Assessing degrees of entanglement of phonon states in atomic Bose gases through the measurement of commuting observables

Robertson, Scott; Michel, Florent; Parentani, Renaud

Abstract

We show that measuring commuting observables can be sufficient to assess that a bipartite state is entangled according to either nonseparability or the stronger criterion of “steerability.” Indeed, the measurement of a single observable might reveal the strength of the interferences between the two subsystems, as if an interferometer were used. For definiteness, we focus on the two-point correlation function of density fluctuations obtained by in situ measurements in homogeneous one-dimensional cold atomic Bose gases. We then compare this situation to that found in transonic stationary flows mimicking a black hole geometry where correlated phonon pairs are emitted on either side of the sonic horizon by the analogue Hawking effect. We briefly apply our considerations to two recent experiments.

Citation

Robertson, S., Michel, F., & Parentani, R. (2017). Assessing degrees of entanglement of phonon states in atomic Bose gases through the measurement of commuting observables. Physical Review D, 96(4), Article 045012. https://doi.org/10.1103/physrevd.96.045012

• Journal Article Type: Article
• Acceptance Date: Jul 3, 2017
• Online Publication Date: Aug 16, 2017
• Publication Date: Aug 16, 2017
• Deposit Date: Jul 4, 2017
• Publicly Available Date: Jul 11, 2017
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 96
• Issue: 4
• Article Number: 045012
• DOI: https://doi.org/10.1103/physrevd.96.045012
• Public URL: https://durham-repository.worktribe.com/output/1356312
• Related Public URLs: https://arxiv.org/abs/1705.06648