Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance

TL;DR

This paper generalizes Tan's universal relations for strongly-interacting Fermi gases near a Feshbach resonance, incorporating a two-channel model with molecular states using quantum field theory techniques.

Contribution

It extends Tan's relations to include a two-channel model with molecular states, providing a more comprehensive understanding of Fermi gases near Feshbach resonances.

Findings

Derived generalized Tan relations for two-channel models.

Showed relations reduce to original Tan relations at large scattering lengths.

Applied quantum field theory methods to establish these universal relations.

Abstract

A set of universal relations between various properties of any few-body or many-body system consisting of fermions with two spin states and a large but finite scattering length have been derived by Shina Tan. We derive generalizations of the Tan relations for a two-channel model for fermions near a Feshbach resonance that includes a molecular state whose detuning energy controls the scattering length. We use quantum field theory methods, including renormalization and the operator product expansion, to derive these relations. They reduce to the Tan relations as the scattering length is made increasingly large.