  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.
