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In a prior paper we found that the Fourier-Legendre series of a Bessel function of the first kind J_{N}\left(kx\right) and of a modified Bessel functions of the first kind I_{N}\left(kx\right) lead to an infinite set of series involving \,_{1}F_{2} hypergeometric functions (extracted therefrom) that could be summed, having values that are inverse powers of the eight primes 1/\left(2^{i}3^{j}5^{k}7^{l}11^{m}13^{n}17^{o}19^{p}\right) multiplying powers of the coefficient k, for the first 22 terms in each series. The present paper shows how to generate additional, doubly infinite summed series involving \,_{1}F_{2} hypergeometric functions from Chebyshev polynomial expansions of Bessel functions, and trebly infinite sets of summed series involving \,_{1}F_{2} hypergeometric functions from Gegenbauer polynomial expansions of Bessel functions., Comment: 15 pages

One of the most important and topical challenges of quantum circuits is their scalability. Rapid Single Flux Quantum (RSFQ) technology is at the forefront of replacing current standard CMOS-based control architectures for a number of applications, including quantum computing and quantum sensor arrays. By condensing the control and readout to SFQ-based on-chip devices that are directly connected to the quantum systems, it is possible to minimise the total system overhead, improving scalability and integration. In this work, we present a novel RSFQ device that generates multi tone digital signals, based on complex pulse train sequences using a Circular Shift Register (CSR) and a comb filter stage. We show that the frequency spectrum of the pulse trains is dependent on a preloaded pattern on the CSR, as well as on the delay line of the comb filter stage. By carefully selecting both the pattern and delay, the desired tones can be isolated and amplified as required. Finally, we propose architectures where this device can be implemented to control and readout arrays of quantum devices, such as qubits and single photon detectors., Comment: Submitted to IEEE Transactions on Quantum Engineering

Physical reservoir computing (PRC) is a computing framework that harnesses the intrinsic dynamics of physical systems for computation. It offers a promising energy-efficient alternative to traditional von Neumann computing for certain tasks, particularly those demanding both memory and nonlinearity. As PRC is implemented across a broad variety of physical systems, the need increases for standardised tools for data processing and model training. In this manuscript, we introduce PRCpy, an open-source Python library designed to simplify the implementation and assessment of PRC for researchers. The package provides a high-level interface for data handling, preprocessing, model training, and evaluation. Key concepts are described and accompanied by experimental data on two benchmark problems: nonlinear transformation and future forecasting of chaotic signals. Throughout this manuscript, which will be updated as a rolling release, we aim to facilitate researchers from diverse disciplines to prioritise evaluating the computational benefits of the physical properties of their systems by simplifying data processing, model training and evaluation., Comment: 19 pages, 5 figures

With the growing prevalence of AI, demand increases for efficient machine learning hardware. Physical systems are sought which combine image feature detection with the essential nonlinearity for tasks such as image classification. Existing physical hardware typically detects features linearly, then employs digital processing for nonlinear activation. Biological vision systems excel at nonlinear image processing. The retina detects features in ganglion cells via lateral inhibition, where cells nonlinearly compete for neuronal firing while supressing neighbouring cells. We present a bio-inspired 'retinomorphic' machine vision platform using an on-chip semiconductor network laser. The system detects multiple features in parallel via spatially-overlapping lasing modes, with integrated nonlinearity provided by antagonistic gain competition between modes - a photonic analogue of retinal inhibition. Parallel feature-detection enhances efficiency relative to feature-detection schemes which operate sequentially or via multiple device copies, with Si-compatible processing and a compact micron-scale footprint relative to existing mm-scale systems. We report 98.05% accuracy on MNIST-digits and 87.85% on Fashion-MNIST, with strong performance on short training datasets.

High-finesse microcavities offer a platform for compact, high-precision sensing by employing high-reflectivity, low-loss mirrors to create effective optical path lengths that are orders of magnitude larger than the device geometry. Here, we investigate the radiation hardness of Fabry-Perot microcavities formed from dielectric mirrors deposited on the tips of optical fibers. The microcavities are irradiated under both conventional (~0.1 Gy/s) and ultrahigh (FLASH, ~20 Gy/s) radiotherapy dose rates. Within our measurement sensitivity of ~40 ppm loss, we observe no degradation in the mirror absorption after irradiation with over 300 Gy accumulated dose. This result highlights the excellent radiation hardness of the dielectric mirrors forming the cavities, enabling new optics-based, real-time, in-vivo, tissue-equivalent radiation dosimeters with ~10 micron spatial resolution (our motivation), as well as other applications in high-radiation environments., Comment: 8 pages, 4 figures

The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can be used for two ends. First, it allows for a simple generalization of the Birkhoff theorem to Schwarzschild (A)de-Sitter spacetime. Second, it provides the means to construct an Abelian endomorphism group on the space of 2-forms. It is observed that taking the trace over this group element-wise induces a further Abelian group which may be identified with a tensor representation of conformal transformations, giving Einstein spacetimes access to their own conformal equivalence class. A further trace over the group yields the curvature invariants of the spacetime. The Kretschmann scalar becomes the topological Euler density, which may be linked in a simple way to the Hawking temperature of horizons., Comment: 19 pages, submitted to EPJ C

We demonstrate a mechanical crystal with an optically programmable defect mode. By applying an optical spring to a single unit cell of a phononic crystal membrane, we smoothly transfer a single mechanical mode into the bandgap, thereby localizing its spatial profile from one spanning the entire crystal to one confined within a few unit cells. This localization is evidenced by an enhanced mechanical frequency shift commensurate with a 37-fold reduction in the mode's participating mass. Our results lay groundwork for a new class of optomechanical systems that control mechanical mode profile and participating mass., Comment: 6 pages, 4 figures

