Optimal Estimation in Weak Value Amplification with a Position Pointer
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 Δx and measuring the probability change ΔPw of successful postselection. Specifically, five estimators are investigated: CCD-detected fringe shift Δx, quadrant photodiode (PDQ) transversal voltage difference (XDIFF), and lock-in amplifier output phase η (for Δx measurement), as well as PDQ total output voltage (SUM) and CCD-detected average photon number Nr (for ΔPw measurement). The measurement precision is characterized by the Allan deviation over a range of input laser powers P0. Generally, measuring the position shift Δx yields higher precision than measuring the probability change ΔPw. At P0=0.5~mW, corresponding to a laser-power-limited regime, direct measurement of the fringe displacement with the CCD achieves a minimum Allan deviation of (5.30±0.10)×10−3~as, approaching the corresponding photon-statistical Cramér--Rao bound (CRB). At P0=50~mW, corresponding to a detector-limited regime, PDQ detection combined with lock-in demodulation provides the best precision, reaching (1.80±0.06)×10−3~as and remaining close to the corresponding CRB. These results demonstrate that the optimal readout depends on the available optical power, detector dynamic range, and technical noise, providing practical guidance for selecting readout strategies in high-precision WVA-based metrology.
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BibTeX
@misc{huang2026optimal,
title = {{Optimal Estimation in Weak Value Amplification with a Position Pointer}},
author = {Jing-Hui Huang and Jing Zhang and Jian Ge and Lichao Liu and Wang Luo and Xiang-Yun Hu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00521},
eprint = {2611.00521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00521},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal Estimation in Weak Value Amplification with a Position Pointer
AU - Jing-Hui Huang
AU - Jing Zhang
AU - Jian Ge
AU - Lichao Liu
AU - Wang Luo
AU - Xiang-Yun Hu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00521
UR - https://arxiv.org/abs/2611.00521
AB - 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 Δx and measuring the probability change ΔP_w of successful postselection. Specifically, five estimators are investigated: CCD-detected fringe shift Δx, quadrant photodiode (PDQ) transversal voltage difference (XDIFF), and lock-in amplifier output phase η (for Δx measurement), as well as PDQ total output voltage (SUM) and CCD-detected average photon number N_r (for ΔP_w measurement). The measurement precision is characterized by the Allan deviation over a range of input laser powers P_0. Generally, measuring the position shift Δx yields higher precision than measuring the probability change ΔP_w. At P_0=0.5~mW, corresponding to a laser-power-limited regime, direct measurement of the fringe displacement with the CCD achieves a minimum Allan deviation of (5.30±0.10)×10^−3~as, approaching the corresponding photon-statistical Cramér--Rao bound (CRB). At P_0=50~mW, corresponding to a detector-limited regime, PDQ detection combined with lock-in demodulation provides the best precision, reaching (1.80±0.06)×10^−3~as and remaining close to the corresponding CRB. These results demonstrate that the optimal readout depends on the available optical power, detector dynamic range, and technical noise, providing practical guidance for selecting readout strategies in high-precision WVA-based metrology.
ER -