Universal random matrix behavior of a Fermionic quantum gas
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.
Related
- A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features
- Work statistics of sudden quantum quenches: A random matrix theory perspective on Gaussianity and its deviations
- Computable fermionic non-Gaussianity from the covariance matrix
- Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity
- Universal Emergence of Bosonic and Fermionic Algebras in a Deterministic Proper-Time Framework
BibTeX
@article{dixmerias2026universal,
title = {{Universal random matrix behavior of a Fermionic quantum gas}},
author = {Maxime Dixmerias and Giuseppe Del Vecchio Del Vecchio and Cyprien Daix and Joris Verstraten and Tim de Jongh and Bruno Peaudecerf and Pierre Le Doussal and Grégory Schehr and Tarik Yefsah},
journal = {Nature Communications},
year = {2026},
month = oct,
doi = {10.1038/s41467-026-77088-w},
eprint = {2510.25735},
archivePrefix = {arXiv},
url = {https://www.nature.com/articles/s41467-026-77088-w},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Universal random matrix behavior of a Fermionic quantum gas
AU - Maxime Dixmerias
AU - Giuseppe Del Vecchio Del Vecchio
AU - Cyprien Daix
AU - Joris Verstraten
AU - Tim de Jongh
AU - Bruno Peaudecerf
AU - Pierre Le Doussal
AU - Grégory Schehr
AU - Tarik Yefsah
PY - 2026
DA - 2026/10/03
JO - Nature Communications
DO - 10.1038/s41467-026-77088-w
UR - https://www.nature.com/articles/s41467-026-77088-w
AB - 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.
SN - 2041-1723
ER -