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arXiv:2107.01686 · Physical Review Research

Many-body coherence and entanglement probed by randomized correlation measurements

Eric Brunner, Andreas Buchleitner, Gabriel Dufour

Published Nov 14, 2022• 11 citations
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Abstract

We show how coherences between identical constituents of a many-body quantum state can be interrogated by suitable correlation functions and identify sufficient conditions under which low-order correlators fully characterize many-body coherences, as controlled by the constituents' mutual distinguishability. The comparison of correlators of different order detects many-body entanglement.

DOI
10.1103/physrevresearch.4.043101

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Basing on the analogy between the coherent states of light and separable states of NNN bosons, we demonstrate that the violation Cauchy-Schwarz inequality for any-order correlation function signals the entanglement among the constituent particles. Rather than restricting to the correlations between the positions of particles, we consider the broadest set of measurements allowed by quantum mechanics. Our result is general -- it applies to any quantum system of bosons, even when the number of particles is not fixed, provided that there is no coherence between different number states. We also demonstrate that the compact expression for the separable state of bosons can be used to relate some known metrological quantities to the particle entanglement in a very simple way.
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Characterizing many-body systems through the quantum correlations between their constituent particles is a major goal of quantum physics. Although entanglement is routinely observed in many systems, we report here the detection of stronger correlations--Bell correlations--between the spins of about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation witness from a many-particle Bell inequality involving only one- and two-body correlation functions. Our measurement on a spin-squeezed state exceeds the threshold for Bell correlations by 3.8 standard deviations. Our work shows that the strongest possible nonclassical correlations are experimentally accessible in many-body systems and that they can be revealed by collective measurements.
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