Magnetic Field Estimation at and beyond 1/N Scaling via an Effective Nonlinearity

We provide evidence, based on direct simulation of the quantum Fisher information, that 1/N scaling of the sensitivity with the number of atoms N in an atomic magnetometer can be surpassed by double-passing a far-detuned laser through the atomic system during Larmor precession. Furthermore, we predict that for N>>1, the proposed double-pass atomic magnetometer can essentially achieve 1/N scaling without requiring any appreciable amount of entanglement.