Three-body parameter for Efimov states in ${}^6\mathrm{Li}$

We present a state-of-the-art reanalysis of experimental results on Efimov resonances in the three-fermion system of ${}^6\mathrm{Li}$. We discuss different definitions of the three-body parameter (3BP) for Efimov states and adopt a definition that excludes effects due to deviations from universal scaling for low-lying states. We develop a finite-temperature model for the case of three distinguishable fermions and apply it to the excited-state Efimov resonance to obtain the most accurate determination to date of the 3BP in an atomic three-body system. Our analysis of ground-state Efimov resonances in the same system yields values for the three-body parameter that are consistent with the excited-state result. Recent work has suggested that the reduced 3BP for atomic systems is a near-universal quantity, almost independent of the particular atom involved. However, the value of the 3BP obtained for ${}^6\mathrm{Li}$ is significantly $(\sim 20\%)$ different from that previously obtained from the excited-state resonance in Cs. The difference between these values poses a challenge for theory.

Figure 1

Finite-temperature fits to the excited-state Efimov resonance. The experimental results obtained for $L_3$ in Ref. [16] for two different temperatures are plotted as blue squares (set A, 30 nK) and red circles (set B, 180 nK). The amplitude scaling factor $\lambda$ is of the order of 1, see the text. The corresponding solid lines are the fixed-temperature fits to both data sets, carried out on a linear scale (see first and fifth rows in Table 1). The black dashed curve is calculated for the zero-temperature limit using the parameters from the fixed-temperature fit to the 30 nK set.

Figure 2

Fitted values for ${\kappa }_{*}$ corresponding to the third column in Table 1. The dashed line indicates the final result ${\kappa }_{*}=0.00678\left(6\right)a_0^{-1}$, as obtained from a weighted average of the four data points of the low-temperature data set (set A; blue squares), and the gray-shaded region shows the corresponding uncertainty. The high-temperature data set (set B; red circles) is not used to derive the final value, but within the uncertainties the values are fully consistent with the result from data set A.

Figure 3

Fits to the ground-state Efimov resonances. All three panels show the same experimental data on the loss rate coefficient $L_3$ from Ref. [14], where the squares, circles, and triangles refer to losses measured in the lowest three spin states. The theoretical curves represent our fits to the data on a linear scale. The solid lines indicate the region used for the fit in which all three scattering lengths are larger than the cutoff value $a_{\min }$. The dashed lines extrapolate the theory to regions not used for the fit.

Figure 4

Dependence of the fitted values for ${\kappa }_{*}$ on the cutoff scattering length $a_{\min }$ for the ground-state Efimov resonance. The blue squares and red circles refer to fits performed with linear and logarithmic $L_3$ scales, respectively. The error bars represent the $1\sigma$ uncertainties from the individual fits. The horizontal dashed line marks the value of ${\kappa }_{*}$ obtained from the excited-state Efimov resonance. The gray-shaded region marks the corresponding error range.