Heuristic machinery for thermodynamic studies of SU(N) fermions with neural networks

TL;DR

This paper introduces a machine learning framework using neural networks to analyze experimental data of SU(N) fermions, enabling sensitive detection of spin symmetry effects and thermodynamic properties from simple measurements.

Contribution

It presents a heuristic machine learning approach that guides thermodynamic studies and detects subtle effects in ultracold fermion experiments, with high accuracy in identifying spin multiplicity.

Findings

Neural network achieves ~94% accuracy in detecting spin multiplicity.

The framework allows direct measurement of thermodynamic compressibility from density fluctuations.

The method can validate theoretical models of SU(N) Fermi liquids.

Abstract

The power of machine learning (ML) provides the possibility of analyzing experimental measurements with an unprecedented sensitivity. However, it still remains challenging to probe the subtle effects directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by using machine learning analysis. We use our machinery to guide the thermodynamic studies in the density profile of ultracold fermions interacting within SU($N$) spin symmetry prepared in a quantum simulator. Although such spin symmetry should manifest itself in a many-body wavefuction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of $\sim$94$\%$ for detection of the spin multiplicity, we investigate how the accuracy depends on various less-pronounced effects with filtered experimental images. Guided by our machinery, we directly measure a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU($N$) Fermi liquids, and to identify less-pronounced effects even for highly complex quantum matter with minimal prior understanding.