Universal Trimers Induced by Spin-Orbit Coupling in Ultracold Fermi Gases

In this Letter we address the issue of how synthetic spin-orbit (SO) coupling can strongly affect three-body physics in ultracold atomic gases. We consider a system which consists of three fermionic atoms, including two spinless heavy atoms and one spin-$1/2$ light atom subjected to an isotropic SO coupling. We find that SO coupling can induce universal three-body bound states with a negative $s$-wave scattering length at a smaller mass ratio, where no trimer bound state can exist if in the absence of SO coupling. The energies of these trimers are independent of the high-energy cutoff, and therefore they are universal ones. Moreover, the resulting atom-dimer resonance can be effectively controlled by SO coupling strength. Our results can be applied to systems like a ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$ mixture.

Figure 1

Schematic of the atom-dimer threshold (green dashed line) and trimer energy in the presence of SO coupling for $6.5<M/m<8.17$ (a), $8.17<M/m<12.9$ (b), $12.9<M/m<13.6$ (c) and $13.6<M/m$ (d). Red solid line in (a)–(c) represents the universal trimer with lowest energy. Blue dashed-dotted line in (c) represents the second universal trimer, and yellow dotted lines in (d) represent Efimov trimers. This is a schematic plot in order to highlight main features. The actual numbers are shown in Fig. 2.

Figure 2

(a) The ratio between the $J=3/2$ trimer energy $E_3$ and atom-dimer threshold energy $|E_{\mathrm{th}}|$, $\gamma =E_3/|E_{\mathrm{th}}|$, as a function of $1/\lambda a$ for different mass ratios $M/m$ labeled in the curve. (b) The “phase diagram” for $J=3/2$ trimer in terms of $1/\lambda a$ and mass ratio $\mu =M/m$.

Figure 3

(a) Trimer energy (in unit of high energy cutoff ${\hslash }^2{\mathrm{\Lambda }}^2/M$) as a function of $\lambda /\mathrm{\Lambda }$ for a given mass ratio $M/m=12$. (b) The lowest trimer energy $E_3$ (in unit of atom-dimer threshold energy $|E_{\mathrm{th}}|$) as a function of mass ratio $\mu =M/m$ for two different high energy cutoff $\mathrm{\Lambda }$’s. Both are plotted at two-body resonance $a=\infty$.

Figure 4

The trimer binding energy $\mathrm{\Delta }{E}_3$ (in unit of atom-dimer threshold energy $|E_{\mathrm{th}}|$ with a given ${\lambda }_0$) as a function of interaction strength $1/{\lambda }_{0}a$ for a given mass ratio $M/m=12$. Dashed line represents the case without SO coupling $\lambda =0$ (sixfold degenerate). Two solid lines represent the cases for $J=3/2$ trimers (fourfold degenerate) and $J=1/2$ trimers (twofold degenerate), respectively, for a given SO coupling strength ${\lambda }_0$.