Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates

TLDR

Many‑particle entanglement remains conceptually challenging, and although spin‑squeezed atomic ensembles have improved quantum metrology, entanglement in these systems is controversial because correlations among indistinguishable atoms are only witnessed by collective measurements. The study aims to directly measure spin correlations between spatially separated regions of a spin‑squeezed Bose‑Einstein condensate using high‑resolution imaging. High‑resolution imaging is employed to directly measure spin correlations between spatially separated parts of a spin‑squeezed Bose‑Einstein condensate. The experiment demonstrates Einstein‑Podolsky‑Rosen steering, allowing prediction of non‑commuting observables in one region from measurements in another with an inferred uncertainty product below the Heisenberg limit, and suggests applications for entanglement‑enhanced imaging of electromagnetic fields and quantum information beyond metrology.

Abstract

Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. While spin-squeezed and other nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems remained controversial because the correlations between the indistinguishable atoms were witnessed by collective measurements only. Here we use highresolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: we can predict measurement outcomes for non-commuting observables in one spatial region based on a corresponding measurement in another region with an inferred uncertainty product below the Heisenberg relation. This could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks beyond metrology.