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arXiv:1301.5846 · Physical Review Letters

Measuring Ultrasmall Time Delays of Light by Joint Weak Measurements

Grégory Strübi, Christoph Bruder

Published Feb 22, 2013• 134 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.110.083605

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We derive a general theory for the joint weak measurement with arbitrary postselection and employ it in the time-delay measurement. Especially, we study two special cases, i.e., the balanced and unbalanced postselection regimes, and present an experiment to verify the theoretical results. The experimental results show that under similar conditions, the signal-to-noise ratio of using joint weak measurement scheme remains higher than 12 dB when the measured time-delay is smaller the ultimate precision limit of the weak-value amplification scheme. Moreover, the joint weak measurement scheme is robust to the misalignment errors and the wavelength-dependency of optical components, which indicates its advantage of improving the measurement precision with convenient laboratory equipments.
Abstract Weak measurement is a novel technique for parameter estimation with higher precision. In this paper we develop a general theory for the parameter estimation based on a weak measurement technique with arbitrary post-selection. The weak-value amplification model and the joint weak measurement model are two special cases in our theory. Applying the developed theory, time-delay estimation is investigated in both theory and experiments. The experimental results show that when the time delay is ultra-small, the joint weak measurement scheme outperforms the weak-value amplification scheme, and is robust against not only misalignment errors but also the wavelength dependence of the optical components. These results are consistent with theoretical predictions that have not been previously verified by any experiment.
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.
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.
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 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.