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In unconventional superconductors, coupled charge and lattice degrees of freedom can manifest in ordered phases of matter that are intertwined. In the cuprate family, fluctuating short-range charge correlations can coalesce into a longer-range charge density wave (CDW) order which is thought to intertwine with superconductivity, yet the nature of the interaction is still poorly understood. Here, by measuring subtle lattice fluctuations in underdoped YBa 2 Cu 3 O 6+ y on quasi-static timescales (thousands of seconds) through X-ray photon correlation spectroscopy, we report sensitivity to both superconductivity and CDW. The atomic lattice shows remarkably faster relaxational dynamics upon approaching the superconducting transition at T c ≈ 65 K. By tracking the momentum dependence, we show that the intermediate scattering function almost monotonically scales with the relaxation distance of atoms away from their average positions above T c and in the presence of the CDW state, while this peculiar trend is reversed for other temperatures. These observations are consistent with an incipient CDW stabilized by local strain. This work provides insights into the crucial role of relaxational atomic fluctuations for understanding the electronic physics cuprates, which are inherently disordered due to carrier doping., Competing Interests: Competing interests statement:The authors declare no competing interest.

Understanding the interplay between charge, nematic, and structural ordering tendencies in cuprate superconductors is critical to unraveling their complex phase diagram. Using pump-probe time-resolved resonant X-ray scattering on the (0 0 1) Bragg peak at the Cu [Formula: see text] and O [Formula: see text] resonances, we investigate nonequilibrium dynamics of [Formula: see text] nematic order and its association with both charge density wave (CDW) order and lattice dynamics in La[Formula: see text]Eu[Formula: see text]Sr[Formula: see text]CuO[Formula: see text]. The orbital selectivity of the resonant X-ray scattering cross-section allows nematicity dynamics associated with the planar O 2[Formula: see text] and Cu 3[Formula: see text] states to be distinguished from the response of anisotropic lattice distortions. A direct time-domain comparison of CDW translational-symmetry breaking and nematic rotational-symmetry breaking reveals that these broken symmetries remain closely linked in the photoexcited state, consistent with the stability of CDW topological defects in the investigated pump fluence regime., Competing Interests: Competing interests statement:The authors declare no competing interest.

X-ray free electron laser experiments have brought unique capabilities and opened new directions in research, such as creating new states of matter or directly measuring atomic motion. One such area is the ability to use finely spaced sets of coherent x-ray pulses to be compared after scattering from a dynamic system at different times. This enables the study of fluctuations in many-body quantum systems at the level of the ultrafast pulse durations, but this method has been limited to a select number of examples and required complex and advanced analytical tools. By applying a new methodology to this problem, we have made qualitative advances in three separate areas that will likely also find application to new fields. As compared to the "droplet-type" models, which typically are used to estimate the photon distributions on pixelated detectors to obtain the coherent x-ray speckle patterns, our algorithm achieves an order of magnitude speedup on CPU hardware and two orders of magnitude improvement on GPU hardware. We also find that it retains accuracy in low-contrast conditions, which is the typical regime for many experiments in structural dynamics. Finally, it can predict photon distributions in high average-intensity applications, a regime which up until now has not been accessible. Our artificial intelligence-assisted algorithm will enable a wider adoption of x-ray coherence spectroscopies, by both automating previously challenging analyses and enabling new experiments that were not otherwise feasible without the developments described in this work., (© 2022 Author(s).)

X-ray photon fluctuation spectroscopy using a two-pulse mode at the Linac Coherent Light Source has great potential for the study of quantum fluctuations in materials as it allows for exploration of low-energy physics. However, the complexity of the data analysis and interpretation still prevent recovering real-time results during an experiment, and can even complicate post-analysis processes. This is particularly true for high-spatial resolution applications using CCDs with small pixels, which can decrease the photon mapping accuracy resulting from the large electron cloud generation at the detector. Droplet algorithms endeavor to restore accurate photon maps, but the results can be altered by their hyper-parameters. We present numerical modeling tools through extensive simulations that mimic previous x-ray photon fluctuation spectroscopy experiments. By modification of a fast droplet algorithm, our results demonstrate how to optimize the precise parameters that lift the intrinsic counting degeneracy impeding accuracy in extracting the speckle contrast. These results allow for an absolute determination of the summed contrast from multi-pulse x-ray speckle diffraction, the modus operandi by which the correlation time for spontaneous fluctuations can be measured., (© 2021. The Author(s).)