We demonstrate the superior robustness of the transition regime in inverse weak-value amplification (IWVA) metrology against key experimental noise sources. For standard IWVA schemes, the transition regime provides enhanced resilience compared to the conventional IWVA regime when subjected to uncorrelated Gaussian technical noise and phase fluctuations. While a larger beam width σ generally suppresses technical noise, we identify that phase fluctuations impose a strict upper bound on the optimal σ . In power-recycled IWVA schemes, where cavity loss and the inherent walk-off effect typically degrade the signal, the transition regime maintains a consistent advantage. Our findings establish the transition regime as the optimal operational point for high-precision measurements, balancing significant signal amplification with robustness against practical noise in both standard and power-recycled configurations.
In this letter, we propose a precision method for phase estimation based on the weak-value amplification (WVA) technique using a monochromatic light source. The anomalous WVA significantly suppresses the technical noise with respect to the intensity difference signal induced by the phase delay when the post-selection procedure comes into play. The phase measured precision of this method is proportional to the weak-value of a polarization operator in the experimental range. Our results compete well with the wide spectrum light phase weak measurements and outperform the standard homodyne phase detection technique.
We report a quantitative evaluation of weak-value amplification (WVA) for longitudinal phase measurements using Allan variance analysis. Building on a recent double-slit interferometry experiment with real weak values [Phys. Rev. Lett. 134, 080802 (2025)], our Allan variance analysis demonstrates measurement of a few attosecond time delay approaching the shot noise limit at short averaging intervals of
T =
0.01−0.1 s, representing two orders of magnitude variance reduction compared to the
T=300 s operating point in prior implementations. We demonstrate that the Allan-variance noise floor scales with the inverse of the detected photon number
1/Nr, confirming shot-noise-limited operation with WVA. Furthermore, this
1/Nr scaling experimentally validates that WVA can outperform conventional measurement under fixed detected photon number and detector saturation, in the presence of technical noise, as theoretically predicted [Phys. Rev. Lett. 118, 070802 (2017)]. Our results provide rigorous, quantitative evidence of the near-optimal noise performance achievable with WVA, establishing a new benchmark for precision optical metrology. This advancement is particularly relevant to applications such as gravitational-wave detection, where signals predominantly occupy the high-frequency regime (
>10 Hz).
Optical interferometry plays an essential role in precision metrology such as in gravitational wave detection, gyroscopes, and environmental sensing. Weak value amplification enables reaching the shot-noise-limit of sensitivity, which is difficult for most optical sensors, by amplifying the interferometric signal without amplifying certain technical noises. We implement a generalized form of weak value amplification on an integrated photonic platform with a multi-mode interferometer. Our results pave the way for a more sensitive, robust, and compact platform for measuring phase, which can be adapted to fields such as coherent communications and the quantum domain. In this work, we show a 7 dB signal enhancement in our weak value device over a standard Mach-Zehnder interferometer with equal detected optical power, as well as frequency measurements with 2 kHz sensitivity by adding a ring resonator.