  In a recent letter [Auzinsh {\it{et. al.}} (physics/0403097)] we have
analyzed the noise properties of an idealized atomic magnetometer that utilizes
spin squeezing induced by a continuous quantum nondemolition measurement. Such
a magnetometer measures spin precession of $N$ atomic spins by detecting
optical rotation of far-detuned probe light. Here we consider maximally
squeezed probe light, and carry out a detailed derivation of the contribution
to the noise in a magnetometric measurement due to the differential AC Stark
shift between Zeeman sublevels arising from quantum fluctuations of the probe
polarization.
