LAUSR

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 φ to be estimated is assumed as uniformly distributed between 0 and 2π, while fixed in each estimation. One estimation of φ can be produced with every two magnetic susceptibility data measured along the two axis respectively, which has imprecision scaling (1.43 ± 0.02)/N 0.687±0.003 with respect to the number N of atomic spins. The measurement scheme is easy to implement and is robust against measurement fluctuation caused by environment noise and measurement defects.