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High-Resolution Momentum Imaging—From Stern’s Molecular Beam Method to the COLTRIMS Reaction Microscope [Book Chapter]

Multi-particle momentum imaging experiments are now capable of providing detailed information on the properties and the dynamics of quantum systems in Atomic, Molecular and Photon (AMO) physics. Historically, Otto Stern can be considered the pioneer of high-resolution momentum measurements of particles moving in a vacuum and he was the first to obtain sub-atomic unit (a.u.) momentum resolution (Schmidt-Böcking et al. in The precision limits in a single-event quantum measurement of electron momentum and position, these proceedings). A major contribution to modern experimental atomic and molecular physics was his so-called molecular beam method, which Stern developed and employed in his experiments. With this method he discovered several fundamental properties of atoms, molecules and nuclei. As corresponding particle detection techniques were lacking during his time, he was only able to observe the averaged footprints of large particle ensembles. Today it is routinely possible to measure the momenta of single particles, because of the tremendous progress in single particle detection and data acquisition electronics. A “state-of-the-art” COLTRIMS reaction microscope can measure, for example, the momenta of several particles ejected in the same quantum process in coincidence with sub-a.u. momentum resolution. Such setups can be used to visualize the dynamics of quantum reactions and image the entangled motion of electrons inside atoms and molecules. This review will briefly summarize Stern’s work and then present in longer detail the historic steps of the development of the COLTRIMS reaction microscope. Furthermore, some benchmark results are shown which initially paved the way for a broad acceptance of the COLTRIMS approach. Finally, a small selection of milestone work is presented which has been performed during the last two decades.

Jahnke, T.↗

An interactive machine learning platform for analyzing multi-particle coincidence data from cold target recoil ion momentum spectroscopy

We present SCULPT (Supervised Clustering and Uncovering Latent Patterns with Training), a comprehensive software platform for analyzing tabulated high-dimensional multi-particle coincidence data from Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) experiments. The software addresses critical challenges in modern momentum spectroscopy by integrating advanced machine learning techniques with physics-informed analysis in an interactive web-based environment. SCULPT implements uniform manifold approximation and projection for non-linear dimensionality reduction to reveal correlations in high-dimensional data. We also discuss potential extensions to deep autoencoders for feature learning and genetic programming for automated discovery of physically meaningful observables. A novel adaptive confidence scoring system provides quantitative reliability assessments by evaluating user-selected clustering quality metrics with predefined weights that reflect each metric’s robustness. The platform features configurable molecular profiles for different experimental systems, interactive visualization with selection tools, and comprehensive data filtering capabilities. Utilizing a subset of SCULPT’s capabilities, we analyze photo-double-ionization data measured using the COLTRIMS method for three-body dissociation of the D 2 O molecule, revealing distinct fragmentation channels and their correlations with physics parameters. The software’s modular architecture and web-based implementation make it accessible to the broader atomic and molecular physics community, significantly reducing the time required for complex multi-dimensional analyses. This opens the door to finding and isolating rare events exhibiting non-linear correlations on the fly during experimental measurements, which can help steer exploration and improve the efficiency of experiments.

Artificial neural networks↗

SCULPT (Supervised Clustering and Uncovering Latent Patterns with Training) v1

SCULPT (Supervised Clustering and Uncovering Latent Patterns with Training) is a comprehensive data visualization and analysis application focused on working with COLTRIMS (COLd Target Recoil Ion Momentum Spectroscopy) data, which is used in atomic and molecular physics experiments. The application offers several powerful features: - Data uploading and processing capabilities for COLTRIMS files - Multiple visualization methods using UMAP (Uniform Manifold Approximation and Projection) for dimensionality reduction - Interactive selection of data points across multiple views - Feature engineering through various methods: - Manual feature selection from calculated physics parameters - Deep autoencoder for dimension reduction - Genetic programming for discovering meaningful features - Mutual information-based feature selection - Multiple clustering approaches (DBSCAN, KMeans, Agglomerative) - Quality metrics for evaluating clustering results - Export capabilities for selections and generated features

Daoud, Hazem [Lawrence Berkeley National Laborator↗

Real-time observation of multi-electron processes in atoms and diatomic molecules

We report on the implementation of a reliable experimental approach to observe, in real-time, electron dynamics in atoms and molecules at the attosecond time scale. The experimental approach combines a source of shape-controlled attosecond pulses, a stabilized XUV/IR interferometer for time-resolved measurements, and a multi-particle imaging system (Coltrims). In addition, we report new capabilities to control electron dynamics in quantum systems.

