Efimov states near a Feshbach resonance

We describe three-body collisions close to a Feshbach resonance by taking into account two-body scattering processes involving both the open and the closed channels. We extract the atom-dimer scattering length and the three-body recombination rate, predicting the existence at negative scattering length of a sharp minimum in the recombination losses due to the presence of a shallow bound level. We obtain very good agreement with the experimental results in atomic ${}^{133}\mathrm{Cs}$ of Kraemer et al. [Nature (London) 440, 315 (2006)], and predict the position of Efimov resonances in a gas of ${}^{39}\mathrm{K}$ atoms.

Figure 1

(Color online) Two- and three-body energy levels as a function of magnetic field for ${}^{133}\mathrm{Cs}$. In order to visualize the Efimov states, both axes display highly nonlinear scales, obtained by plotting ${(B-B_0)}^{1∕5}$ and $E^{1∕10}$. The cross shows the position of the recombination resonance observed in Ref. 3.

Figure 2

Diagrams describing (a) atom-dimer scattering and (b) recombination of three atoms into an atom and a dimer.

Figure 3

(Color online) Three-body recombination length ${\rho }_3$ for ${}^{133}\mathrm{Cs}$: the curves represent our thermally averaged results, while the symbols are the experimental points of Ref. 3 at 10 (+), 200 (×), and $250\mathrm{nK}$ (◻).

Figure 4

(Color online) Recombination length ${\rho }_3∕a$ at $T=0$ for ${}^{39}\mathrm{K}$ at negative detunings. The UT fit (with decay parameter $\eta =0$ [2]) stops at $B-B_0=-52\mathrm{G}$, where $a$ vanishes and changes sign. Inset: ${\rho }_3∕a$ for positive detunings (UT fit with $a_{*}^{\prime }$ given by our model and $\eta =0.06$).

Figure 5

(Color online) Real part of the atom-dimer scattering length: + (−) refers to collisions with the dimer of binding energy $E_b^{+}$ $\left(E_b^{-}\right)$. The shaded region at $B\lesssim B_0$ contains a large number of resonances of $a_{\mathrm{AD}}^{+}$, each in correspondence with the appearance of a new Efimov state. The scales on the axes are obtained by plotting ${(B-B_0)}^{1∕5}$ and $a_{\mathrm{AD}}^{1∕5}$.