Controlling integrability in a quasi-one-dimensional atom-dimer mixture

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length l0 of the transverse confinement is smaller than the dimer size, ∼l02/|a|, where a<0 is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to a6 in the bosonic case and to a8 for the ↑-↑↓ scattering in a two-component fermionic mixture. We show that by tuning a and l0 one can control the "degree of integrability" in a quasi-1D atom-dimer mixture in an extremely wide range leaving thermodynamic quantities unchanged. We find that the relaxation to deeply bound states in the fermionic (bosonic) case is slower (faster) than transitions between different Bethe ansatz states. We propose a realistic experiment for detailed studies of the crossover from integrable to nonintegrable dynamics.