Emergent Inflation of the Efimov Spectrum under Three-Body Spin-Exchange Interactions

We resolve the unexpected and long-standing disagreement between experiment and theory in the Efimovian three-body spectrum of ${}^7\mathrm{Li}$, commonly referred to as the lithium few-body puzzle. Our results show that the discrepancy arises out of the presence of strong nonuniversal three-body spin-exchange interactions, which enact an effective inflation of the universal Efimov spectrum. This conclusion is obtained from a thorough numerical solution of the quantum mechanical three-body problem, including precise interatomic interactions and all spin degrees of freedom for three alkali-metal atoms. Our results show excellent agreement with the experimental data regarding both the Efimov spectrum and the absolute rate constants of three-body recombination, and in addition reveal a general product propensity for such triatomic reactions in the Paschen-Back regime, stemming from Wigner’s spin conservation rule.

Figure 1

Illustration of three-body recombination through two distinct spin-exchange pathways, where the color of particles represents their spin state and two connected particles represent a molecule. In the upper pathway one of the particles conserves its spin throughout the recombination. In the bottom pathway, all three particles partake in spin exchange such that no single spin is conserved. The pathway in which all particles preserve their initial spin is included in all calculations.

Figure 2

Results of our calculations, compared directly with the experimental data of Ref. [26]. Table (a) shows the three-body parameter $a_{-}$ and trimer width ${\eta }_{-}$ obtained using FSS and FMS models. The associated values of the three-body recombination rate coefficient $L_3$ as a function of the scattering length $a$ are shown in (b) and (c), for the two distinct incoming hyperfine states. The fits of $L_3$ to universal theory giving the results in table (a) are shown as dash-dotted lines in matching color. Insets show the two-body scattering length as a function of magnetic field, where the green shaded region matches the range of scattering lengths in the enclosing figure. We note that an additional independent measurement of the Efimov trimer in the $|1,1⟩$ state obtained $a_{-}/r_{\mathrm{vdW}}=-7.76(31)$ and ${\eta }_{-}=0.17$ [27].

Figure 3

Analysis of the electronic spin-propensity rule for three-body recombination. In (a) and (b) we show the components of the incoming two-body radial wave functions $r{\psi }_{\mathrm{in}}(r)$, highlighting the electronic spin components $|\downarrow \downarrow ⟩$ in green and $|\downarrow \uparrow ⟩$ in dash-dotted orange. The resonantly enhanced singlet $|\downarrow \uparrow ⟩$ components dominate the wave function at short distance. In (c) and (d) we show the averaged partial recombination rate ${\mathcal{L}}_3(M_S)$ to channels with total electronic projection $M_S$, with associated nuclear projection $M_I$. The fraction in blue(red) originates from atom-dimer states accessible by two-body(three-body) spin exchange.