Recombination of Three Ultracold Fermionic Atoms

Three-body recombination of identical, spin-polarized fermionic atoms in the ultracold limit is investigated using model interactions. The mechanisms for recombination are parametrized by the “scattering volume” $V_p$ and described in the framework of the adiabatic hyperspherical representation. We have calculated the recombination rate $K_3$ as a function of $V_p$ and have found $K_3\propto |V_p{|}^{8/3}$ for small $|V_p|$. Recombination near a two-body Feshbach resonance can thus be significant.

Figure 1

The lowest 12 adiabatic hyperspherical potential curves for three spin-polarized fermions with $V_p=-1.25\times {10}^5{\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}}^3$ using the ${\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{h}}^2$ potential with $r_0=15\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ The inset shows the potential barrier in the three-body entrance channel, which plays a crucial role in the recombination process.

Figure 2

The recombination rate $K_3$ as a function of $V_p$ for $v_{\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{h}}$ (no symbols) and $v_{\mathrm{v}\mathrm{d}\mathrm{W}}$ (diamonds) from Eq. (2) with $r_0=15\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ The solid lines correspond to the thermally averaged rate at $T=2\mu \mathrm{K}$ and the dashed lines to the energy-dependent rate at $E=2\mu \mathrm{K}$. The inset focuses on the region with small $|V_p|$ showing a Stückelberg oscillation.

Figure 3

The theoretical rates for each molecular orbital angular momenta $m_L$ (dashed lines), the total rate obtained from their weighted average (solid line), and the experimental rate [17] (filled circles) are plotted as functions of the magnetic field strength $B$. Note that $r_0=60\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ was used to give the best fit.