Universal Relation for the Inelastic Two-Body Loss Rate

TL;DR

This paper derives a universal relation linking the inelastic two-body loss rate to the contact in strongly-interacting systems, verified through quantum field theory calculations and applicable to ultracold atomic gases.

Contribution

It introduces a universal relation for the inelastic loss rate using operator product expansion, connecting it to the contact in such systems.

Findings

Derived the universal relation for inelastic loss rate

Verified the relation through low-density limit calculations

Applicable to ultracold atomic gases with inelastic channels

Abstract

Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic 2-body loss rate. A simple universal relation between the loss rate and the contact is obtained by truncating the expansion after the lowest dimension operator. We verify the universal relation explicitly by direct calculations in the low-density limit at nonzero temperature. This universal relation can be tested experimentally using ultracold quantum gases of atoms in hyperfine states that have an inelastic spin-relaxation channel.