74 ATOMIC AND MOLECULAR PHYSICS↗

Controlling $H_{3}^{+}$ Formation From Ethane Using Shaped Ultrafast Laser Pulses

An adaptive learning algorithm coupled with 3D momentum-based feedback is used to identify intense laser pulse shapes that control $H_{3}^{+}$ formation from ethane. Specifically, we controlled the ratio of D 2 H + to $D_{3}^{+}$ produced from the D 3 C-CH 3 isotopologue of ethane, which selects between trihydrogen cations formed from atoms on one or both sides of ethane. We are able to modify the D 2 H + :$D_{3}^{+}$ ratio by a factor of up to three. In addition, two-dimensional scans of linear chirp and third-order dispersion are conducted for a few fourth-order dispersion values while the D 2 H + and $D_{3}^{+}$ production rates are monitored. The optimized pulse is observed to influence the yield, kinetic energy release, and angular distribution of the D 2 H + ions while the $D_{3}^{+}$ ion dynamics remain relatively stable. We subsequently conducted COLTRIMS experiments on C 2 D 6 to complement the velocity map imaging data obtained during the control experiments and measured the branching ratio of two-body double ionization. Two-body $D_{3}^{+}$ + $C_{2}D_{3}^{+}$ is the dominant final channel containing $D_{3}^{+}$ ions, although the three-body D + $D_{3}^{+}$ + $C_{2}D_{2}^{+}$ final state is also observed.

74 ATOMIC AND MOLECULAR PHYSICS↗

Mechanisms and dynamics of the NH + 2 + H + and NH + + H + + H fragmentation channels upon single-photon double ionization of NH 3

We present state-selective measurements on the NH$_2^{+}$ + H$^{+}$ and NH$^{+}$ + H$^{+}$ + H dissociation channels following single-photon double ionization at 61.5 eV of neutral NH$_{3}$, where the two photoelectrons and two cations are measured in coincidence using 3-D momentum imaging. Three dication electronic states are identified to contribute to the NH$_2^{+}$ + H$^{+}$ dissociation channel, where the excitation in one of the three states undergoes intersystem crossing prior to dissociation, producing a cold NH$_2^+$ fragment. In contrast, the other two states directly dissociate, producing a ro-vibrationally excited NH$_2^+$ fragment with roughly 1 eV of internal energy. The NH$^{+}$ + H$^{+}$ + H channel is fed by direct dissociation from three intermediate dication states, one of which is shared with the NH$_2^{+}$ + H$^{+}$ channel. We find evidence of autoionization contributing to each of the double ionization channels. Finally, the distributions of the relative emission angle between the two photoelectrons, as well as the relative angle between the recoil axis of the molecular breakup and the polarization vector of the ionizing field, are also presented to provide insight on the ionization mechanisms for the different dication states.

74 ATOMIC AND MOLECULAR PHYSICS↗

The DREAM Endstation at the Linac Coherent Light Source

Free-electron lasers (FEL), with their ultrashort pulses, ultrahigh intensities, and high repetition rates at short wavelength, have provided new approaches to Atomic and Molecular Optical Science. One such approach is following the birth of a photo electron to observe ion dynamics on an ultrafast timescale. Such an approach presents the opportunity to decipher the photon-initiated structural dynamics of an isolated atomic and molecular species. It is a fundamental step towards understanding single- and non-linear multi-photon processes and coherent electron dynamics in atoms and molecules, ultimately leading to coherent control following FEL research breakthroughs in pulse shaping and polarization control. A key aspect for exploring photoinduced quantum phenomena is visualizing the collective motion of electrons and nuclei in a single reaction process, as dynamics in atoms/ions proceed at femtosecond (10 –15 s) timescales while electronic dynamics take place in the attosecond timescale (10 –18 s). Here, we report on the design of a Dynamic Reaction Microscope (DREAM) endstation located at the second interaction point of the Time-Resolved Molecular and Optical (TMO) instrument at the Linac Coherent Light Source (LCLS) capable of following the photon–matter interactions by detecting ions and electrons in coincidence. The DREAM endstation takes advantage of the pulse properties and high repetition rate of LCLS-II to perform gas-phase soft X-ray experiments in a wide spectrum of scientific domains. With its design ability to detect multi-ions and electrons in coincidence while operating in step with the high repetition rate of LCLS-II, the DREAM endstation takes advantage of the inherent momentum conservation of reaction product ions with participating electrons to reconstruct the original X-ray photon–matter interactions. In this report, we outline in detail the design of the DREAM endstation and its functionality, with scientific opportunities enabled by this state-of-the-art instrument.

47 OTHER INSTRUMENTATION↗