Three-Boson Problem near a Narrow Feshbach Resonance

We consider a three-boson system with resonant binary interactions and show that for sufficiently narrow resonances three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.

Figure 1

The ratio $a_{ad}/a$ versus $R^{*}/a$. The dashed curve is given by Eq. (14) and corresponds to the limit $a\ll R^{*}$. Dotted lines indicate the points $R^{*}/a\approx 2.2$ and $R^{*}/a\approx 0.07$, where the first and the second Efimov states emerge.

Figure 2

The ratio ${\alpha }_{\mathrm{r}\mathrm{e}\mathrm{c}}/a^4$ versus $R^{*}/a$. The dashed curve is given by Eq. (16). Arrows indicate values of $R^{*}/a$ at which ${\alpha }_{\mathrm{r}\mathrm{e}\mathrm{c}}$ vanishes. Scatter points correspond to experimental data taken near the 907 G Feshbach resonance in Na at MIT [1].