This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions may be expanded in sums of pair products of $\,_{2}F_{3}$ functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible as pair-products of generalized Whittaker functions, $\,_{2}F_{1}$ functions, and $\,_{3}F_{2}$ functions into the realm of $\,_{P}F_{Q}$ functions where $P

Physical computing has the potential to enable widespread embodied intelligence by leveraging the intrinsic dynamics of complex systems for efficient sensing, processing, and interaction. While individual devices provide basic data processing capabilities, networks of interconnected devices can perform more complex and varied tasks. However, designing networks to perform dynamic tasks is challenging without physical models and accurate quantification of device noise. We propose a novel, noise-aware methodology for training device networks using Neural Stochastic Differential Equations (Neural-SDEs) as differentiable digital twins, accurately capturing the dynamics and associated stochasticity of devices with intrinsic memory. Our approach employs backpropagation through time and cascade learning, allowing networks to effectively exploit the temporal properties of physical devices. We validate our method on diverse networks of spintronic devices across temporal classification and regression benchmarks. By decoupling the training of individual device models from network training, our method reduces the required training data and provides a robust framework for programming dynamical devices without relying on analytical descriptions of their dynamics.

We extend prior work to derive three additional M-1-dimensional integral representations--over the interval $[0,1]$ --for products of M Slater orbitals that allows their magnitudes of coordinate vector differences (square roots of polynomials) $|{\bf x}_{1}-{\bf x}_{2}|=\sqrt{x_{1}^{2}-2x_{1}x_{2}\cos\theta+x_{2}^{2}}$ to be moved from disjoint products of functions into a single quadratic form whose square my be completed. This provides more alternatives to Fourier transforms that introduce a 3M-dimensional momentum integral for those products of Slater orbitals, followed by another set of M-1-dimensional integral representations to combine those denominators into one denominator having a single (momentum) quadratic form. The current work is also slightly more compact than Gaussian transforms that introduce an M-dimensional integral for products of M Slater orbitals. We have found that two of these M-1-dimensional integral representations over the interval $[0,1]$ are numerically stable, as was the prior version having integrals running over the interval $[0,\infty]$, and one does not need to test for a sufficiently large upper integration limit. For analytical reductions of integrals arising from any of the three, however, there is the possible drawback for large M of there being fewer tabled integrals over $[0,1]$ than over $[0,\infty]$. These representations have integration variables within square roots as arguments of Macdonald functions. In a number of cases, these may be converted to Meijer G-functions for which a single tabled integral exists over the interval $[0,\infty]$ of the prior paper, and from which other forms may be found. Finally, we introduce a fourth integral representation that is not easily generalizable to large M, but may well provide a bridge for finding the requisite integrals for such Meijer G-functions over $[0,1]$., Comment: 23 pages

The Bessel function of the first kind $J_{N}\left(kx\right)$ is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind $I_{N}\left(kx\right)$. The purpose of these expansions in Legendre polynomials was not an attempt to rival established \emph{numerical methods} for calculating Bessel functions, but to provide a form for $J_{N}\left(kx\right)$ useful for \emph{analytical} work in the area of strong laser fields, where analytical integration over scattering angles is essential. Despite their primary purpose, we can easily truncate the series at 21 terms to provide 33-digit accuracy that matches IEEE extended precision in some compilers. The analytical theme is furthered by showing that infinite series of like-powered contributors (involving $\,_{2}F_{3}$ hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the eight primes $1/\left(2^{i}3^{j}5^{k}7^{l}11^{m}13^{n}17^{o}19^{p}\right)$ multiplying powers of the coefficient $k$., Comment: This comprehensive revision makes clear the new series representation's utility for analytical work. It also better highlights the summed series involving $\,_{2}F_{3}$ hypergeometric functions. Despite the analytical purpose, a new appendix gives quadruple-precision polynomial approximations for J_0, J_1, I_0 and I_1, accurate to 33-digits for |x|<=3 and versions useful for integer arithmetic

The wavelength-coverage and sensitivity of JWST now enables us to probe the rest-frame UV - optical spectral energy distributions (SEDs) of galaxies at high-redshift ($z>4$). From these SEDs it is, in principle, through SED fitting possible to infer key physical properties, including stellar masses, star formation rates, and dust attenuation. These in turn can be compared with the predictions of galaxy formation simulations allowing us to validate and refine the incorporated physics. However, the inference of physical properties, particularly from photometry alone, can lead to large uncertainties and potential biases. Instead, it is now possible, and common, for simulations to be \emph{forward-modelled} to yield synthetic observations that can be compared directly to real observations. In this work, we measure the JWST broadband fluxes and colours of a robust sample of $58$ the distributions differ somewhat, though our observed sample size is small and thus susceptible to statistical fluctuations. Likewise, the predicted and observed colour evolution show broad agreement, at least at $58$, though, again, the sample size is small here., Comment: 11 pages, 10 figures, submitted to MNRAS

Arrays of artificial spin ices exhibit reconfigurable ferromagnetic resonance frequencies that can be leveraged and designed for potential applications.However, analytical and numerical studies of the frequency response of artificial spin ices have remained somewhat limited due to the need of take into account nonlocal dipole fields in theoretical calculations or by long computation times in micromagnetic simulations. Here, we introduce Gaenice, a framework to compute magnon dispersion relations of arbitrary artificial spin ice configurations. Gaenice makes use of a tight-binding approach to compute the magnon bands. It also provides the user complete control of the interaction terms included, e.g., external field, anisotropy, exchange, and dipole, making it useful also to compute ferromagnetic resonances for a variety of structures, such as multilayers and ensembles of weakly or non-interacting nanoparticles. Because it relies on a semi-analytical model, Gaenice is computationally inexpensive and efficient, making it an attractive tool for the exploration of large parameter spaces.

