Beating standard quantum limit via two-axis magnetic susceptibility measurement

Abstract: We report a metrology scheme which measures magnetic susceptibility of an atomic spin ensemble along the $x$ and $z$ direction and produces parameter estimation with precision beating the standard quantum limit. The atomic ensemble is initialized via one-axis spin squeezing with optimized squeezing time and parameter $\phi$ to be estimated is assumed as uniformly distributed between 0 and $2\pi$. One estimation of $\phi$ can be produced with every two magnetic susceptibility data measured along the two axis respectively, which has imprecision scaling $(1.43\pm{}0.02)/N<sup>{0.687\pm0.003}$ with respect to the number N of atomic spins. The measurement scheme is easy to implement and thus one step towards practical application of quantum metrology.