Preparation of spin squeezed atomic states by optical phase shift measurement

In this paper we present a state vector analysis of the generation of atomic spin squeezing by the measurement of an optical phase shift. The frequency resolution is improved when a spin squeezed sample is used for spectroscopy in place of an uncorrelated sample. When light is transmitted through an atomic sample some photons will be scattered out of the incident beam, and this has a destructive effect on the squeezing. We present quantitative studies for three limiting cases: the case of a sample of atoms of size smaller than the optical wavelength, the case of a large dilute sample, and the case of a large dense sample.