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Applied Physics Express

Phase estimation based on inverse weak-value using a monochromatic light source

Shiwei Xie, Zhaoxue Li, Yan Liu, Zhiyou Zhang

Published Nov 14, 2019• 4 citations
Publisher

Abstract

Weak-value measurement (WVM) technique, especially the linear WVM technique, has been proved to be useful in high precision metrology. However, the phase shift to be measured is strictly dominated by the input meter, such as the light wavelength and the space position, which are the basic elements of the linear WVM regime. In this work, an inverse WVM technique using a monochromatic light source is presented to achieve precise estimation of the wavelength-independent phase shift. The theoretical analysis in sensitivity and precision indicates that the inverse WVM technique is more applicable to wavelength-independent phase estimation, as compared to the typical linear WVM technique. Furthermore, two possible experimental designs based on the inverse WVM technique are proposed, which may promote the practical applications of this technique in precision metrology.

DOI
10.7567/1882-0786/ab57bc

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Weak-value measurement (WVM) technique, especially the linear WVM technique, has been proved to be useful in high precision metrology. However, the phase shift to be measured is strictly dominated by the input meter, such as the light wavelength and the space position, which are the basic elements of the linear WVM regime. In this work, an inverse WVM technique using a monochromatic light source is presented to achieve precise estimation of the wavelength-independent phase shift. The theoretical analysis in sensitivity and precision indicates that the inverse WVM technique is more applicable to wavelength-independent phase estimation, as compared to the typical linear WVM technique. Furthermore, two possible experimental designs based on the inverse WVM technique are proposed, which may promote the practical applications of this technique in precision metrology.
We theoretically propose and experimentally demonstrate a modulated weak measurement scheme that permits a precise estimation of the extended phase shift. By choosing the frequency and the total post-selected light intensity as the input and output meter variables, respectively, a linear weak measurement model is established that is especially applicable to precise phase estimation. By performing a time-delay-dependent modulation strategy based on the feedback modulation of the experimental outcome, both the high phase-sensitivity and measurement precision can be retained. We have achieved a precision at the order of ∼10−5 rad that can be effectively retained with an increase in the measured phase.
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 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.
Weak measurement refers to a type of quantum measurement that disturbs the system very little. In the framework of weak measurement, Aharonov, Albert, and Vaidman introduced the concept of postselection and thereby defined the weak value. In recent research, weak-value measurement (WVM) has offered a novel perspective for studying intricate problems in quantum mechanics, leading to many conceptual breakthroughs. More importantly in practice, WVM has shown an unprecedented impact on precision sensing. In this review, we begin by presenting the fundamental theory of WVM based on quantum parameter estimation, from which the effects of weak-value amplification and weak-coupling amplification can be derived. The two effects can significantly improve the precision in various sensing schemes based on WVM. We point out the technical advantages that enable the WVM schemes to outperform the conventional ones under the same measurement conditions. Notably, the capability of information compression is underscored, which is garnering increasing attention in the field of quantum metrology. This review aims to show the possibility for broadening the application of WVM to address more critical problems, and on the other hand, for leveraging its advantages to accomplish tasks that are currently unattainable, such that WVM could play a more important role in the future of precision sensing.
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.