To benefit high-power interferometry and the creation of low-noise light sources, we develop a simple lead-compensated photodetector enabling quantum-limited readout from 0.3 mW to 10 mW and 10 k$\Omega$ transimpedance gain from 85 Hz - 35 MHz. Feeding the detector output back to an intensity modulator, we squash the classical amplitude noise of a commercial 1550 nm fiber laser to the shot noise limit over a bandwidth of 700 Hz - 200 kHz, observing no degradation to its (nominally ~100 Hz) linewidth., Comment: 7 pages, 6 figures

Strongly-interacting nanomagnetic arrays are ideal systems for exploring reconfigurable magnonics. They provide huge microstate spaces and integrated solutions for storage and neuromorphic computing alongside GHz functionality. These systems may be broadly assessed by their range of reliably accessible states and the strength of magnon coupling phenomena and nonlinearities. Increasingly, nanomagnetic systems are expanding into three-dimensional architectures. This has enhanced the range of available magnetic microstates and functional behaviours, but engineering control over 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial composed from multilayered artificial spin ice nanoarrays. Comprising two magnetic layers separated by a non-magnetic spacer, each nanoisland may assume four macrospin or vortex states per magnetic layer. This creates a system with a rich $16^N$ microstate space and intense static and dynamic dipolar magnetic coupling. The system exhibits a broad range of emergent phenomena driven by the strong inter-layer dipolar interaction, including ultrastrong magnon-magnon coupling with normalised coupling rates of $\frac{\Delta \omega}{\gamma} = 0.57$, GHz mode shifts in zero applied field and chirality-selective magneto-toroidal microstate programming and corresponding magnonic spectral control.

The history of reionisation is highly dependent on the ionising properties of high-redshift galaxies. It is therefore important to have a solid understanding of how the ionising properties of galaxies are linked to physical and observable quantities. In this paper, we use the First Light and Reionisation Epoch Simulations (FLARES) to study the Lyman-continuum (LyC, i.e. hydrogen-ionising) emission of massive ($M_*>10^8\,\mathrm{M_\odot}$) galaxies at redshifts $z=5-10$. We find that the specific ionising emissivity (i.e. intrinsic ionising emissivity per unit stellar mass) decreases as stellar mass increases, due to the combined effects of increasing age and metallicity. FLARES predicts a median ionising photon production efficiency (i.e. intrinsic ionising emissivity per unit intrinsic far-UV luminosity) of $\log_{10}(\xi_{\rm ion}\rm{/erg^{-1}Hz})=25.40^{+0.16}_{-0.17}$, with values spanning the range $\log_{10}(\xi_{\rm ion}\rm{/erg^{-1}Hz})=25-25.75$. This is within the range of many observational estimates, but below some of the extremes observed. We compare the production efficiency with observable properties, and find a weak negative correlation with the UV-continuum slope, and a positive correlation with the OIII equivalent width. We also consider the dust-attenuated production efficiency (i.e. intrinsic ionising emissivity per unit dust-attenuated far-UV luminosity), and find a median of $\log_{10}(\xi_{\rm ion}\rm{/erg^{-1}Hz})\sim25.5$. Within our sample of $M_*>10^8\,\mathrm{M_\odot}$ galaxies, it is the stellar populations in low mass galaxies that contribute the most to the total ionising emissivity. Active galactic nuclei (AGN) emission accounts for $10-20$ % of the total emissivity at a given redshift, and extends the LyC luminosity function by $\sim0.5$ dex., Comment: 19 pages, 17 figures, accepted for publication in MNRAS

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counter-intuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfv\'en waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, $\alpha=2$ as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed $>$600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: pre-flare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that $\alpha = 1.63 \pm 0.03$. This is below the critical threshold, suggesting that Alfv\'en waves are an important driver of coronal heating., Comment: 1,002 authors, 14 pages, 4 figures, 3 tables, published by The Astrophysical Journal on 2023-05-09, volume 948, page 71

JWST has now made it possible to probe the rest-frame optical line emission of high-redshift galaxies extending to z~9, and potentially beyond. To aid in the interpretation of these emerging constraints, in this work we explore predictions for [OIII] emission in high-redshift galaxies using the First Light and Reionisation Epoch Simulations (FLARES). We produce predictions for the [OIII] luminosity function, its correlation with the UV luminosity, and the distribution of equivalent widths (EWs). We also explore how the [OIII] EW correlates with physical properties including specific star formation rate, metallicity, and dust attenuation. Our predictions are largely consistent with recent observational constraints on the luminosity function, average equivalent widths, and line ratios. However, they fail to reproduce the observed tail of high-EW sources and the number density of extreme line emitters. Possibilities to explain these discrepancies include an additional source of ionising photons and/or greater stochasticity in star formation in the model or photometric scatter and/or bias in the observations. With JWST now rapidly building larger samples and a wider range of emission lines the answer to this remaining discrepancy should be available imminently., Comment: 15 pages, accepted for publication in MNRAS, minor changes from original version

Physical neuromorphic computing, exploiting the complex dynamics of physical systems, has seen rapid advancements in sophistication and performance. Physical reservoir computing, a subset of neuromorphic computing, faces limitations due to its reliance on single systems. This constrains output dimensionality and dynamic range, limiting performance to a narrow range of tasks. Here, we engineer a suite of nanomagnetic array physical reservoirs and interconnect them in parallel and series to create a multilayer neural network architecture. The output of one reservoir is recorded, scaled and virtually fed as input to the next reservoir. This networked approach increases output dimensionality, internal dynamics and computational performance. We demonstrate that a physical neuromorphic system can achieve an overparameterised state, facilitating meta-learning on small training sets and yielding strong performance across a wide range of tasks. Our approach's efficacy is further demonstrated through few-shot learning, where the system rapidly adapts to new tasks.

