Observation of the Second Triatomic Resonance in Efimov’s Scenario

We report the observation of a three-body recombination resonance in an ultracold gas of cesium atoms at a very large negative value of the $s$-wave scattering length. The resonance is identified as the second triatomic Efimov resonance, which corresponds to the situation where the first excited Efimov state appears at the threshold of three free atoms. This observation, together with a finite-temperature analysis and the known first resonance, allows the most accurate demonstration to date of the discrete scaling behavior at the heart of Efimov physics. For the system of three identical bosons, we obtain a scaling factor of 21.0(1.3), close to the ideal value of 22.7.

Figure 1

Observation of the second triatomic Efimov resonance. In (a) we show the effective three-body loss coefficient $L_3$ as a function of the inverse scattering length. Blue squares and red circles are two sets of measurements taken with slightly different trap settings. The error bars include statistical uncertainties from numerical fitting. The black solid line is the theoretical calculation of $L_3$ (based on the parameters of the first Efimov resonance) at 8.65 nK (average temperature of two sets) while the gray-shaded region corresponds to the temperature range between 7.7 and 9.6 nK (see text). The vertical dashed line indicates the position where the resonance would be expected in the zero-temperature limit based on the previously investigated first Efimov resonance [21] and Efimov’s scaling factor. In (b), the fitted loss index $\alpha$ shows a larger deviation from a value of 3 in the regions (gray-shaded) away from the second Efimov resonance (white region, where $\alpha <3.5$), indicating contributions from higher-order recombination processes.

Figure 2

Fits to the second Efimov resonance. The two sets of points represent the same sets of results as in Fig. 1, but limited to the resonance region and with one clear outlyer removed. In addition, the absolute scaling for $L_3$ is changed as we here use the fit values (see text) for the temperature, 8.7 nK for set $A$ and 10.0 nK for set $B$, to calculate the volume $V$. The vertical dashed line is the same as in Fig. 1. The fits to sets $A$ and $B$ are plotted as blue dashed and red dotted lines, respectively.