Universality in bosonic dimer-dimer scattering

Bosonic dimer-dimer scattering is studied near the unitary limit using momentum-space equations for the four-particle transition operators. The impact of the Efimov effect on the dimer-dimer scattering observables is explored, and a number of universal relations is established with high accuracy. The rate for the creation of Efimov trimers via dimer-dimer collisions is calculated.

Figure 1

Schematic representation of the four-boson energy spectrum; only one family ($n$) of multimers is shown. The tetramer (T) energies, atom-trimer (a $+$ t), dimer-dimer (d $+$ d), and dimer-atom-atom (d $+$ a $+$ a) thresholds are displayed as solid, dashed, dashed-dotted, and dotted lines, respectively. They intersect at special values of $a$ described in the text. For a better visualization only qualitative relations are preserved.

Figure 2

Real and imaginary parts of the dimer-dimer scattering length as functions of the atom-atom scattering length. In the left inset $\mathit{Re}{A}_{dd}/a$ (solid curve) and $\mathit{Im}{A}_{dd}/a$ (dotted curve) are shown in the vicinity of the $(n,1)$ tetramer using linear scale. In the right inset $\mathit{Im}{A}_{dd}/a$ is shown in the vicinity of the dimer-dimer and atom-trimer threshold intersection.

Figure 3

Real and imaginary parts of the dimer-dimer effective range parameter as functions of the atom-atom scattering length. In the inset $\mathit{Re}{r}_{dd}/a$ (dash-dotted curve) and $\mathit{Im}{r}_{dd}/a$ (dotted curve) are shown in the vicinity of $\mathit{Re}{A}_{dd}=0$ using linear scale.

Figure 4

Energy dependence of the $S$- and $D$-wave phase shifts and inelasticity parameters for the dimer-dimer scattering at specified values of the atom-atom scattering length. For a better comparison we set $\mathit{Re}{\delta }_L=0$ at $E_{dd}=0$.

Figure 5

Elastic and transfer cross sections for the dimer-dimer scattering at specified values of the atom-atom scattering length.

Figure 6

Temperature dependence of the trimer creation rate at specified values of the atom-atom scattering length; $a/a_n^{dd}=0.3235$ corresponds to the $(n,1)$ resonance that leads to a peak of ${\beta }_{dd}$ at $T=0$.