Measurement of an Efimov Trimer Binding Energy in a Three-Component Mixture of ${}^6\mathrm{Li}$

The binding energy of an Efimov trimer state was precisely determined via radio-frequency association. It is found that the measurement results shift significantly with temperature, but that the shift becomes negligible at the lowest temperature in our experiment. The shift-free part of the trimer binding energy reveals a significant deviation from the nonuniversal theory prediction based on a three-body parameter with a monotonic binding-energy dependence.

Figure 1

(a) Energy levels and transitions associated with the rf association of trimers. Transitions ($A$), ($B$), and ($C$) correspond to an association of Efimov trimer, the bare atomic transition between $|2⟩$ and $|3⟩$, and dissociation of $|12⟩$ dimers, respectively. (b) rf spectrum at 700 G. Dips ($A$), ($B$), and ($C$) show signals of the corresponding transitions in (a). Each data point represents the average over 3–5 measurements.

Figure 2

(a)–(c) Temperature dependence of the rf association spectrum at 705 G. The data were taken at (a) 1370(90) nK, (b) 554(37) nK, and (c) 86.5(4.2) nK. The position of Efimov association (vertical red line) shifts as temperature changes. (d) Temperature dependence of the peak difference at 695 G (red circles), 705 G (blue squares), and 715 G (green diamonds). The black dashed lines show $1.5k_{B}T$ dependence.

Figure 3

Magnetic-field dependence of the binding energy of the Efimov trimer. The blue dotted (green dashed) curve indicates calculated binding energy using constant three-body parameter ${\Lambda }_{685}$ (${\Lambda }_{895}$). The red solid curve is given by our previous nonuniversal theory with monotonic energy-dependent $\Lambda$ adjusted to match both resonances at 685 and 895 G [13, 15]. Measured binding energies are shown with black diamond whose error bars include the $1.5k_{B}T$ temperature shift and uncertainties of the calculated dimer binding energy (2 kHz) and fitting. The red point shows the position of the observed $|1⟩\mathrm{\text{−}}|23⟩$ atom-dimer loss peak [13, 14]. The solid curves labeled as $|12⟩$ and $|23⟩$ are the binding energies of $|12⟩$ and $|23⟩$ dimers, respectively. Insets (a) and (b) show the rf spectra at 700 and 735 G, respectively. The units of the insets are the same as those in Fig. 1b.

Figure 4

Energy dependence of the three-body parameter $\Lambda$ in units of inverse Bohr radius. The black open squares show $\Lambda$ previously determined from three-body loss [12] and atom-dimer loss [13]. The blue dotted line and the green dashed line show constant three-body parameters ${\Lambda }_{685}$ and ${\Lambda }_{895}$, respectively. The solid red curve indicates $\Lambda$ for our interpolated curve in Fig. 3. The black diamonds show the modified energy dependence of $\Lambda$ to reproduce the measured binding energy. Inset shows the magnetic-field dependence of $\Lambda$.