Analytic description of atomic interaction at ultracold temperatures II: Scattering around a magnetic Feshbach resonance

Abstract

Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave $l$, and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary $l$, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary $l$, (b) rigorous definitions of "broad" and "narrow" resonances of arbitrary $l$ and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.

13 pages, 4 figures

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Cited by in corpus (31)

• Efimov Physics: a review
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Universality of the three-body Efimov parameter at narrow Feshbach resonances
• Universal Properties of a Strongly Interacting Fermi Gas at a $p$-wave Resonance
• Precision Test of the Limits to Universality in Few-Body Physics
• Observation of "broad" d-wave Feshbach resonances with a triplet structure
• Quantum-defect theory for $-1/r^4$ type of interactions
• Observation of Efimov Universality across a Non-Universal Feshbach Resonance in \textsuperscript{39}K
• Coupled $\ell$-wave confinement-induced resonances in cylindrically symmetric waveguides
• Effective-range approximations for resonant scattering of cold atoms
• Observation of broad p-wave Feshbach resonances in ultracold ${}^{85}$Rb-${}^{87}$Rb mixtures
• Multichannel interactions of two atoms in an optical tweezer
• Ultracold collision in the presence of synthetic spin-orbit coupling
• Broad Feshbach resonances in ultracold alkali-metal systems
• Probing open- and closed-channel p-wave resonances
• Energy dependent $\ell$-wave confinement-induced resonances
• Feshbach spectroscopy of an ultracold ${}^{41}$K-${}^6$Li mixture and ${}^{41}$K atoms
• Efimov scenario for overlapping narrow Feshbach resonances
• Efimovian three-body potential from broad to narrow Feshbach resonances
• Quantum Defect Theory for Orbital Feshbach Resonance
• Multichannel quantum-defect theory for magnetic Feshbach resonances in heteronuclear group I systems
• Universality in s-wave and higher partial wave Feshbach resonances: an illustration with a single atom near two scattering centers
• Efimov resonance position near a narrow Feshbach resonance in ${}^6$Li-${}^{133}$Cs mixture
• Causality, universality, and effective field theory for van der Waals interactions
• Multichannel quantum defect theory with a frame transformation for ultracold atom-molecule collisions in magnetic fields
• Multichannel quantum-defect theory for anisotropic interactions
• Effective field theory of bosons with finite-range interaction in a disordered environment
• Closed-channel parameters of Feshbach resonances
• Resonance-facilitated three-channel p-wave scattering
• Direct observation of Feshbach enhanced $s$-wave scattering of fermions
• Low Energy Continuum and Lattice Effective Field Theories