# 3/2-Body Correlations and Coherence in Bose-Einstein Condensates

## TL;DR

This paper introduces a variational wave function for weakly interacting Bose-Einstein condensates that accounts for 3/2-body processes, leading to lower energy states and a better understanding of coherence and excitation spectra.

## Contribution

It presents a novel variational approach incorporating 3/2-body processes, improving energy estimates and revealing their role in coherence and excitation dynamics.

## Key findings

- Lower energy ground state compared to mean-field theories.
- Transformation of excitation spectrum into a bubbling mode.
- Identification of 3/2-body processes as key to macroscopic coherence.

## Abstract

We construct a variational wave function for the ground state of weakly interacting bosons that gives a lower energy than the mean-field Girardeau-Arnowitt (or Hartree-Fock-Bogoliubov) theory. This improvement is brought about by incorporating the dynamical 3/2-body processes where one of two colliding non-condensed particles drops into the condensate and vice versa. The processes are also shown to transform the one-particle excitation spectrum into a bubbling mode with a finite lifetime even in the long-wavelength limit. These 3/2-body processes, which give rise to dynamical exchange of particles between the non-condensate reservoir and condensate absent in ideal gases, are identified as a key mechanism for realizing and sustaining macroscopic coherence in Bose-Einstein condensates.