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arXiv:1309.5011 · Physical Review X

Technical Advantages for Weak-Value Amplification: When Less Is More

Andrew N. Jordan, Julián Martínez-Rincón, John C. Howell

Published Mar 6, 2014• 303 citations
arXivHTMLPDF

Abstract

``Weak-value amplification,'' an interference effect that was introduced quantum mechanically, but can also be realized using classical electromagnetic waves, uses only a small fraction of the available events to make precise measurements. How can this be? Theorists reveal that weak-value amplification achieves that by funneling all the information into a small fraction of events.

DOI
10.1103/physrevx.4.011031

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``Weak-value amplification,'' an interference effect that was introduced quantum mechanically, but can also be realized using classical electromagnetic waves, uses only a small fraction of the available events to make precise measurements. How can this be? Theorists reveal that weak-value amplification achieves that by funneling all the information into a small fraction of events.
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Weak value amplification is a classical phenomenon that can enhance the sensitivity of a measurement through clever use of interference. The most well-known paradigm of weak value amplification makes use of a Gaussian pulse, which is typical of pulsed laser systems. In this Letter we show that chirped pulses have a great advantage over Gaussians at detecting frequency shifts thanks to the large phase space area that they cover. As an example, we show that within the typical operative parameters of a radar, we can achieve two orders of magnitude amplification of small frequency shifts \emph{on top of the weak value amplification}. This idea could lead to new metrological avenues in the microwave optics domain, and to Doppler radar technology with unprecedented sensitivity.
Abstract Even though weak measurements and weak value amplification (WVA) are founded on the principles of quantum mechanics and quantum measurements, these have found widespread applications in optics due to their inherent origin in wave interference. Besides their use in addressing foundational questions of quantum mechanics or for resolving quantum paradoxes, weak measurements and WVA have thus been used for numerous metrological applications, e.g., quantification of small optical beam displacement, tiny angular rotation, determination of extremely small phase shifts, spectral shifts, unraveling weak fundamental optical effects, improved optical imaging, amplifying weak signal and extracting small physical parameters and so forth. In this review, after providing the mathematical foundation of weak measurement and WVA, some of the metrological applications of weak measurements in the classical optics domain are briefly summarized, and the controversies and debates on the potential advantages of WVA in the estimation and detection of weak signal are discussed, and the interferometric philosophy of WVA is elucidated. The experimental weak measurement and WVA schemes in the domain of quantum optics are also discussed and highlighted the new perspectives and emerging trends of weak measurements in both the classical and quantum optics domain and their prospects in the development of next‐generation ultra‐sensitive optical devices.
The concept of weak measurement and associated weak value amplification has sharpened our understanding of the measurement process in quantum mechanics. Recent experiments show that elastic scattering events in resonance fluorescence experiments can exhibit weak value amplification effect, by post-selecting a particular measurement outcome. In this article, we theoretically analyse the physics behind this amplification process. We show that, in general, weak interaction and the associated weak value amplification in resonance fluorescence can be derived from the wellknown theory of spontaneous emission put forth by Wigner and Weiskopff. Using this theory we show that in the elastic scattering regime of resonance fluorescence, weak value amplification helps in segregating rare events. To our knowledge, weak value amplification has not been applied earlier in the time domain as a potential tool to study rare events.
The ability to manipulate light has allowed scientists to verify fundamental theories of physics and to develop a new generation of technologies that use photons as a primary resource. Recent developments in quantum measurement theory have offered new alternatives to approach some of the most remarkable problems in quantum physics. Consequently, the principles of quantum mechanics have been exploited in the development of quantum technologies such as optical metrology, quantum communication, and quantum information. In recent years, weak measurements and two of its most remarkable variants: weak value amplification and direct measurement, have been developed and are considered important resources for quantum applications. In this paper, we discuss weak measurements and some significant applications of weak values. We elaborate on how distinct forms of weak values are used to observe and amplify small effects or to directly measure the quantum wave function of photons, a crucial task for schemes for quantum communication and quantum information. We also review some of the most recent methods for weak value amplification and direct measurement that our group has developed.
Abstract Weak measurement (WM) based on post-selection is a useful tool for precision metrology due to the ability of amplifying weak physical effects. In this paper, we reveal the underlying mechanism of the amplification in the post-selected WM based on the weak-value amplification (WVA) and the almost balanced weak-values amplification (ABWVA) strategies. We find that the amplification stems from the interference between the local oscillator and signal components which are respectively associated with the initial system state and the state disturbance induced by the weak coupling. The magnitude of the amplification is proportional to the interference strength which is dominated by the post-selection and the coupling strength. Furthermore, our theory can perfectly explain the amplification limit in the WVA strategy and the anomalous amplification in the ABWVA strategy.