Many-Particle Entanglement Criterion for Superradiantlike States

We derive a many-particle entanglement criterion for mixed states using a relation between single-mode and many-particle nonclassicalities. The criterion relies on the measurement of collective spin observables. It works very well not only in the vicinity of the Dicke states, but also for the superpositions of Dicke states: superradiant ground states of finite or infinite number of particles and time evolution of single-photon superradiance from an extended sample where random phases appear. We also obtain a criterion for ensemble-field entanglement, which is successful for such kinds of states. We also observe an interesting phenomenon: even though the collective excitation of this many-particle system has a sub-Poissonian character, which results in entanglement, the wave function displays bunching.