Efimov Trimer Formation via Ultracold Four-Body Recombination

We discuss the collisional formation of Efimov trimers via ultracold four-body recombination. In particular, we consider the reaction $A+A+A+B\to A_3+B$ with $A$ and $B$ ultracold atoms. We obtain expressions for the four-body recombination rate up to an overall constant and show that it reflects the three-body Efimov physics either as a function of collision energy or as a function of the two-body $s$-wave scattering length between $A$ atoms. In addition, we briefly discuss issues important for experimentally observing this interesting and unexplored process.

Figure 1

The lowest four-body adiabatic hyperspherical potentials $W_{\nu }$ multiplied by $2{\mu }_4{R}_4^2$ to better show their behavior. Black solid lines denote atom-trimer potentials for $\beta =0$ and $n=1$, 2, 3, 4; blue dashed lines, four-body continuum potentials for $\beta =1$ ($s_1=4.465$) and $m=0$, 1, 2; and the red dotted line, the four-body continuum potential with $\beta =2$ ($s_2=6.818$) and $m=0$. We take $R_0=10\mathrm{a}.\mathrm{u}.$ for all curves.

Figure 2

The recombination probability for several transitions ($s_{\beta }$, $m$) labels the initial continuum channel and $n$ labels the final state of the Efimov trimer. The probabilities must be multiplied by the factors indicated. We have taken $R_0=10\mathrm{a}.\mathrm{u}.$ and $a_{AB}=100\mathrm{a}.\mathrm{u}.$.