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Sub-angstrom spatial resolution of electron density coupled with sub-femtosecond temporal resolution is required to directly observe the dynamics of the electronic structure of a molecule after photoinitiation or some other ultrafast perturbation. Meeting this challenge, pushing the field of quantum crystallography to attosecond timescales, would bring insights into how the electronic and nuclear degrees of freedom couple, enable the study of quantum coherences involved in molecular dynamics, and ultimately enable these dynamics to be controlled. Here we propose to reach this realm by employing convergent-beam X-ray crystallography with high-power attosecond pulses from a hard-X-ray free-electron laser. We show that with dispersive optics, such as multilayer Laue lenses of high numerical aperture, it becomes possible to encode time into the resulting diffraction pattern with deep sub-femtosecond precision. Each snapshot diffraction pattern consists of Bragg streaks that can be mapped back to arrival times and positions of X-rays on the face of a crystal. This can span tens of femtoseconds, and can be finely sampled as we demonstrate experimentally. The approach brings several other advantages, such as an increase of the number of observable reflections in a snapshot diffraction pattern, all fully integrated, to improve the speed and accuracy of serial crystallography -- especially for crystals of small molecules., Comment: 18 pages, 7 figures

Let $F$ be a probability distribution on $\mathbb{R}^d$ which admits a bounded density. We investigate the Euler characteristic of the \v{C}ech complex on $n$ points sampled from $F$ i.i.d. as $n\to\infty$ in the thermodynamic limit regime. As a main result, we identify a condition for two probability distributions to yield the same expected Euler characteristic under this construction. Namely, this happens if and only if their densities admit the same excess mass transform. Building on work of Bobrowski, we establish a connection between the limiting expected Euler characteristic of any such probability distribution $F$ and the one of the uniform distribution on $[0,1]^d$ through an integral transform. Our approach relies on constructive proofs, offering explicit calculations of expected Euler characteristics in lower dimensions as well as reconstruction of a distribution from its limiting Euler characteristic. In the context of topological data analysis, where the Euler characteristic serves as a summary of the shape of data, we address the inverse problem and determine what can be discriminated using this invariant. This research sheds light on the relationship between a probability distribution and topological properties of the \v{C}ech complex on its samples in the thermodynamic limit., Comment: 15 pages, 3 figures, 1 table. Comments welcome

Thermalization phenomena, while ubiquitous in quantum systems, have traditionally been viewed as obstacles to be mitigated. In this study, we demonstrate the ability, instead, to harness thermalization to dynamically engineer and stabilize structured quantum states in a mesoscopically large ensemble of spins. Specifically, we showcase the capacity to generate, control, stabilize, and read out 'shell-like' spin texture with interacting $ {}^{ 13}\mathrm{C}$ nuclear spins in diamond, wherein spins are polarized oppositely on either side of a critical radius. The texture spans several nanometers and encompasses many hundred spins. We capitalize on the thermalization process to impose a quasi-equilibrium upon the generated texture; as a result, it is highly stable, immune to spin diffusion, and endures over multiple-minute long periods -- over a million times longer than the intrinsic interaction scale of the spins. Additionally, the texture is created and interrogated without locally controlling or probing the nuclear spins. These features are accomplished using an electron spin as a nanoscale injector of spin polarization, and employing it as a source of spatially varying dissipation, allowing for serial readout of the emergent spin texture. Long-time stabilization is achieved via prethermalization to a Floquet-induced Hamiltonian under the electronic gradient field. Our work presents a new approach to robust nanoscale spin state engineering and paves the way for new applications in quantum simulation, quantum information science, and nanoscale imaging., Comment: 8 + 32 pages

