This is a supplementary material for arxiv:2607.16846.
Kendall shape space description of an atomic trimer
This animation exemplifies how different points on Kendall two-sphere correspond to different triangle shapes, depicted in Figure 1 of main text.


Movie 1 - This shows how a trimer deformation cycle in real space maps to a close orbit around the north pole of Kendall's shape sphere. The yellow equilateral triangles below the trimers correspond to the north pole on Kendall's sphere around which the closed orbit rotate.
Time evolution of a relative stationnary superposition
The time evolution of the This animation shows the time evolution of a relative stationary state depicted in Figure 2 of main text.


Movie 2 - Time evolution of a superposition single eccentric vortex for an angular momentum $l_z=0.8$. The coloring displays the value of the phase $\mathrm{arg}[\psi]$ of the wavefunction, and the elevation shows the density $|\psi|^2$.
References
  1. J. Garaud and A. Niemi,
    Geometric Qubits in Programmable Atomic Trimers.
    Preprint (2026) arXiv .