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

TL;DR

This paper explores how three-body quantum bound states can be more stable than two-body states in a fermionic system, highlighting the role of braiding dynamics and figure-eight orbits in their stability.

Contribution

It introduces the concept that three-body bound states can be more stable than two-body states in fermionic systems, emphasizing the importance of braiding and figure-eight orbits.

Findings

Three-body bound states can form even when two-body states are unstable.

Figure-eight orbits support more stable quantum states.

Distinct resonance structures reveal braiding dynamics signatures.

Abstract

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.