Hamiltonian design in atom-light interactions with rubidium ensembles: A quantum-information toolbox

We study the coupling between collective variables of atomic spin and light polarization in an ensemble of cold Rb-87 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 D-1 and D-2 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.