Resonant two-cluster scattering in a quasi-one-dimensional Bose gas

Abstract

We investigate two-cluster scattering in a quasi-one-dimensional Bose gas. We focus on the effective three-body interaction induced by transverse confinement, which is the leading term for breaking integrability in the quasi-one-dimensional setting. Exploiting the Lüscher formula and the integrability of the Lieb-Liniger Bose gas, we find a finite and positive scattering length for elastic two-cluster scattering. The resulting scattering lengths indicate the emergence of a resonance.

Figures (1)

• Figure 1: Heat map of the even-channel scattering length in the dimensionless and coupling-free form, $m u a_+/a$, as a function of the cluster sizes. The sizes of the first and second clusters are denoted by $\alpha_1$ and $\alpha_2$, respectively, while the value of $m u a_+/a$ is represented by the color scale. Since the even-channel scattering length is invariant under exchanging the cluster sizes, we show the heat map only for $\alpha_2 > \alpha_1$. Throughout this figure, we set $m = 1/2$ and $c = -2$, where the scattering length for the original two-body attraction becomes $a = 1$.