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Research in Optical Sciences

Precision metrology with weak measurements

Lijian Zhang, Animesh Datta, Ian A. Walmsley

Published Jan 1, 2014• 1 citation
Publisher

Abstract

We develop a framework for the precision metrology with weak measurements, and use it to compare the precisions of different measurement strengths. In particular, we show a weak-measurement scheme that can achieve the Heisenberg limit.
DOI
10.1364/qim.2014.qth4a.2

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Weak values and measurements have been proposed as a means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology. Namely, (Q1) Does postselection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyze these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.
Weak measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of a reduced rate of acquiring data, which leads to an increasing uncertainty to determine the level of meter shift. From this point of view, a number of theoretical works have suggested that weak measurements cannot improve the precision, or even damage the metrology information due to the post-selection. In this review, we give a comprehensive analysis of the weak measurements to justify their positive effect on prompting measurement precision. As a further step, we introduce two modified weak measurement protocols to boost the precision beyond the standard quantum limit. Compared to previous works beating the standard quantum limit, these protocols are free of using entangled or squeezed states. The achieved precision outperforms that of the conventional method by two orders of magnitude and attains a practical Heisenberg scaling up to n=106 photons.
This paper explores the application of quantum entanglement, specifically using squeezed states and entangled atom interferometry, to enhance the precision of weak gravitational field measurements. We delve into the theoretical framework of quantum metrology, highlighting the limitations imposed by the Standard Quantum Limit (SQL) and how entanglement can circumvent these limits, approaching the Heisenberg Limit. A detailed methodology is presented, outlining the creation and manipulation of entangled atomic states for gravitational field sensing. We present simulated results demonstrating a significant improvement in measurement sensitivity compared to classical approaches. The discussion contextualizes these findings within existing research, emphasizing the potential for developing advanced quantum sensors for applications ranging from fundamental physics research to geophysical exploration. We conclude by outlining future research directions, including addressing decoherence effects and exploring the scalability of these quantum metrology techniques.
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.