Einstein-Podolsky-Rosen steering, depth of steering and planar spin squeezing in two-mode Bose-Einstein condensates

TL;DR

This paper demonstrates how to prepare and detect EPR steering in two-mode Bose-Einstein condensates using spin squeezing, providing a practical method to infer entanglement and steerability in atomic and photonic interferometers.

Contribution

It extends criteria for two-mode entanglement and EPR steering based on planar spin squeezing, applying them to BEC interferometry and photonic systems with a method to estimate steering depth.

Findings

Spin squeezing indicates entanglement and EPR steering in BECs.

Criteria are predicted to be satisfied under realistic experimental parameters.

A method is provided to estimate the minimum number of particles involved in EPR steering.

Abstract

We show how one can prepare and detect entanglement and Einstein-Podolsky-Rosen (EPR) steering between two distinguishable groups (modes) of atoms in a Bose-Einstein condensate (BEC) atom interferometer. Our paper extends previous work that developed criteria for two-mode entanglement and EPR steering based on the reduced variances of two spins defined in a plane. Observation of planar spin squeezing will imply entanglement, and sufficient planar spin squeezing implies EPR steering, between the two groups of atoms. By using a two-mode dynamical model to describe BEC interferometry experiments, we show that the two-mode entanglement and EPR steering criteria are predicted to be satisfied for realistic parameters. The reported observation of spin squeezing in these parameter regimes suggests it is very likely that the criteria can be used to infer an EPR steering between mesoscopic groups of atoms, provided the total atom number can be determined to sub-Poissonian uncertainty. The criteria also apply to a photonic Mach-Zehnder interferometer. Finally, we give a method based on the amount of planar spin squeezing to determine a lower bound on the number of particles that are genuinely comprise the two-mode EPR steerable state - the so-called two-mode EPR steering depth.