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Collective phenomena in the Tavis-Cummings model has been widely studied,focusing on the phase transition features. In many occasions, it has been usedvariational approaches that consider separated radiation-matters systems. Inthis paper, we examine the role of the quantum entanglement of an assembly oftwo-level emitters coupled to a single-mode cavity; this allows us tocharacterise the quantum correlated state for each regime. Statisticalproperties of the system, e.g., the first four statistical moments, showclearly the structure of the light and matter distributions. Even though thesecond order correlation function goes to one in some regimes, the statisticalanalysis evidence a sharp departure from coherent behaviour, contrarily to thecommon understanding.

Uncover quantumness in the crossover from BEC to quantum-correlated phase