Entanglement and Extreme Spin Squeezing for a Fluctuating Number of Indistinguishable Particles

TL;DR

This paper generalizes entanglement criteria based on spin squeezing to systems with fluctuating particle numbers, providing practical insights for cold atom experiments and justifying previous bounds used in Bose-Einstein condensate studies.

Contribution

It extends the spin squeezing entanglement criteria to fluctuating particle systems and offers operational interpretations relevant for cold atom experiments.

Findings

Generalized $k$-particle entanglement criteria for fluctuating particle numbers.

Provided operational meaning for bounds when particles are indistinguishable.

Validated the use of S{ }rensen-M{ }lmer bounds in Bose-Einstein condensate experiments.

Abstract

We extend the criteria for $k$-particle entanglement from the spin squeezing parameter presented in [A.S. S{\o}rensen and K. M{\o}lmer, Phys. Rev. Lett. {\bf 86}, 4431 (2001)] to systems with a fluctating number of particles. We also discuss how other spin squeezing inequalities can be generalized to this situation. Further, we give an operational meaning to the bounds for cases where the individual particles cannot be addressed. As a by-product, this allows us to show that in spin squeezing experiments with cold gases the particles are typically distinguishable in practise. Our results justify the application of the S{\o}rensen-M{\o}lmer bounds in recent experiments on spin squeezing in Bose-Einstein condensates.