  We provide a framework for understanding recent experiments on squeezing of a
collective atomic pseudo-spin, induced by a homodyne measurement on
off-resonant probe light interrogating the atoms. The detection of light
decimates the atomic state distribution and we discuss the conditions under
which the resulting reduced quantum fluctuations are metrologically relevant.
In particular, we consider a dual probe scheme which benefits from a
cancelation of classical common mode noise sources such that quantum
fluctuations from light and atoms are the main contributions to the detected
signal.
