  In spin-1 collective atomic systems, the spin and nematic-tensor operators
constitute the su(3) Lie algebra whose su(2) subalgebras are shown to give two
distinct classes of squeezing which are unitarily equivalent to spin squeezing
and spin-nematic squeezing. We explicitly construct a unitary operator that
generates an arbitrary squeezed spin-nematic state from an arbitrary Fock
state. In particular, we demonstrate that squeezed spin states can be generated
from a polar state and that squeezed spin-nematic sates can be generated from a
fully spin-polarized state.
