A measurement of atmospheric circular polarization with POLARBEAR

At millimeter wavelengths, the atmospheric emission is circularly polarized owing to the Zeeman splitting of molecular oxygen by the Earth's magnetic field. We report a measurement of the signal in the 150 GHz band using 3 years of observational data with the \textsc{Polarbear} project. Non-idealities of a continuously rotating half-wave plate (HWP) partially convert circularly polarized light to linearly polarized light. While \textsc{Polarbear} detectors are sensitive to linear polarization, this effect makes them sensitive to circular polarization. Although this was not the intended use, we utilized this conversion to measure circular polarization. We reconstruct the azimuthal gradient of the circular polarization signal and measure its dependency from the scanning direction and the detector bandpass. We compare the signal with a simulation based on atmospheric emission theory, the detector bandpass, and the HWP leakage spectrum model. We find the ratio of the observed azimuthal slope to the simulated slope is $0.92 \pm 0.01\rm{(stat)} \pm 0.07\rm{(sys)}$. This ratio corresponds to a brightness temperature of $3.8\,\mathrm{m K}$ at the effective band center of $121.8\,\mathrm{GHz}$ and bandwidth of $3.5\,\mathrm{GHz}$ estimated from representative detector bandpass and the spectrum of Zeeman emission. This result validates our understanding of the instrument and reinforces the feasibility of measuring the circular polarization using the imperfection of continuously rotating HWP. Continuously rotating HWP is popular in ongoing and future cosmic microwave background experiments to modulate the polarized signal. This work shows a method for signal extraction and leakage subtraction that can help measuring circular polarization in such experiments.