Coherent correlation imaging for resolving fluctuating states of matter.

Fluctuations and stochastic transitions are ubiquitous in nanometre-scale systems, especially in the presence of disorder. However, their direct observation has so far been impeded by a seemingly fundamental, signal-limited compromise between spatial and temporal resolution. Here we develop coherent correlation imaging (CCI) to overcome this dilemma. Our method begins by classifying recorded camera frames in Fourier space. Contrast and spatial resolution emerge by averaging selectively over same-state frames. Temporal resolution down to the acquisition time of a single frame arises independently from an exceptionally low misclassification rate, which we achieve by combining a correlation-based similarity metric1,2 with a modified, iterative hierarchical clustering algorithm3,4. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state with nanometre-scale resolution. We uncover an intricate network of transitions between more than 30 discrete states. Our spatiotemporal data enable us to reconstruct the pinning energy landscape and to thereby explain the dynamics observed on a microscopic level. CCI massively expands the potential of emerging high-coherence X-ray sources and paves the way for addressing large fundamental questions such as the contribution of pinning5-8 and topology9-12 in phase transitions and the role of spin and charge order fluctuations in high-temperature superconductivity13,14.

High-sensitivity extreme-ultraviolet transient absorption spectroscopy enabled by machine learning.

We present a novel denoising scheme for spectroscopy experiments employing broadband light sources and demonstrate its capabilities using transient absorption measurements with a high-harmonic source. Our scheme relies on measuring the probe spectra before and after interacting with the sample while capturing correlations between spectral components through machine learning approaches. With the present setup we achieve up to a tenfold improvement in noise suppression in XUV transient absorption spectra compared to the conventional pump on/ pump off referencing method. By utilizing strong spectral correlations in source fluctuations, the use of an artificial neural network facilitates pixel-wise noise reduction without requiring wavelength calibration of the reference spectrum. Our method can be adapted to a wide range of experiments and may be particularly advantageous for low repetition-rate systems, such as free electron lasers as well as laser-driven plasma and HHG sources. The enhanced sensitivity enables the investigation of subtle electron and lattice dynamics in the weak excitation regime, which is relevant for studying photovoltaics and photo-induced phase transitions in strongly correlated materials.

Observation of fluctuation-mediated picosecond nucleation of a topological phase.

Topological states of matter exhibit fascinating physics combined with an intrinsic stability. A key challenge is the fast creation of topological phases, which requires massive reorientation of charge or spin degrees of freedom. Here we report the picosecond emergence of an extended topological phase that comprises many magnetic skyrmions. The nucleation of this phase, followed in real time via single-shot soft X-ray scattering after infrared laser excitation, is mediated by a transient topological fluctuation state. This state is enabled by the presence of a time-reversal symmetry-breaking perpendicular magnetic field and exists for less than 300 ps. Atomistic simulations indicate that the fluctuation state largely reduces the topological energy barrier and thereby enables the observed rapid and homogeneous nucleation of the skyrmion phase. These observations provide fundamental insights into the nature of topological phase transitions, and suggest a path towards ultrafast topological switching in a wide variety of materials through intermediate fluctuating states.

Toroidal grating astigmatism of high-harmonics characterized by EUV Hartmann sensor.

The beam transport of single high-order harmonics in a monochromator arrangement is studied. A toroidal grating combines spectral filtering and focusing in order to produce a small individual spot for each harmonic. Here, the effect of small deviations from perfect alignment is investigated. Experimentally, a Hartmann sensor monitors the EUV wavefront while the grating is subjected to an online alignment procedure. The obtained results are confirmed by a simple theoretical description employing optical matrix methods.

Coherent diffractive imaging beyond the projection approximation: waveguiding at extreme ultraviolet wavelengths.

We study extreme-ultraviolet wave propagation within optically thick nanostructures by means of high-resolution coherent diffractive imaging using high-harmonic radiation. Exit waves from different objects are reconstructed by phase retrieval algorithms, and are shown to be dominated by waveguiding within the sample. The experiments provide a direct visualization of extreme-ultraviolet guided modes, and demonstrate that multiple scattering is a generic feature in extruded nanoscale geometries. The observations are successfully reproduced in numerical and semi-analytical simulations.

Ultrafast high-harmonic nanoscopy of magnetization dynamics.

Light-induced magnetization changes, such as all-optical switching, skyrmion nucleation, and intersite spin transfer, unfold on temporal and spatial scales down to femtoseconds and nanometers, respectively. Pump-probe spectroscopy and diffraction studies indicate that spatio-temporal dynamics may drastically affect the non-equilibrium magnetic evolution. Yet, direct real-space magnetic imaging on the relevant timescales has remained challenging. Here, we demonstrate ultrafast high-harmonic nanoscopy employing circularly polarized high-harmonic radiation for real-space imaging of femtosecond magnetization dynamics. We map quenched magnetic domains and localized spin structures in Co/Pd multilayers with a sub-wavelength spatial resolution down to 16 nm, and strobosocopically trace the local magnetization dynamics with 40 fs temporal resolution. Our compact experimental setup demonstrates the highest spatio-temporal resolution of magneto-optical imaging to date. Facilitating ultrafast imaging with high sensitivity to chiral and linear dichroism, we envisage a wide range of applications spanning magnetism, phase transitions, and carrier dynamics.

Nanoscale magnetic imaging using circularly polarized high-harmonic radiation.

This work demonstrates nanoscale magnetic imaging using bright circularly polarized high-harmonic radiation. We utilize the magneto-optical contrast of worm-like magnetic domains in a Co/Pd multilayer structure, obtaining quantitative amplitude and phase maps by lensless imaging. A diffraction-limited spatial resolution of 49 nm is achieved with iterative phase reconstruction enhanced by a holographic mask. Harnessing the exceptional coherence of high harmonics, this approach will facilitate quantitative, element-specific, and spatially resolved studies of ultrafast magnetization dynamics, advancing both fundamental and applied aspects of nanoscale magnetism.