Spin squeezing and entanglement in spinor-1 condensates

We analyze quantum correlation properties of a spinor-1 (f=1) Bose Einstein condensate using the Gell-Mann realization of SU(3) symmetry. We show that previously discussed phenomena of condensate fragmentation and spin-mixing can be explained in terms of the hypercharge symmetry. The ground state of a spinor-1 condensate is found to be fragmented for ferromagnetic interactions. The notion of two bosonic mode squeezing is generalized to the two spin (U-V) squeezing within the SU(3) formalism. Spin squeezing in the isospin subspace (T) is found and numerically investigated. We also provide new results for the stationary states of spinor-1 condensates.