The central impediment to reducing multidimensional integrals of transition amplitudes to analytic form, or at least to a fewer number of integral dimensions, is the presence of magnitudes of coordinate vector differences (square roots of polynomials) $|{\bf x}_{1}-{\bf x}_{2}|^{2}=\sqrt{x_{1}^{2}-2x_{1}x_{2}\cos\theta+x_{2}^{2}}$ in disjoint products of functions. Fourier transforms circumvent this by introducing a three-dimensional momentum integral for each of those products, followed in many cases by another set of integral transforms to move all of the resulting denominators into a single quadratic form in one denominator whose square my be completed. Gaussian transforms introduce a one-dimensional integral for each such product while squaring the square roots of coordinate vector differences and moving them into an exponential. Addition theorems may also be used for this purpose, and sometimes direct integration is even possible. Each method has its strengths and weaknesses. An alternative integral transform to Fourier transforms and Gaussian transforms is derived herein and utilized. A number of consequent integrals of Macdonald functions, hypergeometric functions, and Meijer G-functions with complicated arguments is given., Comment: 15 pages

Reservoir computing is a neuromorphic architecture that potentially offers viable solutions to the growing energy costs of machine learning. In software-based machine learning, neural network properties and performance can be readily reconfigured to suit different computational tasks by changing hyperparameters. This critical functionality is missing in ``physical" reservoir computing schemes that exploit nonlinear and history-dependent memory responses of physical systems for data processing. Here, we experimentally present a `task-adaptive' approach to physical reservoir computing, capable of reconfiguring key reservoir properties (nonlinearity, memory-capacity and complexity) to optimise computational performance across a broad range of tasks. As a model case of this, we use the temperature and magnetic-field controlled spin-wave response of Cu$_2$OSeO$_3$ that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to a host of different physical reservoir responses. We quantify phase-tunable reservoir performance, characterise their properties and discuss the correlation between these in physical reservoirs. This task-adaptive approach overcomes key prior limitations of physical reservoirs, opening opportunities to apply thermodynamically stable and metastable phase control across a wide variety of physical reservoir systems, as we show its transferable nature using above(near)-room-temperature demonstration with Co$_{8.5}$Zn$_{8.5}$Mn$_{3}$ (FeGe)., Comment: Main manuscript: 14 pages, 5 figures. Supplementary materials: 13 pages, 10 figures

Recent studies in magnetic nanolithography show that a variety of complex magnetic states emerge as a function of a single magnetic island's aspect ratio. We propose a model which, in addition to fitting experiments, predicts magnetic states with continuous symmetry at particular aspect ratios and reveals a duality between vortex and vertex states. Our model then opens new means of engineering novel types of artificial spin systems, and their application to complex magnetic textures in devices and computing., Comment: 3 pages + epsilon + 18 supplementary material

As the field of optomechanics advances, quadratic dispersive coupling (QDC) promise an increasingly feasible class of qualitatively new functionality. However, the leading QDC geometries also generate linear dissipative coupling, and an associated quantum radiation force noise that is detrimental to QDC applications. Here, we propose a simple modification that dramatically reduces this noise without altering the QDC strength. We identify optimal regimes of operation, and discuss advantages within the examples of optical levitation and nondestructive phonon measurement., Comment: 18 pages, 4 figures

All-optical magnetic switching promises ultrafast, high-resolution magnetisation control with the technological attraction of requiring no magnetic field. Existing all-optical switching schemes are driven by ultrafast transient effects, typically requiring power-hungry femtosecond-pulsed lasers and complex magnetic materials. Here, we demonstrate deterministic, all-optical magnetic switching in simple ferromagnetic nanomagnets (Ni$_{81}$Fe$_{19}$, Ni$_{50}$Fe$_{50}$) with sub-diffraction limit dimensions using a focused low-power, linearly-polarised continuous-wave laser. Isolated nanomagnets are switched across a range of dimensions, laser wavelengths and powers. All square-geometry artificial spin ice vertex configurations are written, including ground-state and energetically-unfavourable `monopole-like' states at powers as low as 2.74 mW. Usually, magnetic switching with linearly polarised light is symmetry-forbidden; however, here the laser spot has a similar size to the nanomagnets, producing an absorption distribution dependent on the relative nanoisland-spot displacement. We attribute the observed deterministic switching to the transient dynamics of this asymmetric absorption. No switching is observed in Co samples, suggesting the multi-species nature of NiFe alloys plays a role in reversal. The results presented here usher in cheap, low-power optically-controlled devices with impact across data storage, neuromorphic computation and reconfigurable magnonics.

Two-dimensional materials have been discovered to exhibit non-volatile resistive switching (NVRS) phenomenon. In our work, we reported the universal NVRS behavior in a dozen metal dichalcogenides, featuring low switching voltage, large on/off ratio, fast switching speed and forming free characteristics. A unique conductive-point random access memory (CPRAM) effect is used to explain the switching mechanisms, supported by experimental results from current-sweep measurements., Comment: 3 pages, 5 figures, IEEE conference(2021 5th EDTM)

Videos captured using Transmission Electron Microscopy (TEM) can encode details regarding the morphological and temporal evolution of a material by taking snapshots of the microstructure sequentially. However, manual analysis of such video is tedious, error-prone, unreliable, and prohibitively time-consuming if one wishes to analyze a significant fraction of frames for even videos of modest length. In this work, we developed an automated TEM video analysis system for microstructural features based on the advanced object detection model called YOLO and tested the system on an in-situ ion irradiation TEM video of dislocation loops formed in a FeCrAl alloy. The system provides analysis of features observed in TEM including both static and dynamic properties using the YOLO-based defect detection module coupled to a geometry analysis module and a dynamic tracking module. Results show that the system can achieve human comparable performance with an F1 score of 0.89 for fast, consistent, and scalable frame-level defect analysis. This result is obtained on a real but exceptionally clean and stable data set and more challenging data sets may not achieve this performance. The dynamic tracking also enabled evaluation of individual defect evolution like per defect growth rate at a fidelity never before achieved using common human analysis methods. Our work shows that automatically detecting and tracking interesting microstructures and properties contained in TEM videos is viable and opens new doors for evaluating materials dynamics.

