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We show that the performance of critical quantum metrology protocols, counter-intuitively, can be enhanced by finite temperature. We consider a toy-model squeezing Hamiltonian, the Lipkin-Meshkov-Glick model and the paradigmatic Ising model. We show that the temperature enhancement of the quantum Fisher information can be achieved by adiabatic preparation of the critical state and by preparing it directly in the proximity of the critical point. We also find a relatively simple, however, non-optimal measurement capable of harnessing finite temperature to increase the parameter estimation sensitivity. Therefore, we argue that temperature can be considered as a resource in critical quantum metrology., Comment: 6 pages, 2 figures, improved presentation and discussions

Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here, we introduce a simulation framework for strongly correlated quantum systems that can be represented by model spin Hamiltonians. Our approach leverages reconfigurable qubit architectures to programmably simulate real-time dynamics and introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital-analog simulation toolbox for efficient Hamiltonian time evolution utilizing digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin-spin interactions, and as an example present an implementation proposal based on Rydberg atom arrays. Then, we show how detailed spectral information can be extracted from these dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single-dataset. To illustrate the approach, we show how this method can be used to compute key properties of a polynuclear transition-metal catalyst and 2D magnetic materials., Comment: 21 pages and 11 figures, plus supplementary information

For the numerical solution of the cubic nonlinear Schr\"{o}dinger equation with periodic boundary conditions, a pseudospectral method in space combined with a filtered Lie splitting scheme in time is considered. This scheme is shown to converge even for initial data with very low regularity. In particular, for data in $H^s(\mathbb T^2)$, where $s>0$, convergence of order $\mathcal O(\tau^{s/2}+N^{-s})$ is proved in $L^2$. Here $\tau$ denotes the time step size and $N$ the number of Fourier modes considered. The proof of this result is carried out in an abstract framework of discrete Bourgain spaces, the final convergence result, however, is given in $L^2$. The stated convergence behavior is illustrated by several numerical examples., Comment: arXiv admin note: substantial text overlap with arXiv:2301.10639

Recent advances in generating well controlled dense arrangements of individual atoms in free space have generated interest in understanding how the extended nature of these systems influences superradiance phenomena. Here, we provide an in-depth analysis on how space-dependent light-shifts and decay rates induced by dipole-dipole interactions modify the steady-state properties of coherently driven arrays of quantum emitters. We characterize the steady-state phase diagram, with particular focus on the radiative properties in the steady-state. Interestingly, we find that diverging from the well-established Dicke paradigm of equal all-to-all interactions significantly modifies the emission properties. In particular, the prominent quadratic scaling of the radiated light intensity with particle number in the steady-state -- a hallmark of steady-state Dicke superradiance -- is entirely suppressed, resulting in only linear scaling with particle number. We show that this breakdown of steady-state superradiance occurs due to the emergence of additional dissipation channels that populate not only superradiant states but also subradiant ones. The additional contribution of subradiant dark states in the dynamics leads to a divergence in the time scales needed to achieve steady-states. Building on this, we further show that measurements taken at finite times for extended atom ensembles reveal properties closely mirroring the idealized Dicke scenario., Comment: 14 pages, 6 figures

Spin-orbit coupling is of fundamental interest in both quantum optical and condensed matter systems alike. In this work, we show that optically induced electronic excitations in lattices of V-type atoms exhibit an emergent spin-orbit coupling when the geometry is chiral. This spin-orbit coupling arises naturally from the electric dipole interaction between the atomic sites and leads to a nontrivial topology for the lattice band structure. Using a general quantum optical model, we determine analytically the conditions that give rise to spin-orbit coupling and characterize the behavior under various symmetry transformations. We demonstrate that chirality-induced spin-orbit coupling can result from either the chirality of the underlying lattice geometry or the combination of an achiral lattice with a suitably chosen external quantization axis. We then discuss how these results are influenced by dissipation, which breaks time-reversal symmetry and illuminates the distinction between true and false chirality. Our results demonstrate that chiral atom arrays are a robust platform for realizing spin-orbit-coupled topological states of matter., Comment: accepted version

Pretrained language models (PLMs) form the basis of most state-of-the-art NLP technologies. Nevertheless, they are essentially black boxes: Humans do not have a clear understanding of what knowledge is encoded in different parts of the models, especially in individual neurons. The situation is different in computer vision, where feature visualization provides a decompositional interpretability technique for neurons of vision models. Activation maximization is used to synthesize inherently interpretable visual representations of the information encoded in individual neurons. Our work is inspired by this but presents a cautionary tale on the interpretability of single neurons, based on the first large-scale attempt to adapt activation maximization to NLP, and, more specifically, large PLMs. We propose feature textualization, a technique to produce dense representations of neurons in the PLM word embedding space. We apply feature textualization to the BERT model (Devlin et al., 2019) to investigate whether the knowledge encoded in individual neurons can be interpreted and symbolized. We find that the produced representations can provide insights about the knowledge encoded in individual neurons, but that individual neurons do not represent clearcut symbolic units of language such as words. Additionally, we use feature textualization to investigate how many neurons are needed to encode words in BERT., Comment: To be published in 'BlackboxNLP 2023: The 6th Workshop on Analysing and Interpreting Neural Networks for NLP'. Camera-ready version

Understanding the role of Biogenic Volatile Organic Compounds (BVOCs) in atmospheric chemistry and their impact on oxidants and aerosol formation is essential for global environmental research. BVOC emissions, primarily sourced from biogenic processes, pose a challenge due to the vast diversity of vegetation and ecosystems, as well as temporal changes in land use. While prevalent BVOC emission models categorize vegetation into functional types, the variability in environmental parameters and temporal fluctuations within natural canopies remains inadequately represented. This study introduces an innovative device system designed to address these challenges by integrating the Relaxed Eddy Accumulator and Gas Chromatograph Photoionization Detector (REAPER) in real-time measurement of isoprene fluxes. The system is portable, cost-effective and lightweight, easily to deploy in remote environments. By enabling high temporal resolution measurements, this device overcomes limitations associated with traditional techniques and offers accurate chromatograms. The novel instrument also facilitates real-time data transmission through a cloud-based platform, allowing access to meteorological data, calculated parameters, chromatograms and flux results. This feature supports the deployment of these systems across a wide range of sites and integrates them into existing flux tower networks. In conclusion, this research contributes to the advancement of isoprene fluxes measurement techniques and validation of satellite-based retrievals of isoprene abundances providing a valuable tool for scientists studying atmospheric chemistry and its impacts on the environment in diverse ecosystems, ultimately aiding in our understanding of the complex interplay between biogenic processes and atmospheric chemistry., Comment: 25-pages, 10 figures

Efficient transport and harvesting of excitation energy under low light conditions is an important process in nature and quantum technologies alike. Here we formulate a quantum optics perspective to excitation energy transport in configurations of two-level quantum emitters with a particular emphasis on efficiency and robustness against disorder. We study a periodic geometry of emitter rings with subwavelength spacing, where collective electronic states emerge due to near-field dipole-dipole interactions. The system gives rise to collective subradiant states that are particularly suited to excitation transport and are protected from energy disorder and radiative decoherence. Comparing ring geometries with other configurations shows that that the former are more efficient in absorbing, transporting, and trapping incident light. Because our findings are agnostic as to the specific choice of quantum emitters, they indicate general design principles for quantum technologies with superior photon transport properties and may elucidate potential mechanisms resulting in the highly efficient energy transport efficiencies in natural light-harvesting systems., Comment: 12 pages, 6 figures

Atomic arrays can exhibit collective light emission when the transition wavelength exceeds their lattice spacing. Subradiant states take advantage of this phenomenon to drastically reduce their overall decay rate, allowing for long-lived states in dissipative open systems. We build on previous work to investigate whether or not disorder can further decrease the decay rate of a singly-excited atomic array. More specifically, we consider spatial disorder of varying strengths in a 1D half waveguide and in 1D, 2D, and 3D atomic arrays in free space and analyze the effect on the most subradiant modes. While we confirm that the dilute half waveguide exhibits an analog of Anderson localization, the dense half waveguide and free space systems can be understood through the creation of close-packed, few-body subradiant states similar to those found in the Dicke limit. In general, we find that disorder provides little advantage in generating darker subradiant states in free space on average and will often accelerate decay. However, one could potentially change interatomic spacing within the array to engineer specific subradiant states., Comment: 13 pages, 12 figures; typos corrected, references added, figures slightly modified

We consider the wave equation with focusing power nonlinearity. The associated ODE in time gives rise to a self-similar solution known as the ODE blowup. We prove the nonlinear asymptotic stability of this blowup mechanism outside of radial symmetry in all space dimensions and for all superlinear powers. This result covers for the first time the whole energy-supercritical range without symmetry restrictions., Comment: 45 pages, with minor improvements to match the published version

In this paper we consider an approach to improve the performance of exponential Runge--Kutta integrators and Lawson schemes} in cases where the solution of a related, but usually much simpler, problem can be computed efficiently. While for implicit methods such an approach is common (e.g. by using preconditioners), for exponential integrators this has proven more challenging. Here we propose to extract a constant coefficient differential operator from the semilinear advection-diffusion-reaction equation for which, in many situations, efficient methods are known to compute the required matrix functions. Both a linear stability analysis and {\color{black} extensive} numerical experiments show that the resulting schemes can be unconditionally stable. In fact, we find that exponential integrators of Runge--Kutta type and Lawson schemes can have better stability properties than similarly constructed implicit-explicit schemes. We also derive two new Lawson type integrators that further improve on these stability properties. The overall effectiveness of the approach is highlighted by a number of performance comparisons on examples in two and three space dimensions.

