Universal Relations for Identical Bosons from 3-Body Physics

TL;DR

This paper derives universal relations for identical bosons with large scattering length, linking 2- and 3-body physics to observable tails in momentum distribution and radio-frequency transition rates, influenced by Efimov physics.

Contribution

It introduces universal relations involving the 3-body contact for bosons, extending known 2-body relations and incorporating Efimov effects.

Findings

Momentum distribution has a 1/k^4 tail proportional to 2-body contact.

Radio-frequency transition rate exhibits a 1/omega^{3/2} tail linked to 2-body contact.

Additional 3-body universal relations involve log-periodic functions due to Efimov physics.

Abstract

Systems consisting of identical bosons with a large scattering length satisfy universal relations determined by 2-body physics that are similar to those for fermions with two spin states. They require the momentum distribution to have a large-momentum 1/k^4 tail and the radio-frequency transition rate to have a high-frequency 1/omega^{3/2} tail, both of which are proportional to the 2-body contact. Identical bosons also satisfy additional universal relations that are determined by 3-body physics and involve the 3-body contact, which measures the probability of 3 particles being very close together. The coefficients of the 3-body contact in the 1/k^5 tail of the momentum distribution and in the 1/omega^2 tail of the radio-frequency transition rate are log-periodic functions of k and omega that depend on the Efimov parameter.