How to measure the quantum state of collective atomic spin excitation

The spin state of an atomic ensemble can be viewed as two bosonic modes, i.e., a quantum signal mode and a c-numbered local oscillator mode when large numbers of spin-1/2 atoms are spin polarized along a certain axis and collectively manipulated within the vicinity of the axis. We present a concrete procedure, which determines the spin-excitation-number distribution, i.e., the diagonal elements of the density matrix in the Dicke basis for the collective spin state. By seeing the collective spin state as a statistical mixture of the inherently entangled Dicke states, the physical picture of its multiparticle entanglement is made clear.