Universal trimer in a three-component Fermi gas

We show that the recently measured magnetic field dependence of three-body loss in a three-component mixture of ultracold ${}^6\text{L}\text{i}$ atoms [T. B. Ottenstein et al., Phys. Rev. Lett. 101, 203202 (2008); J. H. Huckans et al., Phys. Rev. Lett. 102, 165302 (2009)] can be explained by the presence of a universal trimer state. Previous work suggested a universal trimer state as a probable explanation, yet it failed to get good agreement between theory and experiment over the whole range of magnetic fields. For our description we adapt the theory of Braaten and Hammer [Phys. Rep. 428, 259 (2006)] for three identical bosons to the case of three distinguishable fermions by combining the three scattering lengths $a_{12}$, $a_{23}$, and $a_{13}$ between the three components to an effective interaction parameter $a_m$. We show that taking into account a magnetic field variation in the lifetime of the trimer state is essential to obtain a complete understanding of the observed decay rates.

Figure 1

(Color online) A sketch of possible three-body processes in a system of three distinguishable fermions. In the case of three large scattering lengths, three different mediated processes have to be taken into account to describe the three-body interaction [see (a) and Eq. (3)]. If one scattering length is significantly smaller than the other two, three-body processes are still possible but there is only one leading contribution [see (b)]. If two scattering lengths are small compared to the third one [see (c)], three-body processes are suppressed compared to the situations described in (a) and (b).

Figure 2

(Color online) (a) Magnetic field dependence of the two-body $s$-wave scattering lengths for different channels in units of Bohr’s radius $a_0$ [20]. (b) The solid line depicts the mean scattering length (dashed line, if one or more of the $a_{ij}>0$). For comparison, the range of the interactions $\left(r_0\approx 60a_0\right)$ is also displayed as a dotted line. (c) Binding energies of the bound dimer states responsible for the Feshbach resonances at 543, 691, 811, and 834 G [21].

Figure 3

(Color online) Measured three-body loss coefficient (black squares) and different models as a function of the magnetic field. The dashed line shows the prediction for three-body loss without resonant enhancement due to trimer states, the short dashed line gives the theoretical result for $K_{3,\text{deep}}\left(a_m\right)$, and the solid line is the model for $K_3$ including a magnetic field dependence of ${\eta }_{\ast }$.