Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics

Abstract

Starting from a system of $N$ radial Schrödinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N\times N$ exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on $N(N+1)/2$ unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\times 2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has 0, 1 or 2 bound states, and 0 or 1 resonance; the potential parameters are explicitly expressed in terms of its bound-state energies, of its resonance energy and width, or of the open-channel scattering length, which solves schematic inverse problems. As a first physical application, exactly-solvable $2\times 2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interplays with a bound or virtual state close to threshold, which results in a large background scattering length.

19 pages, 15 figures

References in corpus (6)

• Resonance Superfluidity: Renormalization of Resonance Scattering Theory
• Measurement of the Zero Crossing in a Feshbach Resonance of Fermionic 6-Li
• Feshbach resonances with large background scattering length: interplay with open-channel resonances
• A two-channel R-matrix analysis of magnetic field induced Feshbach resonances
• Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for Feshbach resonance
• Supersymmetric transformations for coupled channels with threshold differences

Cited by in corpus (9)

• Dynamical regimes of a quantum swap gate beyond the Fermi Golden Rule
• Buffering plasmons in nanoparticle waveguides at the virtual-localized transition
• Single- and coupled-channel radial inverse scattering with supersymmetric transformations
• Eigenphase preserving two-channel SUSY transformations
• Shadow poles in a coupled-channel problem calculated with Berggren basis
• Coupling between scattering channels with SUSY transformations for equal thresholds
• Spectral properties of non-conservative multichannel SUSY partners of the zero potential
• Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models
• Multichannel generalization of eigen-phase preserving supersymmetric transformations