Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Ultrasensitive biased weak measurement for longitudinal phase estimation

Zi-Huai Zhang, Geng Chen, Xiao-Ye Xu, Jian‐Shun Tang, Wen-Hao Zhang, Yong‐Jian Han, Chuan‐Feng Li, Guang‐Can Guo

Published Nov 22, 2016• 41 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.94.053843

Related papers

Strengthen Weak Measurement with Conjugated Destructive Interference

Zi-Huai Zhang, Geng Chen, Xiao-Ye Xu +5 more

Standard weak measurement (SWM) has been proved to be a useful ingredient for measuring small longitudinal phase shifts. [Phys. Rev. Lett. 111, 033604 (2013)]. In this letter, we show that with specfic pre-coupling and postselection, destructive interference can be observed for the two conjugated variables, i.e. time and frequency, of the meter state. Using a broad band source, this conjugated destructive interference (CDI) can be observed in a regime approximately 1 attosecond, while the related spectral shift reaches hundreds of THz. This extreme sensitivity can be used to detect tiny longitudinal phase perturbation. Combined with a frequency-domain analysis, conjugated destructive interference weak measurement (CDIWM) is proved to outperform SWM by two orders of magnitude.

arXiv:1605.09536•May 31, 2016•0 citations

Sub-nanometer optical path difference measurement using biased weak measurement with real weak values

Huang Jing-Hui, Jingzheng Huang, Hongliang Cui +5 more

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.

•Mar 26, 2026•0 citations

Sub-nanometer optical path difference measurement using biased weak measurement with real weak values

Huang Jing-Hui, Jingzheng Huang, Hongliang Cui +5 more

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.

•Mar 26, 2026•0 citations

Ultrasensitive phase estimation with white light

Chuan‐Feng Li, Xiao-Ye Xu, Jian‐Shun Tang +2 more

An improvement of the scheme by Brunner and Simon [Phys. Rev. Lett. 105, 010405 (2010)] is proposed in order to show that quantum weak measurements can provide a method to detect ultrasmall longitudinal phase shifts, even with white light. By performing an analysis in the frequency domain, we find that the amplification effect will work as long as the spectrum is large enough, irrespective of the behavior in the time domain. As such, the previous scheme can be notably simplified for experimental implementations.

arXiv:1102.4902•Physical Review A•Apr 19, 2011•61 citations

Measuring Small Longitudinal Phase Shifts: Weak Measurements or Standard Interferometry?

Nicolas Brunner, Christoph Simon

Recently, weak measurements were used to measure small effects that are transverse to the propagation direction of a light beam. Here we address the question of whether weak measurements are also useful for measuring small longitudinal phase shifts. We show that standard interferometry greatly outperforms weak measurements in a scenario involving a purely real weak value. However, we also present an interferometric scheme based on a purely imaginary weak value, combined with a frequency-domain analysis, which may have the potential to outperform standard interferometry by several orders of magnitude.

arXiv:0911.5139•Physical Review Letters•Jul 2, 2010•397 citations

Measuring Small Longitudinal Phase Shifts via Weak Measurement Amplification

Kai Xu, Xiao‐Min Hu, Chao ZHang +6 more

Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimation. Since many quantities can be converted to phase signal, it is thus interesting and important to consider measuring ultra-small longitudinal phase shifts by using weak measurement. Here, we propose and experimentally demonstrate a novel weak measurement amplification based ultra-small longitudinal phase estimation, which is suitable for polarization interferometry. We realize one order of magnitude amplification measurement of small phase signal directly introduced by Liquid Crystal Variable Retarder and show its robust to finite visibility of interference. Our results may find important applications in high-precision measurements, such as gravitational waves detection.

arXiv:1803.07746•Mar 21, 2018•0 citations
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.
Standard weak measurement (SWM) has been proved to be a useful ingredient for measuring small longitudinal phase shifts. [Phys. Rev. Lett. 111, 033604 (2013)]. In this letter, we show that with specfic pre-coupling and postselection, destructive interference can be observed for the two conjugated variables, i.e. time and frequency, of the meter state. Using a broad band source, this conjugated destructive interference (CDI) can be observed in a regime approximately 1 attosecond, while the related spectral shift reaches hundreds of THz. This extreme sensitivity can be used to detect tiny longitudinal phase perturbation. Combined with a frequency-domain analysis, conjugated destructive interference weak measurement (CDIWM) is proved to outperform SWM by two orders of magnitude.
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.
An improvement of the scheme by Brunner and Simon [Phys. Rev. Lett. 105, 010405 (2010)] is proposed in order to show that quantum weak measurements can provide a method to detect ultrasmall longitudinal phase shifts, even with white light. By performing an analysis in the frequency domain, we find that the amplification effect will work as long as the spectrum is large enough, irrespective of the behavior in the time domain. As such, the previous scheme can be notably simplified for experimental implementations.
Recently, weak measurements were used to measure small effects that are transverse to the propagation direction of a light beam. Here we address the question of whether weak measurements are also useful for measuring small longitudinal phase shifts. We show that standard interferometry greatly outperforms weak measurements in a scenario involving a purely real weak value. However, we also present an interferometric scheme based on a purely imaginary weak value, combined with a frequency-domain analysis, which may have the potential to outperform standard interferometry by several orders of magnitude.
Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimation. Since many quantities can be converted to phase signal, it is thus interesting and important to consider measuring ultra-small longitudinal phase shifts by using weak measurement. Here, we propose and experimentally demonstrate a novel weak measurement amplification based ultra-small longitudinal phase estimation, which is suitable for polarization interferometry. We realize one order of magnitude amplification measurement of small phase signal directly introduced by Liquid Crystal Variable Retarder and show its robust to finite visibility of interference. Our results may find important applications in high-precision measurements, such as gravitational waves detection.