  Cold atoms embedded in a degenerate Fermi system interact via a fermionic
analog of the Casimir force, which is an attraction of a -1/r form at distances
shorter than the Fermi wavelength. Interestingly, the hydrogenic two-body bound
states do not form in this regime because the interaction strength is too weak
under realistic conditions, and yet the three-body bound states can have a
considerably higher degree of stability. As a result, the trimer bound states
can form even when the dimer states are unstable. A quasiclassical analysis of
quantum states supported by periodic orbits singles out the "figure-eight"
orbits, predicting bound states that are more stable than the ones originating
from circular orbits. The discrete energies of these states form families of
resonances with a distinct structure, enabling a direct observation of
signatures of figure-eightbraiding dynamics.
