Note: An atomic self-sustaining magnetic gradiometer with a 1/τ uncertainty property based on Larmor precession

We demonstrate an atomic magnetic gradiometer based on self-sustaining Larmor precession. By coherent optical pumping, we measure the phase of the Larmor precession directly and observe that the gradiometer shows a 1/τ improvement in magnetic field gradient uncertainty over time τ. Since the measurement gives frequency signals, the gradiometer can be easily implemented by mixing and filtering the different frequency signals from two adjacent magnetometers. A gradient sensitivity of 186 fT/Hz/cm^-1) is realized, which is close to the shot-noise limit. In a noisy environment, the gradiometer can still maintain its 1/τ behavior by suppressing 90% of the common-mode noise. This method should be widely applicable to the measurement of magnetic field gradients owing to its simplicity and outstanding performance.