Controlling integrability in a quasi-1D atom-dimer mixture

TL;DR

This paper analytically investigates how tuning parameters in a quasi-1D atom-dimer mixture can control the system's integrability, affecting scattering probabilities and relaxation dynamics, with implications for experimental studies.

Contribution

It introduces a method to tune the degree of integrability in a quasi-1D atom-dimer system by adjusting scattering length and confinement, affecting scattering and relaxation processes.

Findings

Reflection and break-up probabilities scale as a^6 (bosons) and a^8 (fermions).

Controllability of integrability range without changing thermodynamic properties.

Relaxation to bound states varies between fermionic and bosonic cases.

Abstract

We analytically study the atom-dimer scattering problem in the near-integrable limit when the oscillator length l_0 of the transverse confinement is smaller than the dimer size, ~l_0^2/|a|, where a<0 is the interatomic scattering length. The leading contributions to the atom-diatom reflection and break-up probabilities are proportional to a^6 in the bosonic case and to a^8 for the up-(up-down) scattering in a two-component fermionic mixture. We show that by tuning a and l_0 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.