Ultraprecise time-difference measurement via enhanced dual pointers with multiple weak interactions

Abstract: Standard weak measurement with an assistant pointer and single weak interaction constrains measurement precision and quantity of interaction parameters, and a compelling characterization of quantum effect featuring weak-value amplification (WVA) remains elusive. Here, we theoretically and experimentally demonstrate an enhanced dual-pointer WVA scheme based on multiple weak interactions and variable spectrum sources. Developing triple weak interactions, momentum P pointer reaches an optimal time-difference precision of $3.34 \times {10^{-5}}$ as at 6 nm spectral width, and intensity I pointer achieves a displacement resolution of 148.8 fm within 400 kHz linewidth. A quantum effect associated with an anomalous weak value is revealed by an observable violation of a Leggett-Garg inequality. The I-pointer weak value is measured to be 1478 using multiple weak interactions and high signal-to-noise detection, achieving a two-order-of-magnitude WVA enhancement compared to standard weak measurement. Our work opens up a practical avenue for minuscule quantumness measurements in challenging environments.