Pauli crystals in harmonic trap and on a sphere

TL;DR

This paper discusses the formation of Pauli crystals, structures arising from Fermi statistics in trapped ultracold particles, revealing geometric arrangements influenced by quantum principles in harmonic traps and spherical surfaces.

Contribution

It demonstrates the emergence of Pauli crystals in both harmonic traps and spherical geometries, extending understanding of quantum spatial arrangements of non-interacting fermions.

Findings

Pauli crystals form regular geometric structures.

Similar shapes occur on spherical surfaces.

Positions are dictated by Fermi statistics and trapping potential.

Abstract

Recently predicted and observed Pauli crystals are structures formed by trapped ultracold non-interacting particles obeying Fermi statistics. The relative positions of the particles are determined by the trapping potential and the Pauli exclusion principle. Measuring all particles at once, their positions tend to be close to vertices of non-trivial polyhedrons. Similar shapes are found for systems of particles bound to the surface of a sphere.