Spin Squeezing in Finite Temperature Bose-Einstein Condensates : Scaling with the system size

TL;DR

This paper analyzes how finite temperature affects spin squeezing in Bose-Einstein condensates, revealing a finite limit to squeezing at large atom numbers and providing analytical and numerical insights.

Contribution

It introduces a multimode theoretical framework and classical field simulations to study finite temperature effects on spin squeezing in atomic condensates.

Findings

Maximum spin squeezing saturates at large atom numbers due to finite temperature effects.

Analytical results are validated with improved classical field simulations.

The study provides a detailed scaling analysis of spin squeezing with system size.

Abstract

We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number $N\to \infty$ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction $<N_{\rm nc}>/N$ in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.