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

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.

6 + 9 pages, 2 figures. Final version accepted in Quantum Journal

References in corpus (4)

• Quantum-fluctuation-driven crossover from a dilute Bose-Einstein condensate to a macro-droplet in a dipolar quantum fluid
• Deterministic entanglement generation from driving through quantum phase transitions
• Spin squeezing and entanglement
• Relaxation of the collective magnetization of a dense 3D array of interacting dipolar S=3 atoms

Cited by in corpus (1)

• The Coming Decades of Quantum Simulation