Universal three-body parameter in ultracold ${}^4$He${}^{*}$

We have analyzed our recently measured three-body loss rate coefficient for a Bose-Einstein condensate of spin-polarized metastable triplet ${}^4$He atoms in terms of Efimov physics. The large value of the scattering length for these atoms, which provides access to the Efimov regime, arises from a nearby potential resonance. We find the loss coefficient to be consistent with the three-body parameter (3BP) found in alkali-metal experiments, where Feshbach resonances are used to tune the interaction. This provides evidence for a universal 3BP outside the group of alkali-metal elements. In addition, we give examples of other atomic systems without Feshbach resonances but with a large scattering length that would be interesting to analyze once precise measurements of three-body loss are available.

Figure 1

Universal three-body loss curves [Eq. (2)] for ${}^4$He${}^{*}$ with $|a_{-}|/r_{\mathrm{vdW}}=2.3$ (dashed lines) and $|a_{-}|/r_{\mathrm{vdW}}=7.7$ (solid lines), for different values of $\eta$, that match our measured $L_3$ value (see inset).

Figure 2

Graphic representation of the set of $|a_{-}|/r_{\mathrm{vdW}}$ and $\eta$ values for which Eq. (2) matches our observed value of $L_3$, given by the black solid line, where the gray band corresponds to possible values based on our $L_3$ error bar. Also indicated are the $|a_{-}|/r_{\mathrm{vdW}}$ values for the alkali-metal experiments: Cs, 8.6(2),10.2(6),9.5(8),9.5(3) [11] (red diamonds), ${}^7$Li 8.1(3) [5], 9.2(3) [6], 8.3(4) [7] (blue squares), ${}^6$Li 9.3 [30] (green circle), ${}^{85}$Rb 9.23(7) [9] (orange triangle), showing at the same time the observed $\eta$ parameters.