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Dichography: Two-frame Ultrafast Imaging from a Single Diffraction Pattern
Authors:
Linos Hecht,
Andre Al Haddad,
Björn Bastian,
Thomas M. Baumann,
Johan Bielecki,
Christoph Bostedt,
Subhendu De,
Alberto De Fanis,
Simon Dold,
Thomas Fennel,
Fanny Goy,
Christina Graf,
Robert Hartmann,
Georg Jakobs,
Maximilian Joschko,
Gregor Knopp,
Katharina Kolatzki,
Sivarama Krishnan,
Björn Kruse,
Asbjørn Ø. Lægdsmand,
Bruno Langbehn,
Suddhasattwa Mandal,
Tommaso Mazza,
Michael Meyer,
Christian Peltz
, et al. (25 additional authors not shown)
Abstract:
We experimentally demonstrate that pairs of time-delayed ultrabright and ultrashort X-ray pulses of two different colors, delivered by modern X-ray Free Electron Lasers, can provide two time-delayed snapshots of a sample. We introduce Dichography, a method that algorithmically separates the diffraction signals overlapping on the detector and independently retrieves the two images of the specimen.…
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We experimentally demonstrate that pairs of time-delayed ultrabright and ultrashort X-ray pulses of two different colors, delivered by modern X-ray Free Electron Lasers, can provide two time-delayed snapshots of a sample. We introduce Dichography, a method that algorithmically separates the diffraction signals overlapping on the detector and independently retrieves the two images of the specimen. We employ Dichography to reconstruct two views of individual xenon-doped helium nanodroplets with 20 nm spatial resolution. The consistency of structures observed in both images at delays up to 750 fs provides evidence that, under these illumination conditions, significant structural damage only occurs at longer timescales. We further validate the method by imaging pairs of silver nanoparticles intercepted by the same light pulse. Dichography enables a new class of experiments across physics, chemistry, and materials science, making a significant step toward the original promise of X-ray free-electron lasers to capture ultrafast movies of nanomatter.
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Submitted 27 February, 2026; v1 submitted 27 August, 2025;
originally announced August 2025.
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Model-free pattern separation of two-color ultrafast X-ray diffraction
Authors:
Linos Hecht,
Yevheniy Ovcharenko,
Asbjørn Ø. Lægdsmand,
Björn Bastian,
Thomas M. Baumann,
Alessandro Colombo,
Subhendu De,
Alberto De Fanis,
Simon Dold,
Thomas Fennel,
Robert Hartmann,
Katharina Kolatzki,
Sivarama Krishnan,
Björn Kruse,
Aaron C. Laforge,
Bruno Langbehn,
Suddhasattwa Mandal,
Tommaso Mazza,
Cristian Medina,
Christian Peltz,
Thomas Pfeifer,
Björn Senfftleben,
Keshav Sishodia,
Frank Stienkemeier,
Rico Mayro P. Tanyag
, et al. (6 additional authors not shown)
Abstract:
Two-color X-ray imaging with Free Electron Laser pulses offers a powerful approach for probing ultrafast structural dynamics in nanoscale systems, combining (near-)atomic spatial resolution with femtosecond temporal precision. The first X-ray pulse captures the object's initial state, while the second, time-delayed pulse records its subsequent evolution. A key challenge lies in disentangling the t…
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Two-color X-ray imaging with Free Electron Laser pulses offers a powerful approach for probing ultrafast structural dynamics in nanoscale systems, combining (near-)atomic spatial resolution with femtosecond temporal precision. The first X-ray pulse captures the object's initial state, while the second, time-delayed pulse records its subsequent evolution. A key challenge lies in disentangling the two patterns simultaneously recorded by the same detector. We demonstrate the realization of this approach on structurally varying nanoscale particles using two X-ray pulses of different photon energies, 1 and 1.2 keV. Sub-micrometer helium nanodroplets generated in vacuum are irradiated by the two X-ray pulses separated in time by up to 750 femtoseconds. Taking advantage of the high photon-energy resolution of the imaging detector, we separate the overlapping diffraction signals by analyzing individual pixel counts and applying pattern recognition. The helium nanodroplets' spherical shape allows us to cross-validate this approach by fitting the radial scattering profiles with Mie solutions for abichromatic field. The excellent agreement between the two methods, particularly in the sparsely illuminated outer regions of the diffraction patterns where high-resolution structural information is encoded, highlights the quality of this approach and its potential for future advanced X-ray movie techniques.
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Submitted 18 August, 2026; v1 submitted 27 August, 2025;
originally announced August 2025.
