Ultracold Heteronuclear Three-Body Systems: How Diabaticity Limits the Universality of Recombination into Shallow Dimers

The mass-imbalanced three-body recombination process that forms a shallow dimer is shown to possess a rich Efimov-Stückelberg landscape, with corresponding spectra that differ fundamentally from the homonuclear case. A semianalytical treatment of the three-body recombination predicts unusual spectra with intertwined resonance peaks and minima and yields in-depth insight into the behavior of the corresponding Efimov spectra. In particular, the patterns of the Efimov-Stückelberg landscape are shown to depend inherently on the degree of diabaticity of the three-body collisions, which strongly affects the universality of the heteronuclear Efimov states.

Figure 1

(a) The two lowest hyperspherical potential curves $U_{\nu }^{1/3}(R/a_{\mathrm{HH}})$ (orange and blue solid curves) for a HHL system with mass ratio $m_{\mathrm{H}}/m_{\mathrm{L}}=22.1$, $a_{\mathrm{HL}}<0$, $a_{\mathrm{HH}}>0$, and the total energy $\overline{E}$ in units of ${\hslash }^2/m_{\mathrm{H}}{a}_{\mathrm{HH}}^2$ is indicated as a black dotted line. The blue hatched area indicates the 3BP at $R=r_{3\mathrm{b}}$, whereas the gray region depicts the maximum of the $P$-matrix. The green dash-dotted and purple dashed lines denote the dominant two interfering pathways. (b) An illustration of the terms associated with the semiclassical treatment and their connections to the curves shown in (a).

Figure 2

The scaled 3BR coefficient $m_{\mathrm{Cs}}{K}_3/\hslash a_{\text{LiCs}}^4$ at low energy $\overline{E}$ (in units of ${\hslash }^2/m_{\mathrm{H}}{a}_{\mathrm{HH}}^2$) for the ${}^6\mathrm{Li}─{}^{133}\mathrm{Cs}─{}^{133}\mathrm{Cs}$ system as a function of two ratios: the 3BP $r_{3\mathrm{b}}/a_{\text{CsCs}}$ and the interspecies scattering length $|a_{\text{LiCs}}|/a_{\text{CsCs}}$. Panels (b) and (c) show the scaled 3BR calculations within the semiclassical treatment and the $R$-matrix numerical simulations, respectively. Panel (d) depicts the probability $p$ versus $|a_{\text{LiCs}}|/a_{\text{CsCs}}$.

Figure 3

The scaled 3BR $m_{\mathrm{Cs}}{K}_3/\hslash a_{\text{LiCs}}^4$ at $\overline{E}\to 0$ for ${}^6\mathrm{Li}─{}^{133}\mathrm{Cs}─{}^{133}\mathrm{Cs}$ using Eq. (4). Panels (a)–(c) correspond to different nonadiabatic probabilities, namely, $p=(0.8,0.4,0.1)$, respectively. Panels (d) and (e) present schematic illustrations of the diabatic and adiabatic hyperspherical potentials, respectively. The magenta dash-dotted line indicates the quasibound Efimov state, and the gray box depicts the 3BP.