Efimov Physics in Heteronuclear Four-Body Systems

We study three- and four-body Efimov physics in a heteronuclear atomic system with three identical heavy bosonic atoms and one light atom. We show that exchange of the light atom between the heavy atoms leads to both three- and four-body features in the low-energy inelastic rate constants that trace to the Efimov effect. Further, the effective interaction generated by this exchange can provide an additional mechanism for control in ultracold experiments. Finally, we find that there is no true four-body Efimov effect—that is, no infinite number of four-body states in the absence of two- and three-body bound states—resolving a decades-long controversy.

Figure 1

Schematic energy spectrum for $H_{3}L$. Solid lines denote bound states and dashed lines denote resonances.

Figure 2

$K_3$ for $HL+H+H\to H_{2}L+H$ when $M/m=30$. The main peaks in (c) reflect the Efimov physics of $H_{2}L$ and occur where (d) $a_{HH}^{*}$ diverges. The expanded plots (a) and (b) highlight the features on each main peak related to $H_{3}L$ states. The vertical dashed lines indicate where $a_{HH}^{*}=\infty$.

Figure 3

$K_3$ for $HL+H+H\to H_{2}L+H$ with $M/m=50$ simultaneously showing the dependence on $a_{HL}$ and on $a_{HH}^{*}$. The $H_{2}L$ Efimov physics is highlighted by the $a_{HL}-K_3$ projection while the $a_{HH}^{*}-K_3$ projection illustrates the $(HL)H_2$ Efimov physics.

Figure 4

$V_{\mathrm{rel}}$ for $H_{2}L(n)+H\to H_{2}L(n-1)+H$ for (a) $n=1$ and (b) $n=2$. The dashed lines indicate the positions where $|a_{HH}^{*}|=\infty$.