2025-10-02 –, Jean-Baptiste Say Amphitheater
Language: English
The principle of Coulomb explosion imaging is simple: use a powerful x-ray pulse to slap a molecule so hard that it (literally) explodes into its constituting atoms. The fragments can then be measured to produce an indirect image of the molecule.
Currently, a key question in the Coulomb explosion community is what we can actually learn from these measurements. What information is preserved about the state of the molecule just before it exploded?
Our simulations show that if the detectors are perfect, we can use this method to image advanced properties of the molecule, namely the high dimensional shape of its ground-state quantum fluctuations. Unfortunately, we can't directly use the experimental data to this end, because it suffers from several key limitations. We circumvent them by fitting a high-dimensional distribution to the data using gradient-based optimization to perform the fit. Then we simply perform our analysis on the fitted model.
Putting everything together, we demonstrate that the experiment indeed succeeds in imaging subtle quantum properties of the studied molecule.
Molecules are the building block of pretty much everything. However, this doesn't imply that they are easy to study at the most fundamental level. In fact, even when they are isolated, they remain complex quantum systems, challenging to model theoretically and to image experimentally.
To address this challenge, new scientific facilities (called XFEL for X-ray Free Electron Laser) were built to provide scientists with absurdly powerful pulses of x-ray. One of the uses of the high power delivered at these instruments is to induce clean explosions of molecules. By destroying the molecule and measuring the produced fragments, one can infer some information about the molecule just-before-explosion, a technique known as Coulomb explosion imaging. The method is currently gaining popularity, on the one hand because the infrastructures are rapidly improving, and on the other hand because it is one of the few contenders that may one day be able to produce images and movies of arbitrary molecules, a feat currently out of reach for any method.
A key problem is to generalize Coulomb explosion imaging to larger molecules. In general, not all fragments can be detected simultaneously, leading to measurements with a lot of missing information, which complicate the interpretation of the data.
We have developed a method to reconstruct this information, by fitting a high-dimensional Gaussian distribution to the data, through a gradient-descent optimization of the fitted model. We defined the loss function of the problem in such a way that it is not affected by the information missing from the measurements, making it suitable to analyze the experimental data.
Then, with the help of simulation of the Coulomb explosion of a molecule, we were able to link the measurements to fundamental properties of the molecule, namely the shape of its quantum ground-state fluctuations.
A large part of the talk will be dedicated to introducing the concept of Coulomb explosion itself, and to detail the challenge it faces in terms of data analysis. Then I will describe the reconstruction method that I devised, with an emphasis on how the specifics of Julia were helping me. In particular, I'll show the impact that package like Tullio.jl, Zygote.jl and Optim.jl had on the project. Finally, I'll briefly conclude on the physical relevance of my work in relation to the imaging of quantum property of a large molecule.