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Nonlinear reversal of photo-excitation on the attosecond time scale improves ultrafast x-ray diffraction images
Authors:
Anatoli Ulmer,
Phay J. Ho,
Bruno Langbehn,
Stephan Kuschel,
Linos Hecht,
Razib Obaid,
Simon Dold,
Taran Driver,
Joseph Duris,
Ming-Fu Lin,
David Cesar,
Paris Franz,
Zhaoheng Guo,
Philip A. Hart,
Andrei Kamalov,
Kirk A. Larsen,
Xiang Li,
Michael Meyer,
Kazutaka Nakahara,
Robert G. Radloff,
River Robles,
Lara Rönnebeck,
Nick Sudar,
Adam M. Summers,
Linda Young
, et al. (6 additional authors not shown)
Abstract:
The advent of isolated and intense sub-femtosecond X-ray pulses enables tracking of quantummechanical motion of electrons in molecules and solids. The combination of X-ray spectroscopy and diffraction imaging is a powerful approach to visualize non-equilibrium dynamics in systems beyond few atoms. However, extreme x-ray intensities introduce significant electronic damage, limiting material contras…
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The advent of isolated and intense sub-femtosecond X-ray pulses enables tracking of quantummechanical motion of electrons in molecules and solids. The combination of X-ray spectroscopy and diffraction imaging is a powerful approach to visualize non-equilibrium dynamics in systems beyond few atoms. However, extreme x-ray intensities introduce significant electronic damage, limiting material contrast and spatial resolution. Here we show that newly available intense subfemtosecond (sub-fs) x-ray FEL pulses can outrun most ionization cascades and partially reverse x-ray damage through stimulated x-ray emission in the vicinity of a resonance. In our experiment, we compared thousands of coherent x-ray diffraction patterns and simultaneously recorded ion spectra from individual Ne nanoparticles injected into the FEL focus. Our experimental results and theoretical modeling reveal that x-ray diffraction increases and the average charge state decreases in particles exposed to sub-fs pulses compared to those illuminated with 15-femtosecond pulses. Sub-fs exposures outrun most Auger decays and impact ionization processes, and enhance nonlinear effects such as stimulated emission, which cycle bound electrons between different states. These findings demonstrate that intense sub-fs x-ray FEL pulses are transformative for advancing high-resolution imaging and spectroscopy in chemical and material sciences, and open the possibilities of coherent control of the interaction between x-rays and complex specimen beyond few atoms.
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Submitted 24 June, 2025;
originally announced June 2025.
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SPRING: an effective and reliable framework for image reconstruction in single-particle Coherent Diffraction Imaging
Authors:
Alessandro Colombo,
Mario Sauppe,
Andre Al Haddad,
Kartik Ayyer,
Morsal Babayan,
Rebecca Boll,
Ritika Dagar,
Simon Dold,
Thomas Fennel,
Linos Hecht,
Gregor Knopp,
Katharina Kolatzki,
Bruno Langbehn,
Filipe R. N. C. Maia,
Abhishek Mall,
Parichita Mazumder,
Tommaso Mazza,
Yevheniy Ovcharenko,
Ihsan Caner Polat,
Dirk Raiser,
Julian C. Schäfer-Zimmermann,
Kirsten Schnorr,
Marie Louise Schubert,
Arezu Sehati,
Jonas A. Sellberg
, et al. (18 additional authors not shown)
Abstract:
Coherent Diffraction Imaging (CDI) is an experimental technique to gain images of isolated structures by recording the light scattered off the sample. In principle, the sample density can be recovered from the scattered light field through a straightforward Fourier Transform operation. However, only the amplitude of the field is recorded, while the phase is lost during the measurement process and…
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Coherent Diffraction Imaging (CDI) is an experimental technique to gain images of isolated structures by recording the light scattered off the sample. In principle, the sample density can be recovered from the scattered light field through a straightforward Fourier Transform operation. However, only the amplitude of the field is recorded, while the phase is lost during the measurement process and has to be retrieved by means of suitable, well-established phase retrieval algorithms. In this work, we present SPRING, an analysis framework tailored to X-ray Free Electron Laser (XFEL) single-shot single-particle diffraction data that implements the Memetic Phase Retrieval method to mitigate the shortcomings of conventional algorithms. We benchmark the approach on experimental data acquired in two experimental campaigns at SwissFEL and European XFEL. Imaging results on isolated nanostructures reveal unprecedented stability and resilience of the algorithm's behavior on the input parameters, as well as the capability of identifying the solution in conditions hardly treatable so far with conventional methods. A user-friendly implementation of SPRING is released as open-source software, aiming at being a reference tool for the coherent diffraction imaging community at XFEL and synchrotron facilities.
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Submitted 5 March, 2025; v1 submitted 11 September, 2024;
originally announced September 2024.
