Universal Four-Boson States in Ultracold Molecular Gases: Resonant Effects in Dimer-Dimer Collisions

We study the manifestations of universal four-body physics in ultracold dimer-dimer collisions. We show that resonant features associated with three-body Efimov physics and dimer-dimer scattering lengths are universally related. The emergence of universal four-boson states allows for the tunability of the dimer-dimer interaction, thus enabling the future study of ultracold molecular gases with both attractive and repulsive interactions. Moreover, our study of the interconversion between dimers and Efimov trimers shows that $B_2+B_2\to B_3+B$ rearrangement reactions can provide an efficient trimer formation mechanism. Our analysis of the temperature dependence of this reaction provides an interpretation of the available experimental data and sheds light on the possible experimental realization of rearrangement processes in ultracold gases.

Figure 1

(a) Spectrum of the four-boson system from our numerical calculations [6] and (b) a schematic representation of the region important for dimer-dimer collisions (see text). The four-boson states are represented by the less steep (black) solid lines, while the collision thresholds are represented by the steeper (red) solid lines for the atom-atom-dimer and dimer-dimer collisions, and by green-dashed lines for atom-trimer collisions.

Figure 2

(a) Resonant enhancement in the dimer-dimer scattering length $a_{dd}$ [13], plotted as a function of $a$, reflecting the emergence of an universal (broader) four-boson resonance at $a=a_{dd,1}^{*}$ and a (narrower) resonance at $a_{dd,2}^{*}$ [see Fig. 1b]. These resonances allow for the control of the dimer-dimer interactions. (b) The thermally averaged $V_{\mathrm{rel}}^{dd}$ and resonant behavior associated with the four-boson states leading to relaxation into deeply bound states. For $a>a_{dd}^c$, however, $V_{\mathrm{rel}}^{dd}$ is dominated by $B_2+B_2\to B_3+B$ rearrangement collisions. Our results were rescaled to the Cs problem (see text).

Figure 3

Comparison between experimental data [10] (filled circles: $a=800$ a.u.; open circle: $a=500$ a.u.) and our model [Eq. (4)] for the temperature dependence of $V_{\mathrm{rel}}^{dd}$. In our model, the apparent deviation from the Wigner threshold law is caused by the presence of a trimer state just above the dimer-dimer threshold, as indicated by the vertical lines. Inset: Comparison of our model (black-solid line) with numerical rates (the red-solid line is our total rate as a function of $E_{\mathrm{col}}$, and the green-dashed line shows the thermally averaged results as a function of $T$).