Multi-channel scattering and Feshbach resonances: Effective theory, phenomenology, and many-body effects

Abstract

A low energy effective theory based on a microscopic multi-channel description of the atom-atom interaction is derived for the scattering of alkali atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects are demonstrated to be of particular relevance to an experimentally important Feshbach resonance for ${}^{40}$K atoms. We analyze a recent rethermalization rate experiment on ${}^{40}$K and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multi-channel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.

10 pages, 5 figures. Typos corrected. Accepted for PRA

References in corpus (2)

• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• BCS-BEC crossover at finite temperature in the broken-symmetry phase

Cited by in corpus (14)

• Excited Thomas-Efimov levels in ultracold gases
• Stability of a BEC with Higher-order Interactions near a Feshbach Resonance
• Bragg Spectroscopy of Cold Atomic Fermi Gases
• Thomas-Fermi Approximation for a Condensate with Higher-order Interactions
• Three-body losses of a polarized Fermi gas near a p-wave Feshbach resonance in effective field theory
• Heat and spin transport in a cold atomic Fermi gas
• Conditions for Efimov Physics for Finite Range Potentials
• Two-band description of resonant superfluidity in atomic Fermi gases
• Atom-molecule coherence in a one-dimensional system
• Feshbach Resonances and Medium Effects in ultracold atomic Gases
• Attractive polaron formed in doped nonchiral/chiral parabolic system within ladder approximation
• Effective field theory of bosons with finite-range interaction in a disordered environment
• BEC-BCS Crossover with Feshbach Resonance for a Three-Hyperfine-Species Model
• Finite-range bias in fitting three-body loss to the zero-range model