During time evolution of many-body systems entanglement grows rapidly, limiting exact simulations to small-scale systems or small timescales. Quantum information tends however to flow towards larger scales without returning to local scales, such that its detailed large-scale structure does not directly affect local observables. This allows for the removal of large-scale quantum information in a way that preserves all local observables and gives access to large-scale and large-time quantum dynamics. To this end, we use the recently introduced information lattice to organize quantum information into different scales, allowing us to define local information and information currents which we employ to systematically discard long-range quantum correlations in a controlled way. Our approach relies on decomposing the system into subsystems up to a maximum scale and time evolving the subsystem density matrices by solving the subsystem von Neumann equations in parallel. Importantly, the information flow needs to be preserved during the discarding of large-scale information. To achieve this without the need to make assumptions about the microscopic details of the information current, we introduce a second scale at which information is discarded while using the state at the maximum scale to accurately obtain the information flow. The resulting algorithm, which we call local information time evolution (LITE), is highly versatile and suitable for investigating many-body quantum dynamics in both closed and open quantum systems with diverse hydrodynamic behaviors. We present results for energy transport in the mixed-field Ising model and magnetization transport in an open XX spin chain where we accurately determine the diffusion coefficients. The information lattice framework employed here promises to offer insightful results about the spatial and temporal behavior of entanglement in many-body systems., Comment: 29 pages, 17 figures

Clock-spin models are attracting great interest, due to both their rich phase diagram and their connection to parafermions. In this context, we derive an exact local mapping from clock-spin to fermionic partition functions. Such mapping, akin to techniques introduced by Fedotov and Popov for spin $\frac{1}{2}$ chains, grants access to well established numerical tools for the perturbative treatment of fermionic systems in the clock-spin framework. Moreover, in one dimension, it allows to use bosonization to access the low energy properties of clock-spin models. Finally, aside from the direct application in clock-spin models, this new mapping enables the conception of interesting fermionic models, based on the clock-spin counterparts., Comment: 26 pages, 0 figures, Submission to SciPost

We report an experimental approach to excite, stabilize, and continuously track Bloch sphere orbits of dipolar-coupled nuclear spins in a solid. We demonstrate these results on a model system of hyperpolarized 13C nuclear spins in diamond. Without quantum control, inter-spin coupling leads to rapid spin decay in T2*=1.5ms. We elucidate a method to preserve trajectories for over T2'>27s at excursion solid angles up to 16 degrees, even in the presence of strong inter-spin coupling. This exploits a novel spin driving strategy that thermalizes the spins to a long-lived dipolar many-body state, while driving them in highly stable orbits. We show that motion of the spins can be quasi-continuously tracked for over 35s in three dimensions on the Bloch sphere. In this time the spins complete >68,000 closed precession orbits, demonstrating high stability and robustness against error. We experimentally probe the transient approach to such rigid motion, and thereby show the ability to engineer highly stable "designer" spin trajectories. Our results suggest new ways to stabilize and interrogate strongly-coupled quantum systems through periodic driving and portend powerful applications of rigid spin orbits in quantum sensing., Comment: 19 pages, 16 figures. SI: 4 pages, 7 figures. 1 anc movie file (also available on Youtube)

Improvements in X-ray optics critically depend on the measurement of their optical performance. The knowledge of wavefront aberrations, for example, can be used to improve the fabrication of optical elements or to design phase correctors to compensate for these errors. Nowadays, the characterization of such optics is made using intense X-ray sources such as synchrotrons. However, the limited access to these facilities can substantially slow down the development process. Improvements in the brightness of lab-based X-ray micro-sources in combination with the development of new metrology methods, and in particular ptychographic X-ray speckle tracking, enable characterization of X-ray optics in the lab with a precision and sensitivity not possible before. Here, we present a laboratory set-up that utilizes a commercially available X-ray source and can be used to characterize different types of X-ray optics. The set-up is used in our laboratory on a routine basis to characterize multilayer Laue lenses of high numerical aperture and other optical elements. This typically includes measurements of the wavefront distortions, optimum operating photon energy and focal length of the lens. To check the sensitivity and accuracy of this laboratory set-up we compared the results to those obtained at the synchrotron and saw no significant difference. To illustrate the feedback of measurements on performance, we demonstrated the correction of the phase errors of a particular multilayer Laue lens using a 3D printed compound refractive phase plate.