Strongly-interacting artificial spin systems are moving beyond mimicking naturally-occurring materials to emerge as versatile functional platforms, from reconfigurable magnonics to neuromorphic computing. Typically artificial spin systems comprise nanomagnets with a single magnetisation texture: collinear macrospins or chiral vortices. By tuning nanoarray dimensions we achieve macrospin/vortex bistability and demonstrate a four-state metamaterial spin-system 'Artificial Spin-Vortex Ice' (ASVI). ASVI can host Ising-like macrospins with strong ice-like vertex interactions, and weakly-coupled vortices with low stray dipolar-field. Vortices and macrospins exhibit starkly-differing spin-wave spectra with analogue-style mode-amplitude control and mode-frequency shifts of df = 3.8 GHz. The enhanced bi-textural microstate space gives rise to emergent physical memory phenomena, with ratchet-like vortex training and history-dependent nonlinear fading memory when driven through global field cycles. We employ spin-wave microstate fingerprinting for rapid, scaleable readout of vortex and macrospin populations and leverage this for spin-wave reservoir computation. ASVI performs linear and non-linear mapping transformations of diverse input signals as well as chaotic time-series forecasting. Energy costs of machine learning are spiralling unsustainably, developing low-energy neuromorphic computation hardware such as ASVI is crucial to achieving a zero-carbon computational future.

Artificial spin ices are magnetic metamaterials comprising geometrically-tiled interacting nanomagnets. There is significant interest in these systems for reconfigurable magnonics due to their vast microstate landscape. Studies to-date have focused on the in-field GHz spin-wave response, convoluting effects from applied field, nanofabrication-imperfections ('quenched disorder') and microstate-dependent dipolar field landscapes. Here, we study artificial spin ices in pure and disordered microstates and evaluate their zero-field spectra. Removing the applied field allows us to deconvolute contributions to reversal dynamics and spin-wave spectra, directly measuring the dipolar field landscape and quenched disorder. Mode-amplitude provides population readout of nanomagnet magnetisation direction, and hence net magnetisation as well as local vertex populations. We demonstrate microstate-fingerprinting via distinct spectral-readout of three microstates with identical (zero) magnetisation, supported by simulation. These results establish remanence 'spectral-fingerprinting' as a rapid, scalable on-chip readout of both magnetic state and nanoscale dipolar field texture, a critical step in realising next-generation functional magnonic devices., Comment: 32 pages, 6 figures

Artificial spin ice systems have seen burgeoning interest due to their intriguing physics and potential applications in reprogrammable memory, logic and magnonics. Integration of artificial spin ice with functional magnonics is a relatively recent research direction, with a host of promising results. As the field progresses, direct in-depth comparisons of distinct artificial spin systems are crucial to advancing the field. While studies have investigated the effects of different lattice geometries, little comparison exists between systems comprising continuously connected nanostructures, where spin-waves propagate via dipole-exchange interaction, and systems with nanobars disconnected at vertices where spin-wave propagation occurs via stray dipolar-field. Gaining understanding of how these very different coupling methods affect both spin-wave dynamics and magnetic reversal is key for the field to progress and provides crucial system-design information including for future systems containing combinations of connected and disconnected elements. Here, we study the magnonic response of two kagome spin ices via Brillouin light scattering, a continuously connected system and a disconnected system with vertex gaps. We observe distinct high-frequency dynamics and magnetization reversal regimes between the systems, with key distinctions in spin-wave localization and mode quantization, microstate-trajectory during reversal and internal field-profiles. These observations are pertinent for the fundamental understanding of artificial spin systems and broader design and engineering of reconfigurable functional magnonic crystals.

Strongly-interacting nanomagnetic arrays are finding increasing use as model host systems for reconfigurable magnonics. The strong inter-element coupling allows for stark spectral differences across a broad microstate space due to shifts in the dipolar field landscape. While these systems have yielded impressive initial results, developing rapid, scaleable means to access abroad range of spectrally-distinct microstates is an open research problem.We present a scheme whereby square artificial spin ice is modified by widening a 'staircase' subset of bars relative to the rest of the array, allowing preparation of any ordered vertex state via simple global-field protocols. Available microstates range from the system ground-state to high-energy 'monopole' states, with rich and distinct microstate-specific magnon spectra observed. Microstate-dependent mode-hybridisation and anticrossings are observed at both remanence and in-field with dynamic coupling strength tunable via microstate-selection. Experimental coupling strengths are found up to g / 2$\pi$ = 0.15 GHz. Microstate control allows fine mode-frequency shifting, gap creation and closing, and active mode number selection.

A compact frequency-doubled diode-pumped Nd:YAG master-oscillator power-amplifier laser system with programmable microsecond pulse length has been developed. Analog pulse shaping of the output from a single-frequency continuous-wave Nd:YAG oscillator, and subsequent amplification, allowed the generation of rectangular pulses with pulse lengths on the order of the Nd:YAG fluorescence lifetime. Temporally flat-top pulses of 1064 nm light with 520 mJ pulse energy, 2.6 kW peak power, and 200 $\mu$s duration, with linewidth below 10 kHz, were obtained at a repetition rate of 2 Hz. Second harmonic generation in a LBO crystal yielded pulses of 262 mJ and 1.3 kW peak power at 532 nm. The peak power can be maintained within 2.9% over the duration of the laser pulse, and long-term intensity stability of 1.1% was observed. The spatially flat-top beam at 1064 nm used in the amplifier is converted to a Gaussian beam at 532 nm with beam quality factor $M^2=1.41(14)$ during the second harmonic generation. This system has potential as a pump source for Ti:sapphire, dye, or optical parametric amplifiers to generate tunable high-power single-frequency radiation for applications in precision measurements and laser slowing., Comment: 9 pages, 5 figures

