Beating standard quantum limit via two-axis magnetic susceptibility measurement

We report a metrology scheme which measures the magnetic susceptibility of an atomic spin ensemble along the x and z directions 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) assumed as uniformly distributed between 0 and 2\pi while fixed in each estimation. One estimation of \phi can be produced with every two magnetic susceptibility data measured along the two axes respectively, which has an imprecision scaling (1.43\pm0.02)/N^0.687\pm0.003 with respect to the number N of the atomic spins. The measurement scheme is easy to implement and is robust against the measurement fluctuation caused by environment noise and measurement defects.