Test of the Universality of the Three-Body Efimov Parameter at Narrow Feshbach Resonances

We measure the critical scattering length for the appearance of the first three-body bound state, or Efimov three-body parameter, at seven different Feshbach resonances in ultracold ${}^{39}\mathrm{K}$ atoms. We study both intermediate and narrow resonances, where the three-body spectrum is expected to be determined by the nonuniversal coupling of two scattering channels. Instead, our observed ratio of the three-body parameter with the van der Waals radius is approximately the same universal ratio as for broader resonances. This unexpected observation suggests the presence of a new regime for three-body scattering at narrow resonances.

Figure 1

Example of the time evolution of the atom number (circles) and temperature (triangles), fitted to Eq. (1) (solid line) and Eq. (2) (dashed line) to determine the three-body loss coefficient $K_3$.

Figure 2

Three-body loss rate measured in the proximity of five Feshbach resonances of intermediate strength (see Table  for the assignment of the spin state). The experimental data (squares) are fitted to Eq. (3) (solid line).

Figure 3

Three-body loss rate measured in the proximity of two narrow Feshbach resonances in the $m_F=0$ state. The experimental data (squares) are fitted with a Gaussian (dashed line) to determine $a_{-}$ from the position of the loss maximum, and also compared with Eq. (3), using ${\eta }_{-}=0.1$ (solid line). The dash-dotted lines provide a comparison to a $|a{|}^{7/2}$ behavior for low $|a|$.

Figure 4

Ratio of the measured $|a_{-}|$ to $R_{\mathrm{vdW}}$ as a function of the strength of the Feshbach resonances (filled circles). Our data are compared to predictions for $s_{\mathrm{res}}\gg 1$ [21] (open diamond) and for generic $s_{\mathrm{res}}$ [26] (solid line). The gray shaded region shows the scatter in the experimental data for $|a_{-}|/R_{\mathrm{vdW}}$ measured in other atomic species.