Observing Pauli crystals

When I walk to my office each morning, the Pauli exclusion principle prevents my feet from sinking through the floor. Whereas bosons can condense into a single quantum state, fermions, such as electrons in ordinary solids, are forbidden from doing so. Pauli exclusion is the best-known manifestation of Fermi–Dirac statistics, and it accounts for, among other things, the structure of the periodic table and electrical conductivity in metals.

Fermions do not even need to interact to behave as if they repel each other. Unlike ordinary crystals, whose structures are produced by interatomic forces, fermionic particles, merely by being near each other, are prompted to rearrange into distinct structures known as Pauli crystals. Mariusz Gajda and his colleagues at the Polish Academy of Sciences in Warsaw predicted the phenomenon four years ago. And now doctoral student Marvin Holten, postdoc Luca Bayha, and their colleagues, under the direction of Selim Jochim at Heidelberg University, have observed it in the momentum correlations of a few lithium-6 atoms trapped in a two-dimensional plane.

The experiment was tricky and delicate. The researchers essentially spilled a few hundred ultracold Li atoms out of an optical trap until just three or six of the coldest atoms remained at the bottom to initialize the system. Only one of those fermions can reside at the minimum energy. The others rearrange to avoid stepping on each other and violating Pauli exclusion. The rearrangement creates the self-organization. Pauli crystals are hardly solid materials. They exhibit neither the translational symmetry nor the long-range order of a real crystal. The two examples pictured here, compiled from photographs of either 3 or 6 atoms in the trap, show two distinct, ordered structures.

To capture either structure requires some 20 000 snapshots, which collectively build up a probability distribution of the atoms’ momenta. Each time a handful of atoms are optically trapped and cooled, the trap is turned off and a laser illuminates the ensemble. The atoms fluoresce in response and the photons strike a CCD camera to generate a snapshot of the three or six atoms at a single instant. Because every snapshot comes from a different, newly prepared experiment, the researchers had to rotate each image to align their different angular orientations and center each one relative to a common axis. Only then is the Pauli crystal revealed—directly from the atoms’ momentum correlations.

Now that the Heidelberg team has demonstrated Pauli crystals from noninteracting particles, the stage is set for simulating more complicated, highly correlated materials, such as superconductors. (M. Holten et al., Phys. Rev. Lett. 126, 020401, 2021 .)