Review of Universal Relations for Fermions with Large Scattering Length

Eric Braaten

Eric Braaten, H.‐W. Hammer

Eric Braaten

The behavior of fermions with two spin states that interact with a large scattering length is constrained by universal relations that hold for any state of the system. These relations involve a central property of the system called the contact, which measures the number of pairs of fermions with different spins that have small separations. The contact controls the thermodynamics of the system as well as the large-momentum and high-frequency tails of correlation functions. This review summarizes the current theoretical and experimental status of these universal relations.

Eric Braaten, Daekyoung Kang, Lucas Platter

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.

Alexander Galea, Tash Zielinski, Stefano Gandolfi +1 more

Pirmin Lemberger, Nicolas Macris