The Pauli exclusion principle forces fermions to fill increasingly higher energy levels, forming at low temperatures a so-called Fermi sea. Its topology (the shape described by invariants like the Euler characteristic) influences the system's response. Theory predicted that this characteristic is 'encoded' in multi-point density correlations of particles. In an experiment with a two-dimensional gas of lithium-6 atoms, scientists for the first time extracted the Euler characteristic by measuring three- and four-point correlations. The results matched the ideal gas, despite interactions, opening a path to studying many-body topology via correlations. Surprising fact: topology can be 'felt' simply by counting how often atoms are found near each other.
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.