Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities

• URL: http://arxiv.org/abs/2203.13547v2
• Date: Sat, 24 Dec 2022 13:36:30 GMT
• Title: Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities
• Authors: Guillem M\"uller-Rigat, Maciej Lewenstein and Ir\'en\'ee Fr\'erot
• Abstract summary: Spin squeezing inequalities (SSI) represent a major tool to probe quantum entanglement among a collection of few-level atoms. Many experiments can image the populations in all Zeeman sublevels $s=-j, -j+1, dots, j$, potentially revealing finer features of quantum entanglement not captured by SSI. Here we present a systematic approach which exploits Zeeman-sublevel population measurements in order to construct novel entanglement criteria.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spin squeezing inequalities (SSI) represent a major tool to probe quantum entanglement among a collection of few-level atoms, and are based on collective spin measurements and their fluctuations. Yet, for atomic ensembles of spin-$j$ atoms and ultracold spinor gases, many experiments can image the populations in all Zeeman sublevels $s=-j, -j+1, \dots, j$, potentially revealing finer features of quantum entanglement not captured by SSI. Here we present a systematic approach which exploits Zeeman-sublevel population measurements in order to construct novel entanglement criteria, and illustrate our approach on ground states of spin-1 and spin-2 Bose-Einstein condensates. Beyond these specific examples, our approach allows one to infer, in a systematic manner, the optimal permutationally-invariant entanglement witness for any given set of collective measurements in an ensemble of $d$-level quantum systems.

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