Magnetic-field dependence and Efimov resonance broadening in ultracold three-body recombination

We derive an analytic formula which describes the final bound state dependence in ultracold three-body recombination. Using an energy-dependent loss parameter, the recently observed broad resonance in an ultracold gas of ${}^6\mathrm{Li}$ atoms [T. B. Ottenstein, T. Lompe, M. Kohnen, A. N. Wenz, and S. Jochim, Phys. Rev. Lett. 101, 203202 (2008); J. H. Huckans, J. R. Williams, E. L. Hazlett, R. W. Stites, and K. M. O’Hara, Phys. Rev. Lett. 102, 165302 (2009)] is described quantitatively. We also provide an analytic and approximation for the three-body recombination rate which encapsulates the underlying physics of the universal three-body recombination process.

Figure 1

(a) The three s-wave scattering lengths for ${}^6\mathrm{Li}$ are shown in atomic units as a function of magnetic field. (b) The four smallest dimer binding energies from Ref. [20] are shown in atomic units as a function of magnetic field. The total nuclear angular momentum and projection are given, but are unimportant for the results in this work.

Figure 2

A schematic illustration of the two-channel scattering process that controls threshold three-body recombination is shown.

Figure 3

The recombination rate constant predicted from Eq. (2) is shown for fixed $\eta$ (dashed curve) and for energy dependent $\eta$ (solid curve) as a function of magnetic field compared to experimental data from Ref. [15] [(red) circles] and Ref. [16] [(blue) squares].

Figure 4

The numerically calculated recombination rate constant from Fig. 3 (solid curve) compared to the analytic approximation from Eq. (13) is shown (dot-dashed curve) as a function of magnetic field strength.