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Polarization of the Atmosphere as a Foreground for Cosmic Microwave Background Polarization Experiments

We quantify the level of polarization of the atmosphere due to Zeeman splitting of oxygen in the Earth's magnetic field and compare it to the level of polarization expected from the polarization of the cosmic microwave background radiation. The analysis focuses on the effect at mid-latitudes and at large angular scales. We find that from stratospheric balloon borne platforms and for observations near 100 GHz the atmospheric linear and circular polarized intensities is about 10^{-12} and 100 x 10^{-9} K, respectively, making the atmosphere a negligible source of foreground. From the ground the linear and circular polarized intensities are about 10^{-9} and 100 x 10^{-6} K, making the atmosphere a potential source of foreground for the CMB E (B) mode signal if there is even a 1% (0.01%) conversion of circular to linear polarization in the instrument.