Universal three-body dynamics in binary mixtures of ultra-cold atoms

Abstract

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass m and the third particle of mass m 1 in the zero-range limit of the interaction between different particles is given for arbitrary values of the mass ratio m/m 1 and the total angular momentum L. For those L and m/m 1, which correspond to the finite number of vibrational states, all the binding energies are described by the universal function depending on two scaled variables. The detailed study is performed for L = 1; in particular, it is shown that a two-hump structure in the mass-ratio dependencies of the elastic scattering cross section and the three-body recombination rate are connected with arising of the bound states.