Crystallographic image processing (CIP) techniques may be utilized in scanning probe microscopy (SPM) to glean information that has been obscured by signals from multiple probe tips. This may be of particular importance for scanning tunneling microscopy (STM) and requires images from a sample that is periodic in two dimensions. The image-forming current for multiple tips in STM is derived in a more straightforward manner than prior approaches. The Fourier spectrum of the current for p4mm Bloch surface wave functions and a pair of delta function tips reveals the tip-separation dependence of various types of image obscurations. In particular our analyses predict that quantum interference should be visible on a macroscopic scale in the form of bands quite distinct from the basket-weave patterns a purely classical model would create at the same periodic double STM tip separations. A surface wave function that models the essential character of highly (0001) oriented pyrolytic graphite (technically known as HOPG) is introduced and used for a similar tip-separation analysis. Using a bonding H_2 tip wave function with significant spatial extent instead of this pair of infinitesimal Dirac delta function tips does not affect these outcomes in any observable way. This is explained by Pierre Curie's well known symmetry principle. Classical simulations of multiple tip effects in STM images may be understood as modeling multiple tip effects in images that were recorded with other types of SPMs). Our analysis clarifies why CIP and crystallographic averaging work well in removing the effects of a blunt SPM tip (that consist of multiple mini-tips) from the recorded 2D periodic images and also outlines the limitations of this image processing techniques for certain spatial separations of STM mini-tips., Comment: 37 pages, 17 figures

It is prohibitively expensive to deposit customized dielectric coatings on individual optics. One solution is to batch-coat many optics with extra dielectric layers, then remove layers from individual optics as needed. Here we present a low-cost, single-step, monitored wet etch technique for reliably removing (or partially removing) individual SiO$_2$ and Ta$_2$O$_5$ dielectric layers, in this case from a high-reflectivity fiber mirror. By immersing in acid and monitoring off-band reflected light, we show it is straightforward to iteratively (or continuously) remove six bilayers. At each stage, we characterize the coating performance with a Fabry-P\'{e}rot cavity, observing the expected stepwise decrease in finesse from 92,000$\pm$3,000 to 3,950$\pm$50, finding no evidence of added optical losses. The etch also removes the fiber's sidewall coating after a single bilayer, and, after six bilayers, confines the remaining coating to a $\sim$50-$\mu$m-diameter pedestal at the center of the fiber tip. Vapor etching above the solution produces a tapered "pool cue" cladding profile, reducing the fiber diameter (nominally 125 $\mu$m) to $\sim$100 $\mu$m at an angle of $\sim$0.3$^\circ$ near the tip. Finally, we note that the data generated by this technique provides a sensitive estimate of the layers' optical depths. This technique could be readily adapted to free-space optics and other coatings., Comment: 8 pages, 3 figures

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers times an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

The serration of grain boundaries in Inconel 600 caused by heat treatment is studied systematically. A new method based on Fourier transforms is used to analyse the multiple wave-like character of the serrated grain boundaries. A new metric -- the serration index -- is devised and utilised to quantify the degree of serration and more generally to distinguish objectively between serrated and non-serrated boundaries. By considering the variation of the serration index with processing parameters, a causal relationship between degree of serration and solution treatment/cooling rate is elucidated. Processing maps for the degree of serration are presented. Two distinct formation mechanisms arise which rely upon grain boundary interaction with carbides: (i) Zener-type dragging which hinders grain boundary migration and (ii) a faceted carbide growth-induced serration.

Renewable energy projects, such as large offshore wind farms, are critical to achieving low-emission targets set by governments. Stochastic computer models allow us to explore future scenarios to aid decision making whilst considering the most relevant uncertainties. Complex stochastic computer models can be prohibitively slow and thus an emulator may be constructed and deployed to allow for efficient computation. We present a novel heteroscedastic Gaussian Process emulator which exploits cheap approximations to a stochastic offshore wind farm simulator. We also conduct a probabilistic sensitivity analysis to understand the influence of key parameters in the wind farm model which will help us to plan a probability elicitation in the future., Comment: Major revision. 23 Pages, 12 figs

This paper is concerned with a class of partition functions $a(n)$ introduced by Radu and defined in terms of eta-quotients. By utilizing the transformation laws of Newman, Schoeneberg and Robins, and Radu's algorithms, we present an algorithm to find Ramanujan-type identities for $a(mn+t)$. While this algorithm is not guaranteed to succeed, it applies to many cases. For example, we deduce a witness identity for $p(11n+6)$ with integer coefficients. Our algorithm also leads to Ramanujan-type identities for the overpartition functions $\overline{p}(5n+2)$ and $\overline{p}(5n+3)$ and Andrews--Paule's broken $2$-diamond partition functions $\triangle_{2}(25n+14)$ and $\triangle_{2}(25n+24)$. It can also be extended to derive Ramanujan-type identities on a more general class of partition functions. For example, it yields the Ramanujan-type identities on Andrews' singular overpartition functions $\overline{Q}_{3,1}(9n+3)$ and $ \overline{Q}_{3,1}(9n+6)$ due to Shen, the $2$-dissection formulas of Ramanujan and the $8$-dissection formulas due to Hirschhorn., Comment: 45 pages, to appear in Annals of Combinatorics

We present techniques to model and design membrane phononic crystals with low-mass defects, optimized for force sensing. Further, we identify the importance of the phononic crystal mass contrast as it pertains to the size of acoustic bandgaps and to the dissipation properties of defect modes. In particular, we quantify the tradeoff between high mass contrast phononic crystals with their associated robust acoustic isolation, and a reduction of soft clamping of the defect mode. We fabricate a set of phononic crystals with a variety of defect geometries out of high stress stoichiometric silicon nitride membranes, and measured at both room temperature and 4 K in order to characterize the dissipative pathways across a variety of geometries. Analysis of these devices highlights a number of design principles integral to the implementation of low-mass, low-dissipation mechanical modes into optomechanical systems., Comment: 12 pages, 11 figures

