Three-body loss in lithium from functional renormalization

We use functional-integral methods for an estimate of the three-body loss in a three-component ${}^6\text{L}\text{i}$ ultracold atom gas. We advocate a simple picture where the loss proceeds by the formation of a three-atom bound trimer state, the trion. In turn, the effective amplitude for the trion formation from three atoms is estimated from a simple effective boson exchange process. The energy gap of the trion and other key quantities for the loss coefficient are computed in a functional renormalization-group framework.

Figure 1

Three-body loss process involving the trion.

Figure 2

Interaction between atoms $\psi$ and effective bosons $\varphi$ as mediated by the trion field $\chi$.

Figure 3

(Color online) Upper panel: scattering length $a_{12}$ (solid), $a_{23}$ (dashed), and $a_{31}$ (dotted) as a function of the magnetic field $B$ for ${}^6\text{L}\text{i}$. These curves were calculated by Bartenstein et al. [13] and taken from Ref. [8]. Lower panel: binding energy $E_T$ of the three-body bound state $\chi \stackrel{\wedge}{=}{\psi }_1{\psi }_2{\psi }_3$. The solid line shows the result without the inclusion of box diagrams contributing to the atom-boson interaction and it corresponds to the initial value $h^2=100a_0^{-1}$, while the shaded region gives the result in the range $h^2=20a_0^{-1}$ (upper border) to $h^2=300a_0^{-1}$ (lower border). The dashed line corresponds to the calculated binding energy $E_T$ when the refermionization of the atom-boson interaction is taken into account.

Figure 4

(Color online) Loss coefficient $K_3$ in dependence on the magnetic field $B$ as measured in [8] (dots). The solid line is the fit of our model to the experimental curve. We use here a decay width ${\Gamma }_{\chi }$ that is independent of the magnetic field $B$.