Three-Body Bound States of Quantum Particles: Higher Stability Through Braiding

Cold atoms embedded in a degenerate Fermi system interact by a fermionic analog of the Casimir force, in which the fermions play the role of photons. The fermion-mediated RKKY interaction is an attraction of a $-1/r$ form at distances shorter than the Fermi wavelength. While under realistic conditions the interaction strength is too weak to support hydrogenic two-particle bound states, 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. We analyze three-body states associated with "figure-eight" periodic orbits of the classical problem and show that they are more stable than those associated with circular orbits. The spectra of resonances associated with the discrete energies of these states bear distinct signatures of the figure-eight braiding dynamics.