Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities
Guillem Müller-Rigat, Maciej Lewenstein, Irénée Frérot · Quantum · 2022
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,…,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.