Optimal Estimation in Weak Value Amplification with a Position Pointer

arXiv:2611.00521v1 Announce Type: new Abstract: We experimentally evaluate five estimators for weak-value amplification (WVA) using a position pointer to measure birefringence time delays. Two general approaches are considered: measuring the position shift $\Delta x$ and measuring the probability change $\Delta P_w$ of successful postselection. Specifically, five estimators are investigated: CCD-detected fringe shift $\Delta x$, quadrant photodiode (PDQ) transversal voltage difference (XDIFF), and lock-in amplifier output phase $\eta$ (for $\Delta x$ measurement), as well as PDQ total output voltage (SUM) and CCD-detected average photon number $N_r$ (for $\Delta P_w$ measurement). The measurement precision is characterized by the Allan deviation over a range of input laser powers $P_0$.