Karim ALAA EL-DIN

Abstract:

Oxygen and other light elements comprise up to 5 wt% of the Earth's outer-core, and may significantly influence its physical properties and the operation of the geodynamo. Here we report in situ X-ray diffraction measurements of Fe, Fe + 4.5 FeO (atomic proportion), and Fe₂O₃ melts at 177-440 GPa, achieved using laser-driven shock compression at an x-ray free-electron laser. The melts exhibit Fe-O coordination numbers between 4.0(0.4) and 4.5(0.4), indicating predominantly four-fold coordination environments. These coordination states are significantly smaller than those of Fe-bearing lower-mantle phases such as bridgmanite and ferropericlase. Shorter Fe-Fe interatomic distances in compressed iron oxide melts drive the denser packing relative to ambient melts, while the structural differences between Fe + 4.5 FeO and Fe₂O₃ melts under shock indicate that the oxidation state modulates oxygen solubility in liquid Fe. At 177 GPa ( ~ 380 km below the core-mantle boundary) and 3800 K, Fe₂O₃ melts exhibit higher Fe-O coordination, suggesting that local variations in oxygen content could contribute to the stratification in the uppermost outer-core inferred from seismological and geomagnetic observations.

Abstract:

Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, studying many-body thermalization, and the black hole information paradox. Although generating a truly random quantum ensemble is experimentally challenging, approximate realizations are equally valuable and are known to emerge naturally in a variety of physical models, including Rydberg setups. These are referred to as approximate quantum state designs, and verifying their degree of randomness can be a measurement-intensive task, similar to performing full quantum state tomography on many-body systems. In this theoretical work, we present a measurement scheme and analysis techniques to validate the degree of randomness of a quantum ensemble generated by a simulated experimental setup. This is achieved by translating the information residing in the complex many-body state into a succinct representation of classical data using projective measurements in randomly chosen bases, which is then processed using methods of statistical inference such as maximum-likelihood estimation and neural networks, benchmarked against the predictions of shadow tomography. Our scheme only requires individually addressed single-qubit operations to be performed in order to be employed, making it applicable for a range of physical platforms.

Abstract:

<jats:title>Abstract</jats:title> <jats:p>Machine learning (ML) density functional approximations (DFAs) have seen a lot of interest in recent years, often being touted as the replacement for well-established non-empirical DFAs, which still dominate the field. Although highly accurate, ML-DFAs typically rely on large amounts of data, are computationally expensive, and fail to generalize beyond their training domain. In this work we show that differentiable DFT with Kohn-Sham (KS) regularization can be used to accurately capture the behaviour of known local density approximations (LDA) from small sets of synthetic data without using localized density information. At the same time our analysis shows a strong dependence of the learning on both the amount and type of data as well as on model initialization. By enabling accurate learning from sparse energy data, this approach paves the way towards the development of custom ML-DFAs trained directly on limited experimental or high-level quantum chemistry datasets.</jats:p>

Abstract:

Resonant inelastic x-ray scattering (RIXS) is a widely used spectroscopic technique, providing access to the electronic structure and dynamics of atoms, molecules, and solids. However, RIXS requires a narrow bandwidth x-ray probe to achieve high spectral resolution. The challenges in delivering an energetic monochromated beam from an x-ray free electron laser (XFEL) thus limit its use in few-shot experiments, including for the study of high energy density systems. Here we demonstrate that by correlating the measurements of the self-amplified spontaneous emission (SASE) spectrum of an XFEL with the RIXS signal, using a dynamic kernel deconvolution with a neural surrogate, we can achieve electronic structure resolutions substantially higher than those normally afforded by the bandwidth of the incoming x-ray beam. We further show how this technique allows us to discriminate between the valence structures of Fe and Fe2O3, and provides access to temperature measurements as well as M-shell binding energies estimates in warm-dense Fe compounds.

Abstract:

X-ray free-electron lasers are sources of coherent, high-intensity X-rays with numerous applications in ultra-fast measurements and dynamic structural imaging. Due to the stochastic nature of the self-amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two-coloured X-ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networks and decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high-repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X-ray spectroscopy using XFELs, such as in time-resolved X-ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes