Conditions for spin squeezing in a cold 87Rb ensemble

We study the conditions for generating spin squeezing via a quantum non-demolition measurement in an ensemble of cold 87Rb atoms. By considering the interaction of atoms in the 5S_{1/2}(F=1) ground state with probe light tuned near the D2 transition, we show that, for large detunings, this system is equivalent to a spin-1/2 system when suitable Zeeman substates and quantum operators are used to define a pseudo-spin. The degree of squeezing is derived for the rubidium system in the presence of scattering causing decoherence and loss. We describe how the system can decohere and lose atoms, and predict as much as 75% spin squeezing for atomic densities typical of optical dipole traps.