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arXiv:2412.07440

Realization of joint weak measurement in classical optics using optical beam shifts

Ritwik Dhara, Shyamal Guchhait, Sarkar, Meghna, Swain Ashutosh, Niladri Modak, Nirmalya Ghosh

Published Dec 10, 2024• 0 citations
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Abstract

Quantum weak measurements became extremely popular in classical optics to amplify small optical signals for fundamental interests and potential applications. Later, a more general extension, joint weak measurement has been proposed to extract weak value from a joint quantum measurement. However, the detection of joint weak value in the realm of classical optics remains less explored. Here, using the polarization-dependent longitudinal and transverse optical beam shift as a platform, we experimentally realize the quantum joint weak measurement in a classical optical setting. Polarization states are cleverly pre and post-selected, and different single and joint canonical position-momentum observables of the beam are experimentally extracted and subsequently analyzed for successful detection of complex joint weak value. We envision that this work will find usefulness for gaining fundamental insights on quantum measurements and to tackle analogous problems in optics.

DOI
10.48550/arxiv.2412.07440

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Quantum weak measurements became extremely popular in classical optics to amplify small optical signals for fundamental interests and potential applications. Later, a more general extension, joint weak measurement has been proposed to extract weak value from a joint quantum measurement. However, the detection of joint weak value in the realm of classical optics remains less explored. Here, using the polarization-dependent longitudinal and transverse optical beam shift as a platform, we experimentally realize the quantum joint weak measurement in a classical optical setting. Polarization states are cleverly pre and post-selected, and different single and joint canonical position-momentum observables of the beam are experimentally extracted and subsequently analyzed for successful detection of complex joint weak value. We envision that this work will find usefulness for gaining fundamental insights on quantum measurements and to tackle analogous problems in optics.
Quantum weak measurements became extremely popular in classical optics to amplify small optical signals for fundamental interests and potential applications. Later, as a more general extension, joint weak measurement has been proposed to extract the weak value from a joint quantum measurement. However, unlike traditional weak measurements, the detection of a joint weak value in the realm of classical optics remains less explored. Here, using the polarization-dependent longitudinal and transverse optical beam shift as a platform, we experimentally realize a classical optical analog of the quantum joint weak measurement. Polarization states are cleverly pre- and postselected, and different single and joint canonical position-momentum observables of the beam are experimentally extracted and subsequently analyzed for successful detection of the complex joint weak value. We envision that this work will find usefulness for gaining fundamental insights on quantum measurements and to tackle analogous problems in optics.
Background: Weak measurement involves weak coupling between the system and the measuring device (pointer) enables large amplification and high precision measurement of small physical parameters. The outcome of this special measurement procedure involving nearly mutually orthogonal pre- and post-selection of states in such weakly interacting systems leads to weak value that can become exceedingly large and lie outside the eigenvalue spectrum of the measured observable. This unprecedented ability of weak value amplification of small physical parameters has been successfully exploited for various metrological applications in the optical domain and beyond. Even though it is a quantum mechanical concept, it can be understood using the classical electromagnetic theory of light and thus can be realized in classical optics. Objective: Here, we briefly review the basic concepts of weak measurement and weak value amplification, provide illustrative examples of its implementation in various optical domains. The applications involve measuring ultra-sensitive beam deflections, high precision measurements of angular rotation, phase shift, temporal shift, frequency shift and so forth, and expand this extraordinary concept in the domain of nano-optics and plasmonics. Methods: In order to perform weak value amplification, we have used Gaussian beam and spectral response as the pointer subsequently. The polarization state associated with the pointer is used as pre and post-selection device. Results: We reveal the weak value amplification of sub-wavelength optical effects namely the Goos-Hänchen shift and the spin hall shift. Further, we demonstrate weak measurements using spectral line shape of resonance as a natural pointer, enabling weak value amplification beyond the conventional limit, demonstrating natural weak value amplification in plasmonic Fano resonances and so forth. The discussed concepts could have useful implications in various nano-optical systems to amplify tiny signals or effects. Conclusion: The emerging prospects of weak value amplification towards the development of novel optical weak measurement devices for metrological applications are extensively discussed.
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.
We describe how the notion of optical beam shifts (including the spatial and angular Goos-Hänchen shift and Imbert-Federov shift) can be understood as a classical analogue of a quantum measurement of the polarization state of a paraxial beam by its transverse amplitude distribution.Under this scheme, complex quantum weak values are interpreted as spatial and angular shifts of polarized scalar components of the reflected beam.This connection leads us to predict an extra spatial shift for beams with a radially-varying phase dependance.Contents 1. Introduction 2 2. Weak quantum measurement 4 3.The analogy between beam shifts and quantum measurement 5 4. The case of radial and azimuthally varying pointer phase 9 5. Discussion
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure directly in practice (for instance, in optics-a common testing ground for this technique-strong photon-photon interactions would be needed to implement an appropriate von Neumann interaction). Here we derive a general, experimentally feasible, method for extracting these joint weak values from correlations between single-particle observables.
Weak measurement is a potentially powerful tool for studying post-selected quantum systems. The original approach to weak measurement requires a different von Neumann interaction between the quantum system and measurement pointer for weak values of every different observable. When studying weak values of properties of more than one particle, which is necessary for studying entanglement, these interactions can range from difficult to impossible to implement experimentally. For example, the measurement of properties on a pair of optical photons requires a strong Kerr-like nonlinearity at the two-photon level. In a recent work, we described a new method for extracting weak values of operators that can be expressed as products of two local, single-particle operators by studying the correlations in experimentally feasible local, single-particle measurements. In the present work, that theoretical approach is generalized so that weak values of products of N local, single-particle operators can be extracted from the correlations in N single-particle measurements.