Adaptive Time-Varying Parameter Estimation via Weak Measurement

Extending quantum sensing to time-varying parameter estimation is a potential and challenging task in practical application. To achieve this goal, we propose an adaptive method to estimate an unknown timevarying parameter through light-intensity split detection and the insertion of reference phases in the weak measurement. Theoretical analysis and numerical simulation are applied to illustrate the feasibility and practical applications of our method. The results demonstrate that the method has adjustable sensitivity and linear dynamic range, and is robust to nonideal measurement conditions. Moreover, we analyze the precision of our method and show that its precision limit can surpass the standard quantum limit and approach the Heisenberg scaling when using a squeezed light of optimal Gaussian state.