Fermions cannot occupy the same quantum state, and at low temperatures they form an ordered 'Fermi sea,' whose shape is important for the material's properties. Amazingly, from the relative positions of particles (density correlations) one can calculate the topological Euler number that describes this shape — like guessing the shape of a bell from its sound. An experiment with lithium atoms confirmed this connection. What other secrets do quantum patterns hold?
The law discovered by Wolfgang Pauli forbids identical particles from occupying the same spot. Hence, in cold matter, a Fermi sea is born: particles, like water, fill energy levels from bottom to top. The shape of the sea's surface — including 'islands' of emptiness — dictates the properties of the whole system. Experimenters cooled lithium atoms nearly to absolute zero and, using a microscope, tracked how they gather into triplets and quartets. The pattern of these groups, like ripples on water, revealed the topography of the dark depths.
Now this method will probe Fermi seas in liquid helium-3 and even in the unimaginable crush of neutron stars.
🎯 Without the Pauli principle, electrons in atoms would roll down to the lowest level, and all chemical elements would become indistinguishable — the world would turn into a homogeneous mixture.