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How to define temperature in active systems?
Authors:
Lukas Hecht,
Lorenzo Caprini,
Hartmut Löwen,
Benno Liebchen
Abstract:
We are used to measure temperature with a thermometer and we know from everyday life that different types of thermometers measure the same temperature. This experience can be based on equilibrium thermodynamics, which explains the equivalence of different possibilities to define temperature. In contrast, for systems out of equilibrium such as active matter, measurements performed with different th…
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We are used to measure temperature with a thermometer and we know from everyday life that different types of thermometers measure the same temperature. This experience can be based on equilibrium thermodynamics, which explains the equivalence of different possibilities to define temperature. In contrast, for systems out of equilibrium such as active matter, measurements performed with different thermometers can generally lead to different temperature values. In the present work, we systematically compare different possibilities to define temperature for active systems. Based on simulations and theory for inertial active Brownian particles, we find that different temperatures generally lead to different temperature values, as expected. Remarkably, however, we find that different temperatures not only lead to the same values near equilibrium (low Péclet number or high particle mass), but even far from equilibrium, several different temperatures approximately coincide. In particular, we find that the kinetic temperature, the configurational temperature, and temperatures based on higher moments of the velocity distribution constitute a class of temperatures that all assume very similar values over a wide parameter range. Notably, the effective temperature and temperatures exploiting the virial theorem, the Stokes-Einstein relation, or a harmonic confinement form a second class of temperatures whose values approximately coincide with each other but which strongly differ from those of the first class. Finally, we identify advantages and disadvantages of the different possibilities to define temperature and discuss their relevance for measuring the temperature of active systems.
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Submitted 29 November, 2024; v1 submitted 27 July, 2024;
originally announced July 2024.
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AMEP: The Active Matter Evaluation Package for Python
Authors:
Lukas Hecht,
Kay-Robert Dormann,
Kai Luca Spanheimer,
Mahdieh Ebrahimi,
Malte Cordts,
Suvendu Mandal,
Aritra K. Mukhopadhyay,
Benno Liebchen
Abstract:
The Active Matter Evaluation Package (AMEP) is a Python library for analyzing simulation data of particle-based and continuum simulations. It provides a powerful and simple interface for handling large data sets and for calculating and visualizing a broad variety of observables that are relevant to active matter systems. Examples range from the mean-square displacement and the structure factor to…
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The Active Matter Evaluation Package (AMEP) is a Python library for analyzing simulation data of particle-based and continuum simulations. It provides a powerful and simple interface for handling large data sets and for calculating and visualizing a broad variety of observables that are relevant to active matter systems. Examples range from the mean-square displacement and the structure factor to cluster-size distributions, binder cumulants, and growth exponents. AMEP is written in pure Python and is based on powerful libraries such as NumPy, SciPy, Matplotlib, and scikit-image. Computationally expensive methods are parallelized and optimized to run efficiently on workstations, laptops, and high-performance computing architectures, and an HDF5-based data format is used in the backend to store and handle simulation data as well as analysis results. AMEP provides the first comprehensive framework for analyzing simulation results of both particle-based and continuum simulations (as well as experimental data) of active matter systems. In particular, AMEP also allows it to analyze simulations that combine particle-based and continuum techniques such as used to study the motion of bacteria in chemical fields or for modeling particle motion in a flow field. AMEP is available at https://amepproject.de and can be installed via conda and pip.
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Submitted 25 April, 2024;
originally announced April 2024.
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Motility-induced coexistence of a hot liquid and a cold gas
Authors:
Lukas Hecht,
Iris Dong,
Benno Liebchen
Abstract:
If two phases exist at the same time, such as a gas and a liquid, they have the same temperature. This fundamental law of equilibrium physics is known to apply even to many non-equilibrium systems. However, recently, there has been much attention in the finding that inertial self-propelled particles like Janus colloids in a plasma or microflyers could self-organize into a hot gas-like phase that c…
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If two phases exist at the same time, such as a gas and a liquid, they have the same temperature. This fundamental law of equilibrium physics is known to apply even to many non-equilibrium systems. However, recently, there has been much attention in the finding that inertial self-propelled particles like Janus colloids in a plasma or microflyers could self-organize into a hot gas-like phase that coexists with a colder liquid-like phase. Here, we show that a kinetic temperature difference across coexisting phases can occur even in equilibrium systems when adding generic (overdamped) self-propelled particles. In particular, we consider mixtures of overdamped active and inertial passive Brownian particles and show that when they phase separate into a dense and a dilute phase, both phases have different kinetic temperatures. Surprisingly, we find that the dense phase (liquid) cannot only be colder but also hotter than the dilute phase (gas). This effect hinges on correlated motions where active particles collectively push and heat up passive ones primarily within the dense phase. Our results answer the fundamental question if a non-equilibrium gas can be colder than a coexisting liquid and create a route to equip matter with self-organized domains of different kinetic temperatures.