We introduce a passively-aligned, flexure-tuned cavity optomechanical system in which a membrane is positioned microns from one end mirror of a Fabry-Perot optical cavity. By displacing the membrane through gentle flexure of its silicon supporting frame (i.e., to ~80 m radius of curvature (ROC)), we gain access to the full range of available optomechanical couplings, finding also that the optical spectrum exhibits none of the abrupt discontinuities normally found in "membrane-in-the-middle" (MIM) systems. More aggressive flexure (3 m ROC) enables >15 microns membrane travel, milliradian tilt tuning, and a wavelength-scale (1.64 $\pm$ 0.78 microns) membrane-mirror separation. We also provide a complete set of analytical expressions for this system's leading-order dispersive and dissipative optomechanical couplings. Notably, this system can potentially generate orders of magnitude larger linear dissipative or quadratic dispersive strong coupling parameters than is possible with a MIM system. Additionally, it can generate the same purely quadratic dispersive coupling as a MIM system, but with significantly suppressed linear dissipative back-action (and force noise)., Comment: 24 pages, 3 figures

The point-like nature and exquisite magnetic field sensitivity of the nitrogen vacancy (NV) center in diamond can provide information about the inner workings of magnetic nanocircuits in complement with traditional transport techniques. Here we use a single NV in bulk diamond to probe the stray field of a ferromagnetic nanowire controlled by spin transfer (ST) torques. We first report an unambiguous measurement of ST tuned, parametrically driven, large-amplitude magnetic oscillations. At the same time, we demonstrate that such magnetic oscillations alone can directly drive NV spin transitions, providing a potential new means of control. Finally, we use the NV as a local noise thermometer, observing strong ST damping of the stray field noise, consistent with magnetic cooling from room temperature to $\sim$150 K., Comment: 6 pages, 5 figures, plus supplementary information

The spin-wave dynamics of the ferromagnetic nanoarrays termed artificial spin ice (ASI) are known to vary depending on their magnetic microstate. However, little work has been done to characterise this relationship. Recent advances in control over the magnetic configuration of ASI bring designs harnessing the interplay between spin-wave eigenmodes and the microstate within reach, offering diverse applications including reconfigurable magnonic crystals, microwave filters and microstate read-out probes. These designs hinge on a strong understanding of the underlying spin wave-microstate correspondence. Here, we analyse the effects of the magnetic microstate on spin-wave spectra of honeycomb ASI systems via micromagnetic simulation. We find the spin-wave spectrum to be highly-tunable via the microstate to an enhanced degree relative to existing magnonic crystals, with mode shifting and (de)activation realised by reversing individual nanoislands. Symmetries of ASI systems and the chirality of magnetic defects are found to play important roles in determining the high-frequency response.

Let $p_k(n)$ be given by the $k$-th power of the Euler Product $\prod _{n=1}^{\infty}(1-q^n)^k=\sum_{n=0}^{\infty}p_k(n)q^{n}$. By investigating the properties of the modular equations of the second and the third order under the Atkin $U$-operator, we determine the generating functions of $p_{8k}(2^{2\alpha} n +\frac{k(2^{2\alpha}-1)}{3})$ $(1\leq k\leq 3)$ and $p_{3k} (3^{2\beta}n+\frac{k(3^{2\beta}-1)}{8})$ $(1\leq k\leq 8)$ in terms of some linear recurring sequences. Combining with a result of Engstrom about the periodicity of linear recurring sequences modulo $m$, we obtain infinite families of congruences for $p_k(n)$ modulo any $m\geq2$, where $1\leq k\leq 24$ and $3|k$ or $8|k$. Based on these congruences for $p_k(n)$, infinite families of congruences for many partition functions such as the overpartition function, $t$-core partition functions and $\ell$-regular partition functions are easily obtained., Comment: 26 pages, replaced references, corrected typos

Here, we report the intriguing observation of stable non-volatile resistance switching (NVRS) in single-layer atomic sheets sandwiched between metal electrodes. NVRS is observed in the prototypical semiconducting (MX2, M=Mo, W; and X=S, Se) transitional metal dichalcogenides (TMDs), and insulating hexagonal boron nitride (h-BN), which alludes to the universality of this phenomenon in non-metallic 2D monolayers, and features forming-free switching. This observation of NVRS phenomenon, widely attributed to ionic diffusion, filament and interfacial redox in bulk oxides and electrolytes, inspires new studies on defects, ion transport and energetics at the sharp interfaces between atomically-thin sheets and conducting electrodes. From a contemporary perspective, switching is all the more unexpected in monolayers since leakage current is a fundamental limit in ultra-thin oxides. Emerging device concepts in non-volatile flexible memory fabrics, and brain-inspired (neuromorphic) computing could benefit substantially from the pervasive NVRS effect and the associated wide materials and engineering co-design opportunity. Experimentally, a 50 GHz radio-frequency (RF) monolayer switch is demonstrated, which opens up a new application for electronic zero-static power RF switching technology.

The computing systems used by LHC experiments has historically consisted of the federation of hundreds to thousands of distributed resources, ranging from small to mid-size resource. In spite of the impressive scale of the existing distributed computing solutions, the federation of small to mid-size resources will be insufficient to meet projected future demands. This paper is a case study of how the ATLAS experiment has embraced Titan---a DOE leadership facility in conjunction with traditional distributed high- throughput computing to reach sustained production scales of approximately 52M core-hours a years. The three main contributions of this paper are: (i) a critical evaluation of design and operational considerations to support the sustained, scalable and production usage of Titan; (ii) a preliminary characterization of a next generation executor for PanDA to support new workloads and advanced execution modes; and (iii) early lessons for how current and future experimental and observational systems can be integrated with production supercomputers and other platforms in a general and extensible manner.

