RUI New Generation of AI-Augmented Quantum Monte Carlo Libraries to Guide the Search for Exotic Superfluid Phases in Cold Atoms

This project will interface well-established state-of-the-art numerical techniques with innovative artificial intelligence tools to compute equilibrium and dynamical properties of strongly correlated Fermi superfluids. In the very active field of ultracold atoms, the results of this project will guide experimental searches for exotic superfluid phases, such as non-trivial superfluid states of matter that rely on unconventional pairing mechanisms or the existence of fascinating topological superfluids.

The new insights that will come from this project may have a deep impact in physics, even beyond the field of cold atoms, and may pave the way for a deeper understanding of superfluid states in unconventional superconductors and in nuclear matter. Novel data analysis tools and visualization techniques will be developed to capture the most important physical mechanisms.

The PI plans to dedicate substantial effort to make the methods and topics accessible to as many people as possible, and to address novel ways to teach quantum mechanics. Students will be able to run virtual experiments and to explore new phases of matter and will have a unique opportunity to learn how to become the scientists of the future.

A new generation of auxiliary-field quantum Monte Carlo techniques will be proposed: artificial intelligence tools will guide a self-consistent procedure to minimize the bias due to the approximations underlying the technique. This will be achieved through the optimization of the trial wave function within a feedback process which learns from the quantum Monte Carlo data.

This project is expected to generate accurate non-perturbative data for Fermi superfluids. The study will address both equilibrium properties, like pairing, density and spin correlations, and dynamical properties, like spectral functions and dynamical structure factors, which give access to the low-energy excitations of the systems. The accurate numerical data will provide guidance to the experiments in the major challenge of detecting new exotic phases in cold atoms, with particular focus on complex intertwined orders in spin-polarized systems when spin-orbit coupling is present.

Substantial advances in the fundamental understanding of the physical mechanisms underlying such superfluid phases are also expected. The formation of Cooper pairs with finite momentum in spin-polarized systems will be addressed, the interplay with density and spin order will be studied and the role of spin-orbit coupling will be investigated, in connection with the possibility of observing non-trivial topological properties.

The study of the manifold of excited states of a system through the calculation of dynamical correlations will allow the PI to directly compare the predictions with spectroscopy and scattering experiments and to compute the dispersion of collective modes, which is crucial for the experimental detection of exotic phases. In addition to guiding experimental searches, the results will also serve as valuable benchmarks for many-body theories and computational methods for strongly correlated systems, where simple perturbative approaches are doomed to fail.

Finally, the efforts that the PI plans to dedicate to the development of novel visualization tools to capture the key physical mechanisms are expected to create the best environment to train the next generation of students, teachers and researchers in quantum mechanics, starting from their undergraduate studies.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.