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arXiv:1005.5306 · Physical Review A

Feshbach resonances of harmonically trapped atoms

Philipp‐Immanuel Schneider, Yulian V. Vanne, Alejandro Sáenz

Published Mar 4, 2011• 8 citations
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Abstract

Employing a short-range two-channel description, we derive an analytic model of atoms in isotropic and anisotropic harmonic traps at a Feshbach resonance. On this basis we obtain a parametrization of the energy-dependent scattering length that differs from the one previously employed. We validate the model by comparison to full numerical calculations for $^{6}\mathrm{Li}$-$^{87}\mathrm{Rb}$ and explain quantitatively the experimental observation of a resonance shift and trap-induced molecules in exited bands. Finally, we analyze the bound state admixture and Landau-Zener transition probabilities.

DOI
10.1103/physreva.83.030701

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Bound states and collisions of atoms with two-channel two-body interactions in harmonic waveguides are analyzed. The closed-channel contributions to two-atom bound states become dominant in the case of a weak resonance. At low energies and values of the nonresonant scattering length the problem can be approximated by a one-dimensional resonant model. The three-body problem becomes nonintegrable and the properties of triatomic molecules become different from those predicted by the integrable Lieb-Liniger-McGuire model.
A zero-range approach to atom-molecule coupling is developed in analogy to the Fermi-Huang pseudopotential approach to collisions. It is shown by explicit comparison to an exactly solvable finite-range model that replacing the molecular bound-state wave function with a regularized delta function can reproduce the exact scattering amplitude in the long-wavelength limit. Using this approach, we find an analytical solution to the two-channel Feshbach resonance problem for two atoms in a spherical harmonic trap, highlighting the strong dependence of the effective scattering length and bare-molecule population on the atom-molecule coupling strength.