Heavy-Heavy-Light Atomic System in a Spherical Harmonic Trap

Obtaining quantum defects is an essential step in understanding the physics of Rydberg molecules with complicated interactions. The present study explores analogous systems where the long range Coulomb interaction is replaced by a spherical harmonic oscillator potential. The analysis considers a system of two molecules that are subject to a 3-dimensional harmonic trap with an additional short-range interaction between them, and it develops a generalized quantum defect theory for a spherical 3D oscillator potential as a first step, to obtain smoothly energy-dependent quantum defects. Next, we consider a third light atom added to the system, which has a short-range interaction with one of the two initially trapped heavy atoms, and determine the Born-Oppenheimer potential curves and eigenstates of the system. The results show the emergence of a rich plateau of exotic bound states analogous to the trilobite and butterfly states observed in ultra-long-range Rydberg molecules.