports users in reading, interpreting, and extracting information from visual data representations. General-purpose onboarding tools and libraries are applicable for explaining a wide range of graphical user interfaces but cannot handle specific visualization requirements. This paper describes a first step towards developing an onboarding library called VisAhoi, which is easy to integrate, extend, semi-automate, reuse, and customize. VisAhoi supports the creation of onboarding elements for different visualization types and datasets. We demonstrate how to extract and describe onboarding instructions using three well-known high-level descriptive visualization grammars - Vega-Lite, Plotly.js, and ECharts. We show the applicability of our library by performing two usage scenarios that describe the integration of VisAhoi into a VA tool for the analysis of high-throughput screening (HTS) data and, second, into a Flourish template to provide an authoring tool for data journalists for a treemap visualization. We provide a supplementary website that demonstrates the applicability of VisAhoi to various visualizations, including a bar chart, a horizon graph, a change matrix or heatmap, a scatterplot, and a treemap visualization.