Universal Random Matrix Behavior of a Fermionic Quantum Gas

TL;DR

This paper experimentally validates the application of Random Matrix Theory to strongly-interacting ultracold Fermi gases, confirming its predictions for counting statistics and the Fermi-sphere point process at the single-atom level.

Contribution

It provides the first experimental validation of RMT predictions for strongly-interacting Fermi gases using in situ single-atom counting.

Findings

RMT accurately describes counting statistics in strongly-interacting Fermi gases

Experimental validation of the Fermi-sphere point process

First direct observation of RMT predictions in ultracold atomic systems

Abstract

The pursuit of universal governing principles is a foundational endeavor in physics, driving breakthroughs from thermodynamics to general relativity and quantum mechanics. In 1951, Wigner introduced the concept of a statistical description of energy levels of heavy atoms, which led to the rise of Random Matrix Theory (RMT) in physics. The theory successfully captured spectral properties across a wide range of atomic systems, circumventing the complexities of quantum many-body interactions. Rooted in the fundamental principles of stochasticity and symmetry, RMT has since 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 describing 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. Our measurements show that, while the system is strongly attractive, each spin-component is extremely well described by RMT predictions based on Fredholm determinants. Our results constitutes the first experimental validation of the Fermi-sphere point process through the lens of RMT, and establishes its relevance for strongly-interacting systems.