Effective-range approximations for resonant scattering of cold atoms

Abstract

Studies of cold atom collisions and few-body interactions often require the energy dependence of the scattering phase shift, which is usually expressed in terms of an effective-range expansion. We use accurate coupled-channel calculations on ${}^6$Li, ${}^{39}$K and ${}^{133}$Cs to explore the behavior of the effective range in the vicinity of both broad and narrow Feshbach resonances. We show that commonly used expressions for the effective range break down dramatically for narrow resonances and near the zero-crossings of broad resonances. We present an alternative parametrization of the effective range that is accurate through both the pole and the zero-crossing for both broad and narrow resonances. However, the effective range expansion can still fail at quite low collision energies, particularly around narrow resonances. We demonstrate that an analytical form of an energy and magnetic field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length.

Corrected a plotting error in Fig. 2(a). and clarified corresponding text. Now matches published version. 12 pages, 7 figures

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Cited by in corpus (26)

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• Pinpointing Feshbach Resonances and Testing Efimov Universalities in ${}^{39}$K
• Tailored single-atom collisions at ultra-low energies
• The three-body parameter for Efimov states in lithium-6
• Cold Atom Quantum Simulator for Dilute Neutron Matter
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• A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions
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• Mott-Insulator-Aided Detection of Ultra-Narrow Feshbach Resonances
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• The effects of trap-confinement and interatomic interactions on Josephson effects and macroscopic quantum self-trapping for a Bose-Einstein Condensate
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• Supersymmetric inversion of effective-range expansions
• Bound and scattering states in harmonic waveguides in the vicinity of free space Feshbach resonances
• Finite-range model potentials for resonant interactions
• Modeling atom-atom interactions at low energy by Jost-Kohn potentials
• Effective field theory of bosons with finite-range interaction in a disordered environment
• Improved effective-range expansions for small and large values of scattering length
• Weighted Hartree-Fock-Bogoliubov method for interacting fermions: An application to ultracold Fermi superfluids
• A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential