We experimentally demonstrate an ultra-sensitive technique for measuring sub-nanometer optical path differences (OPDs) using the biased weak measurement (BWM) protocol. By employing real weak values with a classical coherent light source and introducing a bias phase procedure, this method directly amplifies small OPDs in interferometry, achieving significantly enhanced amplification compared to conventional measurement (CM) and standard weak measurement (SWM). In a proof-of-principle experiment of sub-nanometer OPD measurement, BWM achieves nearly 4× signal improvement within the linear response range relative to SWM, and an 85× improvement over CM. The signal-to-noise ratio of BWM and SWM exhibits an order-of-magnitude enhancement on average compared to CM. Furthermore, we experimentally determine a minimum OPD resolution of 3.1×10-4nm, corresponding to a time delay of 1 ×10-3attoseconds and a phase shift of 3.0× 10-6rad. These results highlight the potential of weak measurement protocols for high-precision longitudinal phase estimation using narrow-band sources and common optical components.
We experimentally demonstrate an ultra-sensitive technique for measuring sub-nanometer optical path differences (OPDs) using the biased weak measurement (BWM) protocol. By employing real weak values with a classical coherent light source and introducing a bias phase procedure, this method directly amplifies small OPDs in interferometry, achieving significantly enhanced amplification compared to conventional measurement (CM) and standard weak measurement (SWM). In a proof-of-principle experiment of sub-nanometer OPD measurement, BWM achieves nearly 4× signal improvement within the linear response range relative to SWM, and an 85× improvement over CM. The signal-to-noise ratio of BWM and SWM exhibits an order-of-magnitude enhancement on average compared to CM. Furthermore, we experimentally determine a minimum OPD resolution of 3.1×10-4nm, corresponding to a time delay of 1 ×10-3attoseconds and a phase shift of 3.0× 10-6rad. These results highlight the potential of weak measurement protocols for high-precision longitudinal phase estimation using narrow-band sources and common optical components.
We experimentally demonstrate an ultra-sensitive technique for measuring sub-nanometer optical path differences (OPDs) using the biased weak measurement (BWM) protocol. By employing real weak values with a classical coherent light source and introducing a bias phase procedure, this method directly amplifies small OPDs in interferometry, achieving significantly enhanced amplification compared to conventional measurement (CM) and standard weak measurement (SWM). In a proof-of-principle experiment of sub-nanometer OPD measurement, BWM achieves nearly 4× signal improvement within the linear response range relative to SWM, and an 85× improvement over CM. The signal-to-noise ratio of BWM and SWM exhibits an order-of-magnitude enhancement on average compared to CM. Furthermore, we experimentally determine a minimum OPD resolution of 3.1×10-4nm, corresponding to a time delay of 1 ×10-3attoseconds and a phase shift of 3.0× 10-6rad. These results highlight the potential of weak measurement protocols for high-precision longitudinal phase estimation using narrow-band sources and common optical components.
We experimentally demonstrate a sub-nanometer optical path difference (OPD) metrology scheme based on biased weak measurement (BWM) with real weak values using a classical coherent light source. By introducing a controlled bias phase in a Mach-Zehnder interferometric configuration, the proposed approach enables enhanced detection of sub-nanometer OPD variations while maintaining compatibility with common optical components and narrowband light sources. We systematically compare the measurement response, sensitivity, and signal-to-noise ratio (SNR) of BWM with those of standard weak measurement (SWM) and conventional interferometric measurement (CM) under identical experimental conditions. Relative to SWM, BWM provides an approximately fourfold enhancement in measurement response within the linear operating range, while achieving a (94 ± 10)-fold signal amplification compared with CM. Furthermore, the measured SNR exhibits an order-of-magnitude improvement over CM under detector-saturation-limited measurement conditions. Experimentally, the BWM scheme achieves a minimum detectable OPD of (5.6 ± 0.36) × 10 −4 nm, obtained from Allan deviation analysis. These results highlight the potential of weak measurement as a practical strategy for high-precision optical path metrology and precision interferometric sensing.
We introduce an ultrasensitive interferometric protocol that combines weak value amplification (WVA) with traditional interferometry. This protocol WVA+interferometry uses weak value amplification of the relative delay between two paths to enhance interferometric sensitivity. As an example, we demonstrate a proof-of-principle experiment that achieves few-attosecond timing resolution (few nanometer path length resolution) with a double-slit interferometer using only common optical components. Since our example uses only the spatial shift of double-slit interference fringes, its precision is not limited by the timing resolution of the detectors but is instead limited by the fundamental shot noise associated with classical light and the diminished technical noise. We experimentally demonstrate that the signal-to-noise ratio can be improved by one to two orders of magnitude relative to a measurement that does not use WVA. Two key conclusions are drawn: (i) Most conventional interferometric techniques primarily rely on determining the path difference (time delay or longitudinal phase), with their precision constrained by technical noise. Our protocol offers a robust solution for minimizing the technical noise in traditional interferometry, with precision in principle approaching the shot-noise limit. (ii) Although WVA has achieved significant advancements in ultrasensitive longitudinal phase measurement, its applicability is constrained by the need for broad spectral bandwidths and high-resolution spectrometers. Contrary to previous assumptions, we demonstrate that quantum-limited WVA time delay measurements are achievable with narrow band light using real weak values. Thus, the cost-effectiveness and practicality of the proposed WVA+interferometry protocol using narrow band light broaden the scope of WVA applications. This protocol holds potential for broad applications in optical metrology, quantum optics and quantum information, biomedical imaging, and interferometric telescopes for astrophysics.
Weak value amplification has been applied to various small physical quantities estimation, however there still lacks a practical feasible protocol to amplify ultra-small longitudinal phase, which is of importance in high precision measurement. Very recently, a different amplification protocol within the framework of weak measurements is proposed to solve this problem, which is capable of measuring any ultra-small longitudinal phase signal that conventional interferometry tries to do. Here we experimentally demonstrate this weak measurements amplification protocol of ultra-small longitudinal phase and realize one order of magnitude amplification in the same technical condition, which verifies the validity of the protocol and show higher precision and sensitivity than conventional interferometry. Our results significantly broaden the area of applications of weak measurements and may play an important role in high precision measurements.
Standard weak measurement (SWM) has been proved to be a useful ingredient for measuring small longitudinal phase change (LPC) [X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and Guang-Can Guo, Phys. Rev. Lett. 111, 033604 (2013)]. In these SWM proposals, the working regime is selected where the relative phase between orthogonal components is zero, and the LPC can be detected by measuring the shift of the meter state, i.e., the time and frequency domain, which are conjugated observables. Here, we show that an extra bias phase can significantly improve the sensitivity of measuring LPC. This bias phase can be introduced by a precoupling process. Together with a special postselection, a destructive interference can be observed in both the time and frequency domain. Using a broadband source, this conjugated destructive interference occurs in a regime less than 1 as, while the related spectral shift reaches hundreds of THz, resulting in sensitivity outperforming SWM by two orders of magnitude.
How to realize the detection of tiny birefringence is an important but challenging issue for investigations and applications in optics. In weak measurements, weak-value amplification has been widely applied to the precise estimation of time delay. Here, we show that the linear amplification in weak measurements has the potential to outperform standard weak-value amplification for ultra-small parameter characterization. The higher measurement accuracy in the linear amplification enables us to achieve a measurement of stress-induced birefringence with a high resolution of 5×10−10. Compared with existing methods, the accuracy based on weak measurements for birefringence detection can improve two orders of magnitude. Our method may have important applications in a variety of fields involving the precise measurement of time delay or birefringence.