Beating standard quantum limit via two-axis magnetic susceptibility measurement

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. One estimation of φ can be produced with every two magnetic susceptibility data measured along the two axis respectively, which has imprecision scaling \(1.43pm{}0.02\)/N^0.687pm0.003 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.