Universal random matrix behavior of a Fermionic quantum gas

Since its initial use by Wigner in describing heavy atom spectra, random matrix theory (RMT) has found applications and revealed universal laws in diverse physical contexts, from quantum field theory to disordered systems and wireless communications. A particularly compelling application arises in the mathematical structure of the many-body wavefunction of non-interacting Fermi gases, which underpins a complex spatial organization driven by Pauli’s exclusion principle. However, experimental validation of the counting statistics predicted in such systems has remained elusive. Here, we probe at the single-atom level ultracold atomic Fermi gases made of two interacting spin states, obtaining direct access to their counting statistics in situ. We show that, while the system is strongly attractive, each spin component is described to a high accuracy by RMT predictions based on Fredholm determinants. Our results constitute an experimental validation of the Fermi-sphere point process through the lens of RMT, and establish its relevance for strongly-interacting systems. Random matrix theory (RMT) is used to describe non-interacting ultracold Fermi gases. Here, the authors directly probe the full counting statistics in a 2D system of 6Li atoms with two interacting spin states, by means of a continuum quantum gas microscopy technique. The measured number and spacing statistics agree well with predictions from RMT, also in the strongly interacting regime.