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We describe a criterion for the detection of entanglement between twomulti-boson systems. The criterion is based on calculating correlations ofGell-Mann matrices with a fixed boson number on each subsystem. This appliesnaturally to systems such as two entangled spinor Bose-Einstein condensates. Weapply our criterion to several experimentally motivated examples, such as an $S^z S^z $ entangled BECs, ac Stark shift induced two-mode squeezed BECs, andphotons under parametric down conversion. We find that entanglement can bedetected for all parameter regions for the most general criterion. Alternativecriteria based on a similar formalism are also discussed together with theirmerits.

Correlation-based entanglement criterion in bipartite multiboson systems