Feshbach resonance described by the boson fermion coupling

TL;DR

This paper explores how the Feshbach resonance can be modeled using the Boson-Fermion approach, revealing the emergence of resonant fermion scattering through subsystem disentanglement and canonical transformations.

Contribution

It demonstrates the generation of resonant fermion scattering within the BF model and analyzes feedback effects on scattering strength in normal and superconducting states.

Findings

Resonant scattering emerges after subsystem disentanglement.

Feedback effects influence scattering amplitude.

Analysis covers both normal and superconducting phases.

Abstract

We consider a possibility to describe the Feshbach resonance in terms of the Boson Fermion (BF) model. Using such model we show that after a gradual disentangling of the boson from fermion subsystem the resonant type scattering between fermions is indeed generated. We decouple the subsystems via: (a) the single step, and (b) the continuous canonical transformation. With the second one we investigate the feedback effects effectively leading to the finite amplitude of the scattering strength. We study them in detail in: the normal $T>T_{c}$ and superconducting $T \leq T_{c}$ states.