Aerial image segmentation is the basis for applications such as automatically creating maps or tracking deforestation. In true orthophotos, which are often used in these applications, many objects and regions can be approximated well by polygons. However, this fact is rarely exploited by state-of-the-art semantic segmentation models. Instead, most models allow unnecessary degrees of freedom in their predictions by allowing arbitrary region shapes. We therefore present a refinement of our deep learning model which predicts binary space partitioning trees, an efficient polygon representation. The refinements include a new feature decoder architecture and a new differentiable BSP tree renderer which both avoid vanishing gradients. Additionally, we designed a novel loss function specifically designed to improve the spatial partitioning defined by the predicted trees. Furthermore, our expanded model can predict multiple trees at once and thus can predict class-specific segmentations. As an additional contribution, we investigate the impact of a non-optimal training process in comparison to an optimized training process. While model architectures optimized for aerial images, such as PFNet or our own model, show an advantage under non-optimal conditions, this advantage disappears under optimal training conditions. Despite this observation, our model still makes better predictions for small rectangular objects, e.g., cars.

A filtered Lie splitting scheme is proposed for the time integration of the cubic nonlinear Schr\"odinger equation on the two-dimensional torus $\mathbb{T}^2$. The scheme is analyzed in a framework of discrete Bourgain spaces, which allows us to consider initial data with low regularity; more precisely initial data in $H^s(\mathbb{T}^2)$ with $s>0$. In this way, the usual stability restriction to smooth Sobolev spaces with index $s>1$ is overcome. Rates of convergence of order $\tau^{s/2}$ in $L^2(\mathbb{T}^2)$ at this regularity level are proved. Numerical examples illustrate that these convergence results are sharp.

Chirality, or handedness, is a geometrical property denoting a lack of mirror symmetry. Chirality is ubiquitous in nature and is associated with the non-reciprocal interactions observed in complex systems ranging from biomolecules to topological materials. Here, we demonstrate that chiral arrangements of dipole-coupled atoms or molecules can facilitate the unidirectional transport of helical photonic excitations without breaking time-reversal symmetry. We show that such helicity dependent transport stems from an emergent spin-orbit coupling induced by the chiral geometry, which results in nontrivial topological properties. We also examine the effects of collective dissipation and find that many-body coherences lead to helicity dependent photon emission: an effect we call helical superradiance. Our results demonstrate an intimate connection between chirality, topology, and photon helicity that may contribute to molecular photodynamics in nature and could be probed with near-term quantum simulators., Comment: Revised paper, see also companion paper "Chirality-induced emergent spin-orbit coupling in topological atomic lattices"

Data types and codata types are, as the names suggest, often seen as duals of each other. However, most programming languages do not support both of them in their full generality, or if they do, they are still seen as distinct constructs with separately defined type-checking, compilation, etc. Rendel et al. were the first to propose variants of two standard program transformations, de- and refunctionalization, as a test to gauge and improve the symmetry between data and codata types. However, in previous works, codata and data were still seen as separately defined language constructs, with de- and refunctionalization being defined as similar but separate algorithms. These works also glossed over interactions between the aforementioned transformations and evaluation order, which leads to a loss of desirable $\eta$ expansion equalities. We argue that the failure of complete symmetry is due to the inherent asymmetry of natural deduction as the logical foundation of the language design. Natural deduction is asymmetric in that its focus is on producers (proofs) of types, whereas consumers (contexts, continuations, refutations) have a second-class status. Inspired by existing sequent-calculus-based language designs, we present the first language design that is fully symmetric in that the issues of polarity (data type vs codata types) and evaluation order (call-by-value vs call-by-name) are untangled and become independent attributes of a single form of type declaration. Both attributes, polarity and evaluation order, can be changed independently by one algorithm each. In particular, defunctionalization and refunctionalization are now one algorithm. Evaluation order can be defined and changed individually for each type, independently from polarity. By allowing only certain combinations of evaluation order and polarity, the aforementioned $\eta$ laws can be restored., Comment: 23 pages, 11 figures

Ordered atomic arrays with subwavelength lattice spacing emit light collectively. For fully inverted atomic arrays, this results in an initial burst of radiation and a fast build up of coherences between the atoms at initial times. Based on a cumulant expansion of the equations of motion, we derive exact analytical expressions for the emission properties and numerically analyze the full many-body problem resulting in the collective decay process for unprecedented system sizes of up to a few hundred atoms. We benchmark the cumulant expansion approach and show that it correctly captures the cooperative dynamics resulting in superradiance. For fully inverted arrays, this allows us to extract the scaling of the superradiant peak with particle number. For partially excited arrays where no coherences are shared among atoms, we also determine the critical number of excitations required for the emergence of superradiance in one- and two-dimensional geometries. In addition, we study the robustness of superradiance in the case of non-unit filling and position disorder., Comment: 13 pages, 7 figures