An all-optical intrinsic atomic gradiometer with sub-20 fT/cm/$\sqrt{\rm Hz}$ sensitivity in a 22 $μ$T earth-scale magnetic field

In this work we demonstrate a high sensitivity atomic gradiometer capable of operation in earth-field level environments. We apply a light-pulse sequence at four times the Larmor frequency to achieve gradiometer sensitivity <20 fT/cm/$\sqrt{\rm Hz}$ at the finite field strength of 22 $μ$T. The experimental timing sequence can be tuned to the field magnitude of interest. Our one dimensional all-optical gradiometer performs a differential measurement between two regions of a single vapor cell on a 4 cm baseline. Our results pave the way for extensions to operation in higher dimensions, vector sensitivity, and more advanced gradiometers.