Numerical Calculations of Efimov States in Ultracold Atomic Systems

Abstract: In systems of ultracold atoms,  the  quantum  Efimov  effect  can  appear where identical bosons form an infinite tower of bound trimer states in the resonant limit, at the bound dimer dissociation threshold. The most characteristic feature of this effect is that their energy spectrum obey a geometric scaling law, which is universal in the sense that it emerges irrespective of the nature of the two body forces. Using  a  model  potential,  constructed  to  resemble the two body interaction between alkali atoms,  which was  fine tuned to control the  scattering  length,  energy  eigenvalues  for  the  two-  and  threebody problem were calculated numerically. The results where  fitted  to  the analytic theory and the appearance of the first Efimov state was positioned at a scattering length of -9.23rvdW , which is in good  agreement  with  the universal value -9.2rvdW .