Confinement-induced Efimov resonances in Fermi-Fermi mixtures

A Fermi-Fermi mixture of ${}^{40}\text{K}$ and ${}^6\text{L}\text{i}$ does not exhibit the Efimov effect in a free space, but the Efimov effect can be induced by confining only ${}^{40}\text{K}$ in one dimension. Here the Efimov’s three-body parameter is controlled by the confinement length. We show that the three-body recombination rate in such a system in the dilute limit has a characteristic logarithmic-periodic dependence on the effective scattering length with the scaling factor 22.0 and can be expressed by formulas similar to those for identical bosons in three dimensions. The ultracold mixture of ${}^{40}\text{K}$ and ${}^6\text{L}\text{i}$ in the one-dimensional–three-dimensional mixed dimensions is thus a promising candidate to observe the Efimov physics in fermions.

Figure 1

Two-body scattering of $A$ (solid line) and $B$ (dotted line) atoms. The double line represents the scattering amplitude $i{\mathcal{A}}_2$.

Figure 2

Three-body scattering of two $A$ and one $B$ atoms.

Figure 3

(Color online) Two periods of $\frac{m_A}{{\overline{p}}_z^2{a}_{\text{eff}}^4}\alpha$ as a function of $a_{\text{eff}}{\kappa }_{\ast }>0$ at ${\eta }_{\ast }=0$, 0.1, and 0.5 for $m_A/m_B=6.67$. Curves behind data points are from the two-parameter fit by Eq. (9).

Figure 4

(Color online) Two periods of $\frac{m_A}{{\overline{p}}_z^2{a}_{\text{eff}}^4}\alpha$ as a function of $a_{\text{eff}}{\kappa }_{\ast }<0$ at ${\eta }_{\ast }=0.01$, 0.1, and 0.5 for $m_A/m_B=6.67$. Curves behind data points are from the two-parameter fit by Eq. (10).