Cold Atoms Paint a Pattern with Forbidden Symmetry ✛ ✎ ✦

Original: "Self-organized quasicrystals and their excitations in dipolar Bose-Einstein condensates via optical feedback"

· Liang-Jun He, Fabian Maucher, Yong-Chang Zhang

arXiv:2607.10141 · 2026-07-11 · arXiv non-exclusive · independent analysis · 1 min

Quantum Gases

In an ultracold cloud of atoms, a structure with 12-fold symmetry spontaneously emerges — impossible for ordinary crystals.

In a special state, Bose–Einstein condensate, atoms lose their individuality and move as a single wave. It was predicted by Satyendra Nath Bose and Albert Einstein. In such a medium, a quasicrystal can be born — a pattern where strict symmetry doesn't require repetition, like an infinite, non-repeating mosaic.

To create it, they take a cloud of dysprosium atoms — tiny magnets (dipolar interaction). A laser beam reflected from a mirror is passed through it, creating optical feedback (quantum optics and interference). Two competing influences arise — magnetic and light. They overlap like two stencils with different spacing, forcing the atoms into a pattern with 12-fold symmetry. These excitation waves were predicted back in the 1940s by Lev Landau. Calculating the structure was made possible by numerical simulation and accounting for quantum fluctuations.

This quasicrystal remains superfluid: it flows without friction even though it acquires rigid order. Such a hybrid is unthinkable in the ordinary world.

The resulting method is a controllable platform for studying the quantum thermodynamics of such systems. By changing the atoms' magnetic strength or the illumination parameters, one can obtain patterns with other symmetries, such as ten-pointed stars.

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Ordinary crystals can only have symmetry axes of order 1, 2, 3, 4, and 6—twelve-fold symmetry is mathematically forbidden in a periodic lattice.

Sci-fi writers described 'quasicrystalline armor' in the novel 'Quark'—now scientists are creating its prototypes in the lab.

\varepsilon(k_\perp) = \sqrt{\frac{\hbar^2 k_\perp^2}{2m}\left(\frac{\hbar^2 k_\perp^2}{2m} + 2\rho_{2D} \tilde{U}_{\text{int}}(k_\perp) + 3\gamma_{2D} \rho_{2D}^{3/2}\right)}

The excitation energy depends on the wave vector, density, and Fourier transform of the total effective interaction – like musical notes for quantum waves, where the slightest change in the orchestra's lineup alters the melody.

V_{\text{opt}}(r_\perp - r_\perp') = \hbar \tilde{\gamma} \cos\left(\frac{k_l}{4d} |r_\perp - r_\perp'|^2\right)

The optically derived potential oscillates with transverse distance, creating a "lattice" of light: k_l is the laser wave number, d is the distance to the mirror, and the parameter \tilde{\gamma} sets the strength of the light brush.

Scientists

Felix Bloch Satyendra Nath Bose Albert Einstein John Bardeen

Concepts

exciton condensate quasiparticle Bose–Einstein statistics Bose-Einstein condensate quasicrystal quasistar polaron Goldstone's theorem Gross–Pitaevskii equation polariton excitation majorana modes boson bubble collision quantum point contact

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Cold Atoms Paint a Pattern with Forbidden Symmetry ✛ ✎ ✦