Formation and properties of cold quasi-one-dimensional molecules with Feshbach resonance interaction

Bound states of cold atoms with two-channel two-body interactions in harmonic waveguides are analyzed. The two-atom problem can be approximated by a one-dimensional model at low energies and small values of the non-resonant scattering length [1,2]. In the case of a strong resonance, two-atom bound states contain mostly the contributions of the open channel. The closed channel contribution becomes dominant in weak resonances, such as the 543 G resonance in $^{6}$Li. The results are applicable both to bosonic and fermionic atoms. The formation of molecules by three-body association of indistinguishable bosonic atoms becomes allowed thanks to the non-integrability of the resonant one-dimensional three-body problem. This problem is analyzed by a numerical solution of the Faddeev-Lovelace equations [3]. A large value of the association rate coefficient of more then $10^{-4} \mathrm{cm}^2/\mathrm{s}$ is predicted in the vicinity of the weak Feshbach resonance in Na. The rate vanishes at large detunings, since the integrability is restored, and both at zero and at high collision energies. 1. V. A. Yurovsky, Phys. Rev. A {\bf 71}, 012709 (2005). 2. V. A. Yurovsky, physics/0601073. 3. V. A. Yurovsky, A. Ben-Reuven, and M. Olshanii, physics/0512033.