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 dist
ribution 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.
