Pauli crystals -- interplay of symmetries

TL;DR

This paper uses numerical modeling to analyze Pauli crystals formed by ultracold fermionic atoms in various traps, highlighting their unique symmetry-breaking features and differences from Coulomb crystals, emphasizing the quantum nature of the Pauli exclusion principle.

Contribution

It demonstrates how Pauli crystals form in different trapping potentials and compares their structure to Coulomb crystals, emphasizing the quantum origin of their formation.

Findings

Pauli crystals do not share trap symmetry due to measurement and quantum state effects.

The structure of Pauli crystals differs significantly from Coulomb crystals.

The exclusion principle induces many-particle correlations beyond simple repulsion.

Abstract

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. Numericalmodeling 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.