Session X03: Focus Session: Machine Learning Approaches to Ultrafast Science

Deep neural networks trained with synthetic Hamilton matrices for non-linear photo-ionization spectra from fluctuating pulses

We construct deep neural networks, which can map fluctuating photo-electron spectra obtained from noisy pulses to spectra from noise-free pulses. The network is trained on spectra generated with noisy pulses and random Hamilton matrices, representing systems which could exist but do not necessarily exist. 

Such networks can "purify" fluctuating spectra, that is, map them to those from Fourier-limited Gaussian pulses [1]. Furthermore, the  neural-network-based maps can predict spectra of double pulses, pulses with a chirp and even partially-coherent pulses from fluctuating spectra generated by noisy pulses. Finally, we demonstrate that along with purification of a fluctuating double-pulse spectrum, one can estimate the time-delay of the underlying double pulse, an attractive feature for single-shot spectra from SASE FELs [2]. We demonstrate our approach with resonant two-photon ionization, a non-linear process, sensitive to details of the laser pulse.   

Bayesian inferencing and deterministic anisotropy for molecular geometry retrieval in gas phase diffraction experiments

Ultrafast molecular gas phase diffraction is a vital tool for retrieving time dependent molecular structures. We are often limited in the systems we can study since we generally require complex molecular dynamics simulations to interpret the results. We develop an alternative analysis to approximate the molecular geometry distribution |Ψ(r, t)|² that does not require such complex simulations. We achieve coordinate-space resolution of 1 pm to 10 fm while uniquely defining the molecular structure. We demonstrate our method’s viability by retrieving the ground state geometry distribution |Ψ(r)|² for simulated stretched NO₂ and measured N₂O. Our method expands the capabilities of ultrafast molecular gas phase diffraction to measure other variables, like the width of |Ψ(r, t)|². By not relying on complex simulations and with ~100 fm resolution, our method has the potential to effectively turn ultrafast molecular gas phase diffraction into a discovery oriented technique, exploring systems that are prohibitively difficult to simulate   

Few-fs resolution of a photoactive protein traversing a conical intersection

The structural dynamics of a molecule are determined by the underlying potential energy landscape.  Conical intersections are funnels connecting otherwise separate potential energy surfaces.  Posited almost a century ago, conical intersections remain the subject of intense scientific interest.  In biology, they play a pivotal role in vision, photosynthesis, and DNA stability.  Accurate theoretical methods for examining conical intersections are at present limited to small molecules. Experimental investigations are challenged by the required time resolution and sensitivity.  Current structure-dynamical understanding of conical intersections is thus limited to simple molecules with around 10 atoms, on timescales of about 100 fs or longer.  Spectroscopy can achieve better time resolutions, but provides indirect structural information.  Here, we present few-femtosecond, atomic-resolution videos of the Photoactive Yellow Protein, a 2,000-atom protein, passing through a conical intersection.  These videos, extracted from experimental data by machine learning, reveal the dynamical trajectories of de-excitation via a conical intersection, yield the key parameters of the conical intersection controlling the de-excitation process, and elucidate the topography of the electronic potential energy surfaces involved.

 

* In collaboration with: A. Hosseinizadeh, N. Breckwoldt, R. Fung, R. Sepehr, M. Schmidt, P.    Schwander, and R. Santra.   

Imaging a complex molecular structure with laser-induced electron diffraction and machine learning

Imaging a molecular structure with electron or X-ray diffraction relies on finding a global extremum in a multi-dimensional solution space [1]. Laser-induced electron diffraction (LIED) [2] is a powerful laser-based method that images the structure of a single gas-phase molecule with combined sub-atomic picometre and atto-to-femtosecond spatio-temporal resolution [3]. In LIED, the structural information of the molecule is extracted from the coherently scattered electron wave packet, driven by an intense laser field after photoionization. However, retrieving the molecular geometry from a diffraction pattern becomes progressively difficult with increasing molecular structure and is a general challenge for any diffraction-based imaging technique. A machine learning (ML)-based approach is tailored to overcome this limitation since it achieves pattern matching in a complex solution space with high precision. We demonstrate the accurate retrieval of the three-dimensional structure of the chiral molecule Fenchone (C₁₀H₁₆O) by implementing LIED in combination with an ML algorithm [4]. Our results show that ML-LIED provides new opportunities to determine the structure of large and complex molecules.

[1] A. Sanchez-Gonzalez et al., Nat. Commun. 8, 15461 (2017).

[2] T. Zuo et al., Chem. Phys. Lett. 259, 313 (1996).

[3] A. Sanchez et al., Nat. Commun. 12, 1520 (2021).

[4] X. Liu et al., Comm. Chem. 4, 154 (2021).   

Ghost-imaging enhanced SASE x-ray free-electron laser spectral characterization

X-ray free-electron lasers (XFELs) provide ultrahigh intensity x-ray pulses with brightness 10 orders of magnitude larger than the synchrotron radiation light source. It opens the door of nonlinear light-matter interaction investigation in the x-ray regime. However, most XFELs around the world work in the self-amplified spontaneous radiation (SASE) mode, which starts from initial random bunching within the electron beam and generates spectrally stochastic x-ray pulses. Spectral characterization of the SASE pulses is important for x-ray spectroscopy. For hard x rays crystal Bragg diffraction and for soft x rays grating diffraction have been used to split the x rays and measure a reference spectrum.  Alternatively, the photoelectron spectrum from a dilute gas can act as a transparent beam splitter and the x-ray spectrum can be derived.  In this talk, we will discuss enhanced x-ray spectral characterization from photoelectron spectra using a ghost-imaging method [1]. The SASE pulses at European XFEL are measured by 16 electron time-of-flight (eToF) and a grating spectrometer simultaneously.  A response matrix is learned by comparing the eToF and spectrometer measurements of thousands of SASE pulses. The response matrix extracted can be used to predict yet-to-be-measured SASE pulses with excellent energy resolution.   

Ultrafast Molecular Imaging Using 4-Fold Covariance: Coincidence Insight with Covariance Speed

Momentum resolved coincidence measurements have traditionally served as the gold standard for measuring dissociative ionization of molecules. Covariance measurements can provide similar physical insights and have enabled much higher data taking rates (∼ 100×) [1], allowing for studies as a function of laser intensity, pulse duration, pump-probe delay etc. While powerful, covariance was only demonstrated for up to three particles, limiting its use in Coulomb explosion imaging (CEI) of larger molecules [2]. Here we develop some mathematical tools to compute higher order covariances, and demonstrate four fold covariance for CEI of deuterated formaldehyde (CD2O).

[1] Allum, F., Cheng, C., Howard, A.J., Bucksbaum, P.H., Brouard, M., Weinacht, T. and Forbes, R., 2021. Multi-Particle Three-Dimensional Covariance Imaging:“Coincidence” Insights into the Many-Body Fragmentation of Strong-Field Ionized D2O. The Journal of Physical Chemistry Letters, 12(34), pp.8302-8308.

[2] Zhaunerchyk, V., Frasinski, L.J., Eland, J.H. and Feifel, R., 2014. Theory and simulations of covariance mapping in multiple dimensions for data analysis in high-event-rate experiments. Physical Review A, 89(5), p.053418.