Assessing degrees of entanglement of phonon states in atomic Bose gases through the measurement of commuting observables
arXiv:1705.06648 · doi:10.1103/PhysRevD.96.045012
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.
18 pages, 6 figures
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