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Submitted 20 March, 2024; v1 submitted 27 November, 2023;
originally announced November 2023.
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Melting, bubble-like expansion and explosion of superheated plasmonic nanoparticles
Authors:
Simon Dold,
Thomas Reichenbach,
Alessandro Colombo,
Jakob Jordan,
Ingo Barke,
Patrick Behrens,
Nils Bernhardt,
Jonathan Correa,
Stefan Düsterer,
Benjamin Erk,
Thomas Fennel,
Linos Hecht,
Andrea Heilrath,
Robert Irsig,
Norman Iwe,
Patrice Kolb,
Björn Kruse,
Bruno Langbehn,
Bastian Manschwetus,
Philipp Marienhagen,
Franklin Martinez,
Karl-Heinz Meiwes Broer,
Kevin Oldenburg,
Christopher Passow,
Christian Peltz
, et al. (10 additional authors not shown)
Abstract:
We report on time-resolved coherent diffraction imaging of gas-phase silver nanoparticles, strongly heated via their plasmon resonance. The x-ray diffraction images reveal a broad range of phenomena for different excitation strengths, from simple melting over strong cavitation to explosive disintegration. Molecular dynamics simulations fully reproduce this behavior and show that the heating induce…
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We report on time-resolved coherent diffraction imaging of gas-phase silver nanoparticles, strongly heated via their plasmon resonance. The x-ray diffraction images reveal a broad range of phenomena for different excitation strengths, from simple melting over strong cavitation to explosive disintegration. Molecular dynamics simulations fully reproduce this behavior and show that the heating induces rather similar trajectories through the phase diagram in all cases, with the very different outcomes being due only to whether and where the stability limit of the metastable superheated liquid is crossed.
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Submitted 1 September, 2023;
originally announced September 2023.
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Three-Dimensional Coherent Diffractive Imaging of Isolated Faceted Nanostructures
Authors:
Alessandro Colombo,
Simon Dold,
Patrice Kolb,
Nils Bernhardt,
Patrick Behrens,
Jonathan Correa,
Stefan Düsterer,
Benjamin Erk,
Linos Hecht,
Andrea Heilrath,
Robert Irsig,
Norman Iwe,
Jakob Jordan,
Björn Kruse,
Bruno Langbehn,
Bastian Manschwetus,
Franklin Martinez,
Karl-Heinz Meiwes-Broer,
Kevin Oldenburg,
Christopher Passow,
Christian Peltz,
Mario Sauppe,
Fabian Seel,
Rico Mayro P. Tanyag,
Rolf Treusch
, et al. (7 additional authors not shown)
Abstract:
The structure and dynamics of isolated nanosamples in free flight can be directly visualized via single-shot coherent diffractive imaging using the intense and short pulses of X-ray free-electron lasers. Wide-angle scattering images even encode three-dimensional morphological information of the samples, but the retrieval of this information remains a challenge. Up to now, effective three-dimension…
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The structure and dynamics of isolated nanosamples in free flight can be directly visualized via single-shot coherent diffractive imaging using the intense and short pulses of X-ray free-electron lasers. Wide-angle scattering images even encode three-dimensional morphological information of the samples, but the retrieval of this information remains a challenge. Up to now, effective three-dimensional morphology reconstructions from single shots were only achieved via fitting with highly constrained models, requiring a priori knowledge about possible geometrical shapes. Here we present a much more generic imaging approach. Relying on a model that allows for any sample morphology described by a convex polyhedron, we reconstruct wide-angle diffraction patterns from individual silver nanoparticles. In addition to known structural motives with high symmetries, we retrieve imperfect shapes and agglomerates which were not accessible previously. Our results open new routes towards true 3D structure determination of single nanoparticles and, ultimately, 3D movies of ultrafast nanoscale dynamics.
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Submitted 8 August, 2022;
originally announced August 2022.
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An Introduction to Modeling Approaches of Active Matter
Authors:
L. Hecht,
J. C. Ureña,
B. Liebchen
Abstract:
This article is based on lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter". It provides an introductory overview of modeling approaches for active matter and is primarily targeted at PhD students (or other readers) who encounter some of these approaches for the first time. The aim of the article is to help put the described modeling approac…
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This article is based on lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter". It provides an introductory overview of modeling approaches for active matter and is primarily targeted at PhD students (or other readers) who encounter some of these approaches for the first time. The aim of the article is to help put the described modeling approaches into perspective.
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Submitted 25 February, 2021;
originally announced February 2021.