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Pauli exclusion principle belongs to a class of fundamental laws of quantum mechanics. It does not allow for two identical fermions to occupy the same quantum state. This principle plays a very important role in determining a structure of matter – from nucleons, nuclei, atoms, molecules, super- and semiconductors up to such exotic systems like white dwarfs and neutron stars. Pauli exclusion in a nonrelativistic theory leads to a fully antisymmetric wave-function of identical fermions. In turn, this particular kind of symmetry is responsible for a strong high-order correlations between particles which are present even if they do not interact. The correlations resulting from Pauli principle have unexpected geometrical implications – the particles are forced to arrange themselves in some characteristic patterns in space. This crystalline structures are coined Pauli Crystals, Epl 115, 20012 (2016).
One might think that Pauli Crystals are pure academic objects not existing in a real world. Ideal gas concept as well as a single shot observation of a many-body quantum system in its ground state with a resolution allowing to distinguish a single particle seem to be unbeatable obstacles.

The experimental group of prof. Selim Jochim from Heidelberg decided to look for these structures in the lab. In the recent  preprint arxiv.org/abs/2005.03929 they report on the first observation of Pauli Crystals. The observation was possible due to enormous progress in cooling, trapping and manipulating of ultra-cold atoms achieved by the cold atom community during last few decades. Dilute clouds of atoms cooled to nanokelvin temperatures are perfect systems allowing for a direct observation of Quantum Mechanics at action. In my talk I will give details of theoretical description of Pauli Crystals predicted by the IF PAN team and will report on the recent experimental realization of this idea by the Heidelberg group.

https://phys.org/news/2020-05-team-germany-pauli-crystals.html