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 $l_0$ of the transverse confinement is smaller than the dimer size, $\sim l_0^2/\left|a\right|$, 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 $\uparrow$-$\uparrow \downarrow$ 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.

Figure 1

The quantity $1-{\left|t\left(q\right)\right|}^2$ versus $q^2/E_d$ below the break-up threshold for several values of $E_d$. Numerical solutions of Eq. (12) are obtained by taking into account the first three (solid), the first two (dash-dotted), or only the ground (dotted) transverse states. The dashed lines is our perturbative result valid for small $E_d$. The dip at $q^2/E_d=0.5$ in the case $E_d=4$ is discussed in the text.