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arXiv:1803.08644 · Physical Review A

Robust interferometry against imperfections based on weak value amplification

Chen Fang, Jingzheng Huang, Guihua Zeng

Published Jun 11, 2018• 14 citations
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Abstract

Optical interferometry has been widely used in various high-precision applications. Usually, the minimum precision of an interferometry is limited by various technical noises in practice. To suppress such kinds of noises, we propose a scheme which combines the weak measurement with the standard interferometry. The proposed scheme dramatically outperforms the standard interferometry in the signal-to-noise ratio and the robustness against noises caused by the optical elements' reflections and the offset fluctuation between two paths. A proof-of-principle experiment is demonstrated to validate the amplification theory.

DOI
10.1103/physreva.97.063818

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Optical interferometry has been widely used in various high-precision applications. Usually, the minimum precision of an interferometry is limited by various technical noises in practice. To suppress such kinds of noises, we propose a scheme which combines the weak measurement with the standard interferometry. The proposed scheme dramatically outperforms the standard interferometry in the signal-to-noise ratio and the robustness against noises caused by the optical elements' reflections and the offset fluctuation between two paths. A proof-of-principle experiment is demonstrated to validate the amplification theory.
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.
We propose a scheme called difference weak measurement, and we illustrate its advantages for measuring a small longitude phase shift in high precision. Compared to the standard interferometry and standard weak measurement schemes, the proposed scheme has a much higher resolution in the presence of various practical imperfections, such as alignment error and light intensity variation error. Moreover, we highlight the advantage of utilizing a complex weak value, where its imaginary part can reduce the harmful effect induced by channel decoherence. Finally, we propose a closed-loop scenario to solve the narrow dynamic range problem that exists in the current weak measurement schemes. The difference weak measurement scheme simultaneously fulfills the requirements of high precision, wide dynamic range, and strong robustness, which makes it a powerfully practical tool for phase-shift measurement and other metrological tasks.
Improving the phase resolution of interferometry is crucial for high-precision measurements of various physical quantities. Systematic phase errors dominate the phase uncertainties in most realistic optical interferometers. Here, we propose and experimentally demonstrate a weak measurement scheme to considerably suppress the phase uncertainties by the direct amplification of the phase shift in optical interferometry. Given an initial ultrasmall phase shift between orthogonal polarization states, we observe a phase amplification effect with a factor of 388. Our weak measurement scheme provides a practical approach to significantly improve the interferometric phase resolution, which is favorable for precision measurement applications.
An effective approach for general measurement based on weak value amplification using non-Gaussian broadband light sources is demonstrated. This scheme can reduce the difficulty of preparing the measurement apparatus and correcting the systematic error caused by the imperfection of device's wave function, thus making the weak-value amplification scheme more convenient and robust for practical field applications. The influence of several common noise sources in a general application based on weak value amplification is analyzed theoretically and examined experimentally. A purely imaginary weak-value phase measurement system is considered for the noise model verification experimentally. In this we show how to optimize the precision of measurement in a unique solution that takes into account the interplay between precision and uncertainty, and explicate the ramifications of such a compromising and pragmatic approach.
Phase estimation has attracted much attention in the field of sensing, where weak measurement has become an effective solution for the study of small physical quantities because of its anomalous amplification property. However, it is difficult for weak measurement to cope with large low-frequency noise signals in the environment due to its extremely narrow linear range, which makes the extension of weak measurement to practical applications a challenging task. In order to solve this issue, we propose and experimentally verify a phase demodulation scheme based on weak measurement, which solves the problem of working point offset caused by the noise through artificially introducing a high-frequency carrier and performing demodulation operations on the output light. The experimental results show that the scheme can improve the signal-to-noise ratio by 17 dB compared to standard weak measurement and ensures low distortion in phase demodulation. Moreover, the scheme is not limited to a specific modulation depth, which greatly improves the robustness of the scheme.
We propose to use weak measurements away from the weak-value amplification regime to carry out precision measurements of time delays of light. Our scheme is robust to several sources of noise that are shown to only limit the relative precision of the measurement. Thus, they do not set a limit on the smallest measurable phase shift, contrary to standard interferometry and weak-value-based measurement techniques. Our idea is not restricted to phase-shift measurements and could be used to measure other small effects using a similar protocol.