Effective range from tetramer-dissociation data for cesium atoms

The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated with effective range corrections. The effective range correction is extracted with a weighted average given by $3.9\pm 0.8R_{\mathrm{vdW}}$, where $R_{\mathrm{vdW}}$ is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs${}_2$ system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position.

Figure 1

The scaling function $\mathcal{A}$ expressing the dependence of $a_{1,2}^T/a_1^{-}$ in $a_{1,1}^T/a_1^{-}$ and $r_0/a_1^{-}$. Calculations are performed in a leading-order expansion of the solutions of the FY equations with the two-body amplitude (1). (See text for further explanation.)

Figure 2

Lower-order effective range correction for the scaling plot $a_{1,2}^T/a_1^{-}=\mathcal{A}(a_{1,1}^T/a_1^{-},r_0/a_1^{-})$ for the correlation between the positions of the peaks for successive tetramer resonances at the continuum threshold, compared to other theoretical results and experimental data. We present our results for different $r_0$ intervals (the upper solid line is from [11]) compared to a few recent calculations as indicated inside the frame [Refs. [13] (triangles), [16] (diamonds), and [30] (square)]. The experimental data of Refs. [6, 8, 9] are also indicated inside the figure. The lowest band (gray) corresponds to $r_0$ for the van der Waals–like potential for cesium atoms with values within the interval $0.4\lesssim -r_0/a_1^{-}\lesssim 0.5$ for a reference value of $a_1^{-}\simeq -9R_{\mathrm{vdW}}$ (see Table ).