We present a robust sideband laser locking technique that is ideally suited for applications requiring low probe power and heterodyne readout. By feeding back to a high-bandwidth voltage controlled oscillator, we lock a first-order phase-modulation sideband to a table-top high-finesse Fabry-Perot cavity, achieving a feedback bandwidth of 3.5 MHz with a single integrator, limited fundamentally by the signal delay. The directly measured transfer function of the closed feedback loop agrees with a model assuming ideal system components, and from this we suggest a modified design that should realistically achieve a bandwidth exceeding 6 MHz with a near-causally limited feedback gain of $4\times 10^7$ at 1 kHz. The off-resonance optical carrier is used for alignment-free heterodyne readout, alleviating the need for a second laser or additional optical modulators., Comment: 7 pages, 3 figures

By patterning a freestanding dielectric membrane into a photonic crystal reflector (PCR), it is possible to resonantly enhance its normal-incidence reflectivity, thereby realizing a thin, single-material mirror. In many PCR applications, the operating wavelength (e.g. that of a low-noise laser or emitter) is not tunable, imposing tolerances on crystal geometry that are not reliably achieved with standard nanolithography. Here we present a gentle technique to finely tune the resonant wavelength of a SiN PCR using iterative hydrofluoric acid etches. With little optimization, we achieve a 57-nm-thin photonic crystal having an operating wavelength within 0.15 nm (0.04 resonance linewidths) of our target (1550 nm). Our thin structure exhibits a broader and less pronounced transmission dip than is predicted by plane wave simulations, and we identify two effects leading to these discrepancies, both related to the divergence angle of a collimated laser beam. To overcome this limitation in future devices, we distill a series of simulations into a set of general design considerations for realizing robust, high-reflectivity resonances., Comment: 6 pages, 3 figures, 1 table

We study the effect of cavity damping asymmetries on backaction in a "membrane-in-the-middle" optomechanical system, where a mechanical mode modulates the coupling between two photonic modes. We show that in the adiabatic limit, this system generically realizes a dissipative optomechanical coupling, with an effective position-dependent photonic damping rate. The resulting quantum noise interference can be used to ground-state cool a mechanical resonator in the unresolved sideband regime. We explicitly demonstrate how quantum noise interference controls linear backaction effects, and show that this interference persists even outside the adiabatic limit. For a one-port cavity in the extreme bad-cavity limit, the interference allows one to cancel all linear backaction effects. This allows continuous measurements of position-squared, with no stringent constraints on the single-photon optomechanical coupling strength. In contrast, such a complete cancellation is not possible in the good cavity limit. This places strict bounds on the optomechanical coupling required for quantum non-demolition measurements of mechanical energy, even in a one-port device., Comment: 9 pages, 5 figures

In the field of optomechanics, radiation forces have provided a particularly high level of control over the frequency and dissipation of mechanical elements. Here we propose a class of optomechanical systems in which light exerts a similarly profound influence over two other fundamental parameters: geometry and mass. By applying an optical trap to one lattice site of an extended phononic crystal, we show it is possible to create a tunable, localized mechanical mode. Owing to light's simultaneous and constructive coupling with the structure's continuum of modes, we estimate that a trap power at the level of a single intracavity photon should be capable of producing a significant effect within a realistic, chip-scale device., Comment: 6 pages, 2 figures

In force sensing, optomechanics, and quantum motion experiments, it is typically advantageous to create lightweight, compliant mechanical elements with the lowest possible force noise. Here we report wafer-scale batch fabrication and characterization of high-aspect-ratio, nanogram-scale Si$_3$N$_4$ "trampolines" having quality factors above $4 \times 10^7$ and ringdown times exceeding five minutes (1 mHz linewidth). We measure a thermally limited force noise sensitivity of 16.2$\pm$0.8 aN/Hz$^{1/2}$ at room temperature, with a spring constant ($\sim$1 N/m) 2-5 orders of magnitude larger than those of competing technologies. We also characterize the suitability of these devices for high-finesse cavity readout and optomechanics applications, finding no evidence of surface or bulk optical losses from the processed nitride in a cavity achieving finesse 40,000. These parameters provide access to a single-photon cooperativity $C_0 \sim 8$ in the resolved-sideband limit, wherein a variety of outstanding optomechanics goals become feasible., Comment: 8 pages, 4 figures, 1 table

In this study, the mechanism driving the narrow lower-thermospheric winter-to-summer meridional circulation is thoroughly investigated for the first time using the Specified Dynamics configuration runs of the Whole Atmosphere Community Climate Model eXtended (SD-WACCMX) simulations and the TIMED Doppler Interferometer (TIDI) observations. The mean meridional circulation in the SD-WACCMX is qualitatively consistent with the TIDI measurements, though the magnitude in the SD-WACCMX is about 50% weaker. The lower-thermospheric winter-to-summer circulation is mainly driven by the resolved wave forcing, including the tides and internally generated inertia gravity waves (GWs). The momentum forcing from the parameterized sub-grid scale GWs is not as significant as the resolved wave forcing in driving the lower-thermospheric meridional circulation. The GW parameterization scheme in the SD-WACCMX only includes GWs with phase velocities in the range of ±45 m/s, which might result in most of the parameterized sub-grid GWs dissipating and breaking in the mesosphere and hardly impacting the lower thermosphere. Only including slow GWs in the SD-WACCMX parameterization could potentially lead to the underestimation of the meridional wind in the model. Analysis also indicates the lower-thermospheric meridional circulation is stronger in the summer hemisphere, which is attributed to the hemispheric asymmetry in the resolved wave momentum forcing. This study underlines the importance of the whole atmosphere coupling through wave propagation and dissipation. This understanding can guide the model development with an accurate representation of underlying physical processes in the mesosphere and lower thermosphere which drives the lower-thermospheric circulation as well as the overall dynamics of this region.