Three-body bound states of quantum particles: Higher stability through braiding

Motivated by recent cold atom experiments exploring the phase structure of Bose-Fermi mixtures, we propose novel emergent bound states. 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-eight braiding dynamics.

Figure 1

(a) Schematic of attractive force between bosons (blue), mediated by the inward pressure due to scattering of fermions (red). (b) A two-body orbit. (c) A circular three-body orbit. (d) A figure-eight three-body orbit.