Near two-body unitarity, the three-boson system is characterized by an approximate discrete scale invariance manifest in a geometric tower of bound states (the Efimov effect). In the absence of a strong four-body force, the four-boson system has two states associated with each Efimov state, one very nearly unstable, the other several times deeper. We study correlations between the excited- and ground-state properties, such as binding energies and radii, up to next-to-leading order in an effective field theory for short-range forces. We obtain the parameters in these correlations from similar correlations arising from existing precise calculations based on short-range potentials. We also derive correlations among excited-state properties that emerge from the proximity of the state to the break-up threshold into a boson and a three-boson bound state, using an effective field theory for ``halo'' states.
We treat three-dimensional bosonic clusters with up to
N=40 atoms, interacting additively through two-body van der Waals potentials, in the near-threshold regime. Our study includes super-borromean systems with
N atoms for which all subsystems are unbound. We determine the energetics and structural properties such as the expectation value of the interparticle distance as a function of the coupling strength. It has been shown that the coupling strength
g∗(N), for which the
N-body system becomes unbound, is bounded by the coupling constant ${g}_{*}^{(N\ensuremath{-}1)}$, for which the next smaller system with $N\ensuremath{-}1$ atoms becomes unbound, i.e., ${g}_{*}^{(N)}\ensuremath{\geqslant}(N\ensuremath{-}1){g}_{*}^{(N\ensuremath{-}1)}∕N$. By fitting our numerically determined ground-state energies to a simple functional form with three fitting parameters, we determine the relationship between
g∗(N) and ${g}_{*}^{(N\ensuremath{-}1)}$. Our trimer and tetramer energies fall on the so-called Tjon line, which has been studied in nuclear physics. We confirm the existence of generalized Tjon lines for larger clusters. Signatures of the universal behavior of weakly bound three-dimensional clusters can possibly be observed in ultracold Bose gases.
We report on the investigation of endothermic and nearly thermoneutral atom-exchange collisions in an ultracold atom-dimer mixture. By developing an indirect preparation method based on a molecular bound-bound transition, we are able to directly observe an endothermic collision with a tunable energy threshold and study the state-to-state collision dynamics. The collision rate coefficients show a striking threshold phenomenon. The influence of the reverse process on the collision dynamics is observed for the endothermic and nearly thermoneutral collisions. We carry out zero-range quantum-mechanical scattering calculations to obtain the collision rate coefficients, and the three-body parameter is determined by comparison with the experiments. The observed endothermic and nearly thermoneutral collisions may be employed to implement quantum simulation of the Kondo effect with ultracold molecules.