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

Understand

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.