Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly-interacting Fermi Gas

TL;DR

This paper introduces a short-time operator product expansion method to derive and extend universal relations in rf spectroscopy of strongly-interacting Fermi gases, linking few-body physics to many-body properties.

Contribution

It presents a novel application of the operator product expansion to derive universal relations in rf spectroscopy of Fermi gases, providing a new theoretical framework.

Findings

Universal relations derived using operator product expansion

Extension of relations to include large frequency tails

Method connects few-body physics with many-body phenomena

Abstract

Universal relations that hold for any state provide powerful constraints on systems consisting of fermions with two spin states interacting with a large scattering length. In radio-frequency (rf) spectroscopy, the mean shift in the rf frequency and the large frequency tail of the rf transition rate are proportional to the contact, which measures the density of pairs with small separations. We show that these universal relations can be derived and extended by using the short-time operator product expansion of quantum field theory. This is a general method for identifying aspects of many-body physics that are controlled by few-body physics.