Classification of spin and multipolar squeezing

We investigate various types of squeezing in a collective su(2J+1) system consisting of spin-J particles (J>1/2). We show that the squeezing in the collective su(2J+1) system can be classified into unitary equivalence classes, each of which is characterized by a set of squeezed and anti-squeezed observables forming an su(2) subalgebra in the su(2J+1) algebra. The dimensionality of the unitary equivalence class is fundamentally related to its squeezing limit. We also demonstrate the classification of the squeezing among the spin and multipolar observables in a collective su(4) system.