Beyond-mean-field effects in mixtures: few-body and many-body aspects

TL;DR

This paper introduces the concept of beyond-mean-field effects in ultracold Bose-Bose mixtures, focusing on quantum stabilization, the Lee-Huang-Yang correction, and the emergence of higher-order interactions.

Contribution

It provides a detailed derivation of the leading BMF correction in Bose-Bose mixtures and discusses conditions under which this correction becomes analytically expandable.

Findings

Derivation of the Lee-Huang-Yang correction for Bose-Bose mixtures

Identification of conditions where BMF correction becomes analytic

Discussion of the Bogoliubov approach's predictive capabilities

Abstract

The discovery of ultracold dilute liquids has significantly elevated our interest in various phenomena which go under the name of beyond-mean-field (BMF) physics. In these lecture notes we give an elementary introduction to the quantum stabilization and liquefaction of a collapsing weakly interacting Bose-Bose mixture. A detailed derivation of the leading BMF correction, also known as the Lee-Huang-Yang (LHY) term, in this system is presented in a manner suitable for further generalizations and extensions. Although the LHY term is a nonanalytic function of the density $n$, under certain conditions the leading BMF correction becomes analytic and can be expanded in integer powers of $n$, effectively introducing three-body and higher-order interactions. We discuss why and how well the Bogoliubov approach can predict these few-body observables.