Weakly bound atomic trimers in ultracold traps

TL;DR

This paper predicts the energies of weakly bound three-atom states (trimers) in ultracold traps using experimental data on two- and three-body interactions, highlighting the small influence of deep-bound states in certain cases.

Contribution

It provides a method to predict trimer energies in ultracold atomic systems based on experimental recombination data and scattering lengths, including the effect of deep-bound states.

Findings

Predicted trimer energies for specific atomic states.

Recombination coefficients as a function of trimer energies.

Deep-bound state contributions are small for certain systems.

Abstract

The experimental three-atom recombination coefficients of the atomic states $^{23}$Na$|F=1,m_F=-1>$, $^{87}$Rb$|F=1,m_F=-1>$ and $^{85}$Rb$|F=2,m_F=-2>$, together with the corresponding two-body scattering lengths, allow predictions of the trimer bound state energies for such systems in a trap. The recombination parameter is given as a function of the weakly bound trimer energies, which are in the interval $ 1<m(a/\hbar)^2 E_3< 6.9$ for large positive scattering lengths, $a$. The contribution of a deep-bound state to our prediction, in the case of $^{85}$Rb$|F=2,m_F=-2>$, for a particular trap, is shown to be relatively small.