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Femtotesla direct magnetic gradiometer using a single multipass cell

We describe a direct gradiometer using optical pumping with opposite circular polarization in two $^{87}$Rb atomic ensembles within a single multipass cell. A far-detuned probe laser undergoes a near-zero paramagnetic Faraday rotation due to the intrinsic subtraction of two contributions exceeding 3.5 rad from the highly-polarized ensembles. We develop analysis methods for the direct gradiometer signal and measure a gradiometer sensitivity of $10.1$ fT/cm$\sqrt{\mathrm{Hz}}$. We also demonstrate that our multipass design, in addition to increasing the optical depth, provides a fundamental advantage due to the significantly reduced effect of atomic diffusion on the spin noise time-correlation, in excellent agreement with theoretical estimate.