We show that by introducing the two-mode correlated Holstein–Primakoff transformation the correlated spin coherent state can be identified as a two-mode correlated binomial state. This fact can be used to describe populations on the three levels of an assembly of identical atoms.
Using the q analog of the Holstein-Primakoff boson realization of the su(2) generators, we show that a type of q-deformed binomial state that corresponds to the Heine distribution can be identified as an su(2)q coherent state. This fact is a q extension of the fact that the ordinary binomial state is a particular su(2) coherent state when the Holstein-Primakoff transformation is employed.