Multilayer Laue lenses were used for the first time to focus x-rays from an X-ray Free Electron Laser (XFEL). In an experiment, which was performed at the European XFEL, we demonstrated focusing to a spot size of a few tens of nanometers. A series of runs in which the number of pulses per train was increased from 1 to 2, 3, 4, 5, 6, 7, 10, 20 and 30 pulses per train, all with a pulse separation of 3.55 us, was done using the same set of lenses. The increase in the number of pulses per train was accompanied with an increase of x-ray intensity (transmission) from 9% to 92% at 5 pulses per train, and then the transmission was reduced to 23.5 % when the pulses were increased further. The final working condition was 30 pulses per train and 23.5% transmission. Only at this condition we saw that the diffraction efficiency of the MLLs changed over the course of a pulse train, and this variation was reproducible from train to train. We present the procedure to align and characterize these lenses and discuss challenges working with the pulse trains from this unique x-ray source.

Saliency-driven image and video coding for humans has gained importance in the recent past. In this paper, we propose such a saliency-driven coding framework for the video coding for machines task using the latest video coding standard Versatile Video Coding (VVC). To determine the salient regions before encoding, we employ the real-time-capable object detection network You Only Look Once~(YOLO) in combination with a novel decision criterion. To measure the coding quality for a machine, the state-of-the-art object segmentation network Mask R-CNN was applied to the decoded frame. From extensive simulations we find that, compared to the reference VVC with a constant quality, up to 29 % of bitrate can be saved with the same detection accuracy at the decoder side by applying the proposed saliency-driven framework. Besides, we compare YOLO against other, more traditional saliency detection methods., Comment: 5 pages, 3 figures, 2 tables; Originally submitted at IEEE ICASSP 2021

We demonstrate that genuinely non-Hermitian topological phases and corresponding topological phase transitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic non-Hermitian Su-Schrieffer-Heeger model. We emulate this model by a 1D chain of spinless electrons evolving under unitary dynamics and subject to periodic measurements that are stochastically invoked. The non-Hermitian topology is visible in topological invariants adapted to the context of monitored circuits. For instance, the topological phase diagram of the monitored realization of the non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal polarization computed from an effective Hamiltonian of the monitored system. Importantly, our monitored circuit realization allows direct access to steady state biorthogonal expectation values of generic observables, and hence, to measure physical properties of a genuine non-Hermitian model. We expect our results to be applicable more generally to a wide range of models that host non-Hermitian topological phases., Comment: 4.5 pages, 3 figures

We report the observation of long-lived Floquet prethermal discrete time crystalline (PDTC) order in a three-dimensional position-disordered lattice of interacting dipolar-coupled 13C nuclei in diamond at room temperature. We demonstrate a novel strategy of "two-frequency" driving, involving an interleaved application of slow and fast drives that simultaneously prethermalize the spins with an emergent quasi-conserved magnetization along the x-axis, while enabling continuous and highly resolved observation of their dynamic evolution when periodically kicked away from x. The PDTC order manifests itself in a robust period doubling response of this drive-induced quasi-conserved spin magnetization interchanging between x and -x; our experiments allow a unique means to study the formation and melting of PDTC order. We obtain movies of the time-crystalline response with a clarity and throughput orders of magnitude greater than previous experiments. Parametric control over the drive frequencies allows us to reach PDTC lifetimes up to 396 Floquet cycles which we measure in a single-shot experiment. Such rapid measurement enables detailed characterization of the entire PDTC phase diagram, rigidity and lifetime, informing on the role of prethermalization towards stabilizing the DTC response. The two-frequency drive approach represents the simplest generalization of DTCs to multi-frequency drives; it expands the toolkit for realizing and investigating long-lived non-equilibrium phases of matter stabilized by emergent quasi-conservation laws., Comment: 8 pages, 5 figures. SI: 15 pages, 19 figures. 4 anc movie files (also available on Youtube)