Possible Efimov Trimer State in a Three-Hyperfine-Component Lithium-6 Mixture

We consider the Efimov trimer theory as a possible framework to explain recently observed losses by inelastic three-body collisions in a three-hyperfine-component ultracold mixture of lithium 6. Within this framework, these losses would arise chiefly from the existence of an Efimov trimer bound state below the continuum of free triplets of atoms, and the loss maxima (at certain values of an applied magnetic field) would correspond to zero-energy resonances where the trimer dissociates into three free atoms. Our results show that such a trimer state is indeed possible given the two-body scattering lengths in the three-component lithium mixture and gives rise to two zero-energy resonances. The locations of these resonances appear to be consistent with observed losses.

Figure 1

Top panel: Variation of the two-body scattering lengths $a_{12}$, $a_{13}$, and $a_{23}$ for the lowest three hyperfine components of lithium 6 as a function of magnetic field. These curves were calculated by P. S. Julienne and taken from Ref. 12. Middle panel: Energy of the Efimov trimer (solid curve) just below the three-body threshold as a function of magnetic field with ${\Lambda }_0=(0.42a_0{)}^{-1}$. The shaded area corresponds to the width of the Efimov state, i.e., the imaginary part of its energy, for $\eta =0.115$. The estimated energy of possible resonant trimers from all other spin channels with the same total projection $m_F=-3/2$ is indicated by dashed curves. Bottom panel: Experimental (dots, taken from Ref. 12) and theoretical (curves) three-body inelastic collision loss rate coefficient as a function of magnetic field. The dashed curve is obtained by adjusting the short-range loss parameter $\eta$ to fit the experimental data ($\eta =0.157$), and the solid curve by adjusting it to fit the shape of the left peak ($\eta =0.115$).

Figure 2

Probability density $\rho (R)$—defined by Eq. (7)—of the lowest three-body scattering state for different values of the magnetic field. In all cases, the wave function $\Psi$ is normalized to be asymptotically equal to the noninteracting limit $8J_2(KR)/(KR{)}^2$, where $J_2$ is the Bessel function and $K$ is the wave number. This limit is indicated by the dashed curve. Here $K$ is set by the size of the numerical grid.