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arXiv:2505.02837 · Physical Review Letters

Pauli Crystal Superradiance

Daniel Ortuño-Gonzalez, Rui Lin, Justyna Stefaniak, Alexander Baumgärtner, Gabriele Natale, Tobias Donner, R. Chitra

Published Dec 23, 2025• 1 citation
arXivHTMLPDF

Abstract

Pauli crystals are unique geometric structures of noninteracting fermions, resembling crystals, that emerge solely from Fermi statistics and confinement. Unlike genuine quantum crystals that arise from interparticle interactions, Pauli crystals do not break translation symmetry but nonetheless exhibit nontrivial many-body correlations. In this Letter, we explore Pauli crystal formation in a cavity-fermion setup. We analytically show that when coupled to a cavity, degeneracy in Pauli crystals can trigger zero-threshold transitions to superradiance. This superradiance is accompanied by the emergence of a genuine quantum crystalline state, wherein the atomic density is periodically modulated. We substantiate our findings using state-of-the-art numerical simulations. The combined interplay between statistics, confinement geometry, and interactions mediated by light thus facilitates a novel pathway to quantum crystallization.

DOI
10.1103/g5fp-ws7z

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Pauli crystals are unique geometric structures of noninteracting fermions, resembling crystals, that emerge solely from Fermi statistics and confinement. Unlike genuine quantum crystals that arise from interparticle interactions, Pauli crystals do not break translation symmetry but nonetheless exhibit nontrivial many-body correlations. In this Letter, we explore Pauli crystal formation in a cavity-fermion setup. We analytically show that when coupled to a cavity, degeneracy in Pauli crystals can trigger zero-threshold transitions to superradiance. This superradiance is accompanied by the emergence of a genuine quantum crystalline state, wherein the atomic density is periodically modulated. We substantiate our findings using state-of-the-art numerical simulations. The combined interplay between statistics, confinement geometry, and interactions mediated by light thus facilitates a novel pathway to quantum crystallization.
Abstract It is conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures, called Pauli crystals, are predicted for a two‐dimensional (2D) system of free fermions under harmonic confinement. In this work, the possibility of this outcome is pursued and a theoretical model is considered that may capture both qualitatively and quantitatively, the key features of the abovementioned setup. The results for and 6 particles show that the minimum energy configuration corresponds to and is in good quantitative agreement with the reported values of Pauli crystals seen in single‐shot imaging data obtained via the configuration density technique. Numerical results for larger systems of and 30 particles show that the crystalline configurations observed are not the same as the classical Wigner crystal structures that emerge should the confined charged particles interact with a Coulomb potential. An important question floated is whether such crystalline structures do really exist in a quantum system or whether they are artifacts of the methods used to analyze them.
Pauli crystals are ordered geometric structures that emerge in trapped noninteracting fermionic systems due to their underlying Pauli repulsion. The deformation of Pauli crystals - often called melting - has been recently observed in experiments, but the mechanism that leads to it remains unclear. We address this question by studying the melting dynamics of N=6 N = 6 fermions as a function of periodic driving and experimental imperfections in the trap (anisotropy and anharmonicity) by employing a combination of numerical simulations and Floquet theory. Surprisingly, we reveal that the melting of Pauli crystals is not simply a direct consequence of an increase in system energy, but is instead related to the trap geometry and the population of the Floquet modes. We show that the melting is absent in traps without imperfections and triggered only by a sufficiently large shaking amplitude in traps with imperfections.
We study a one-dimensional array of bosons with infinite-range interactions mediated by a laser-driven dissipative optical cavity. The cavity-mediated infinite-range interactions open up an alternative pathway to crystallization, hitherto only known for dipolar bosons due to their long-range interactions. In parameter ranges attainable in state-of-the-art experiments, we systematically compare observables for bosons and fermions with infinite-range interactions. At sufficiently large laser pump powers, many observables, including density distributions in real and momentum space, correlation functions, eigenvalues of the one-body density matrix, and superradiance order parameters, become identical for bosons and fermions. We map out the emergence of this cavity-induced crystallization as a function of pump power and contact interactions. We discover that cavity-mediated interactions can compensate a reduction by several orders of magnitude in the strength of the contact interactions needed to trigger crystallization.
Recently observed Pauli crystals are structures formed by trapped ultracold atoms with the Fermi statistics. Interactions between these atoms are switched off, so their relative positions are determined by joined action of the trapping potential and the Pauli exclusion principle. Numerical modeling is used in this paper to find the Pauli crystals in a two-dimensional isotropic harmonic trap, three-dimensional harmonic trap, and a two-dimensional square well trap. The Pauli crystals do not have the symmetry of the trap—the symmetry is broken by the measurement of positions and, in many cases, by the quantum state of atoms in the trap. Furthermore, the Pauli crystals are compared with the Coulomb crystals formed by electrically charged trapped particles. The structure of the Pauli crystals differs from that of the Coulomb crystals, this provides evidence that the exclusion principle cannot be replaced by a two-body repulsive interaction but rather has to be considered to be a specifically quantum mechanism leading to many-particle correlations.
The Pauli exclusion principle is a fundamental law underpinning the structure of matter. Because of their antisymmetric wave function, no two fermions can occupy the same quantum state. Here, we report on the direct observation of the Pauli principle in a continuous system of up to six particles in the ground state of a two-dimensional harmonic oscillator. To this end, we sample the full many-body wave function by applying a single atom resolved imaging scheme in momentum space. We find so-called Pauli crystals as a manifestation of higher order correlations. In contrast to true crystalline phases, these unique high-order density correlations emerge even without any interactions present. Our work lays the foundation for future studies of correlations in strongly interacting systems of many fermions.
Exchange statistics endows identical particles with an effective "statistical potential", whose familiar exact form is two-body and purely repulsive for fermions. Here we construct an exact collective many-body form: the thermodynamics of NNN trapped ideal fermions maps onto classical distinguishable particles governed by a single potential -- exactly for harmonic confinement at all temperatures, and to leading semiclassical order for arbitrary potentials. The associated force separates canonically into pairwise contributions, which for N≥3N\geq 3N≥3 can turn attractive, governed by a simple geometric criterion. Classical minimization reproduces observed few-body Pauli-crystal symmetries and agrees with the N=55N=55N=55 ground-state probability maximum at sub-percent shell accuracy. Heating drives discrete structural transitions accompanied by a crossover of the strongest force from attractive to repulsive. Both the potential and its forces are directly computable from existing single-shot imaging data, turning quantum exchange into measurable classical mechanics.