Entanglement like properties in Spin-Orbit Coupled Ultra Cold Atom and violation of Bell like Inequality

TL;DR

This paper demonstrates entanglement between motional and internal states in spin-orbit coupled ultracold atoms and shows violation of Bell-like inequalities, offering insights into quantum non-contextuality and fundamental quantum principles.

Contribution

It reveals entanglement in synthetic spin-orbit coupled ultracold atoms and demonstrates Bell-like inequality violation, linking microscopic quantum effects to macroscopic condensates.

Findings

Entanglement between motional and spin degrees of freedom.

Violation of Bell-like inequalities in ultracold atoms.

Implications for testing quantum non-contextuality.

Abstract

We show that the general quantum state of synthetically spin-orbit coupled ultra cold bosonic atom whose condensate was experimentally created recently ( Y. J. Lin {\it et al.}, Nature, {\bf 471}, 83, (2011)), shows entanglement between motional degrees of freedom ( momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provides a unique opportunity to verify fundamental principle like quantum non-contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such atom-laser system and how that influneces quantities like entanglement entropy, violation of Bell like Inequality etc. We also discuss the implication of our result in testing the quantum non-contextuality and Bell's Inequality vioaltion by macroscopic quantum object like Bose-Einstein Condensate of ultra cold atoms.