  We study the coupling between collective variables of atomic spin and light
polarization in an ensemble of cold 87Rb probed with polarized light. The
effects of multiple hyperfine levels manifest themselves as a rank-2 tensor
polarizability, whose irreducible components can be selected by means of probe
detuning. The D1 and D2 lines of Rb are explored and we identify different
detunings which lead to Hamiltonians with different symmetries for rotations.
As possible applications of these Hamiltonians, we describe schemes for spin
squeezing, quantum cloning, quantum memory, and measuring atom number.
