Analytical model of overlapping Feshbach resonances

Abstract

Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled channels calculations for several cases of overlapping resonances in the collisions of two ${}^7$Li atoms or two Cs atoms.

8 pages

References in corpus (13)

• Observation of an Efimov spectrum in an atomic system
• Ultracold Molecules in the Ro-Vibrational Triplet Ground State
• Precise characterization of ^6Li Feshbach resonances using trap-sideband resolved RF spectroscopy of weakly bound molecules
• Observation of universality in ultracold 7Li three-body recombination
• Observation of an Efimov-like resonance in ultracold atom-dimer scattering
• Feshbach resonances, weakly bound molecular states and coupled-channel potentials for cesium at high magnetic fields
• Determination of atomic scattering lengths from measurements of molecular binding energies near Feshbach resonances
• Finite range corrections near a Feshbach resonance and their role in the Efimov effect
• Study of Efimov physics in two nuclear-spin sublevels of 7Li
• Quantum Langevin model for exoergic ion-molecule reactions and inelastic processes
• Quantum Defect Theory for High Partial Wave Cold Collisions
• A two-channel R-matrix analysis of magnetic field induced Feshbach resonances
• Controlled collisions of two ultracold atoms in separate harmonic traps

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• Fitting ultracold resonances without a fit
• Efimov energy level rebounding off the atom-dimer continuum
• Accurate simulation of Efimov physics in ultracold atomic gases with realistic three-body multichannel interactions
• Characterization of Feshbach resonances in ${}^6\mathrm{Li}{-}^7\mathrm{Li}$ using improved interaction potentials