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Physical Review A

Experimental investigation of high-efficiency weak-value amplification of nonunitary evolution

Zhipeng Li, Yi‐Tao Wang, Shang Yu, Wei Liu, Meng Yu, Yuan-Ze Yang, Zhaoan Wang, Nai‐Jie Guo, Xiaodong Zeng, Jian‐Shun Tang, Chuan‐Feng Li, Guang‐Can Guo

Published Jul 20, 2022• 2 citations
Publisher

Abstract

High-sensitivity metrology plays an important role in parameter estimation, and weak-value amplification is a significant tool used to enhance sensitivity. However, the efficiency of weak-value amplification is always affected by the postselection probability and meter loss. In this article we report on the realization of a device for weak interaction that realizes the nonunitary evolution based on a spatial light modulator and applies the weak-value amplification of nonunitary evolution. The weak-value amplification of nonunitary evolution can achieve efficiency nearly ninefold that of unitary evolution experimentally under specific settings, because of the quadratic relation between the meter shift and the norm of the weak value $|{A}_{w}|$. This work demonstrates the superiority of nonunitary evolution in weak-value amplification, provides an experimental scheme of weak interaction for other forms of nonunitary evolution, and possesses the potential to be combined with other techniques for higher efficiency.

DOI
10.1103/physreva.106.012608

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High-sensitivity metrology plays an important role in parameter estimation, and weak-value amplification is a significant tool used to enhance sensitivity. However, the efficiency of weak-value amplification is always affected by the postselection probability and meter loss. In this article we report on the realization of a device for weak interaction that realizes the nonunitary evolution based on a spatial light modulator and applies the weak-value amplification of nonunitary evolution. The weak-value amplification of nonunitary evolution can achieve efficiency nearly ninefold that of unitary evolution experimentally under specific settings, because of the quadratic relation between the meter shift and the norm of the weak value ∣Aw∣|{A}_{w}|∣Aw​∣. This work demonstrates the superiority of nonunitary evolution in weak-value amplification, provides an experimental scheme of weak interaction for other forms of nonunitary evolution, and possesses the potential to be combined with other techniques for higher efficiency.
We discuss interferometric parameter estimation of the amplitude, instead of the phase, via weak value amplification. The considered weak interaction introduces modulation on the amplitude of the wave function; therefore, the two-party state experiences a nonunitary evolution. With the same pre- and postselection states as those of original weak value amplification, a much larger anomalous amplification factor can be attained. The shift in the intensity profile at the dark port and the signal-to-noise ratio for the parameter of interest get further amplified by the weak value, compared to phase-based weak value amplification. Although the nonunitary evolution introduces loss, more information about the parameter of interest can be extracted. Thus the weak value amplification is extended to measurement of amplitude and nonunitary processes. We also discuss possible applications of this idea for precisely measuring tiny rotations or enhancing the image contrast of transparent objects.
The weak-value amplification is extensively considered in precision metrology in order to achieve a higher sensitivity. Despite the practical benefits in amplifying small physical quantities, its metrological advantage still arouses a broad debate due to the low postselection probability of success. In this paper, by employing the quantum Fisher information metric, we show that the precision of estimating an unknown parameter can be improved by introducing a precoupling process with properly chosen interaction operators. We point out this result is credible for both real and imaginary weak values. By tracking the meter wave functions, we find this enhancement of estimation precision comes from a precoupling induced modulation of the meter wave function, thus the most sensitive regime with respect to the parameter is reached. In addition, the estimation error is investigated by considering the difference between the theoretical and estimated value. The analysis suggests that this kind of error can be effectively suppressed by averaging the estimations resulted from different initial meter states. These results are finally illustrated by an exact numerical simulation where the advantages of our proposal are displayed by the comparison to the standard weak-value amplification scheme.
Weak-value amplification has been used to enhance the sensitivity of a linear detector response to small interaction parameters. However, the generation of a large weak value gives rise to reduction in postselection probability, which restricts the feasibility of the weak-value amplification technique. Recently, theoretical works have shown that the use of entanglement can increase the efficiency of the weak-value amplification method. Specifically, it is proven that by entangling nnn particles of a system, the maximum postselection probability scales quadratically with nnn [Pang, Dressel, and Brun, Phys. Rev. Lett. 113, 030401 (2014)]. In this work, we demonstrate an experimental realization of entanglement-assisted weak-value amplification in a photonic system, which shows that importing quantum entanglement can indeed improve the efficiency of weak-value amplification.
Weak value amplification has been applied to various small physical quantities estimation, however there still lacks a practical feasible protocol to amplify ultra-small longitudinal phase, which is of importance in high precision measurement. Very recently, a different amplification protocol within the framework of weak measurements is proposed to solve this problem, which is capable of measuring any ultra-small longitudinal phase signal that conventional interferometry tries to do. Here we experimentally demonstrate this weak measurements amplification protocol of ultra-small longitudinal phase and realize one order of magnitude amplification in the same technical condition, which verifies the validity of the protocol and show higher precision and sensitivity than conventional interferometry. Our results significantly broaden the area of applications of weak measurements and may play an important role in high precision measurements.
Achieving higher sensitivity is an earnest purpose for precision metrology. As a response to this goal, the weak-value amplification approach has been developed for measuring ultrasmall physical effects, realizing sensitivity that had never been reached before. Encouraged by the successes, many efforts have been devoted to obtain ultimate sensitivity of weak-value amplification. However, the benefit would be easily compromised in practice, because the cost of significant reduction on signal intensity leads to an ultralow signal-to-noise ratio. In this work, we bridge this gap by proposing an alternative weak-value amplification approach, which provides sensitivity several orders of magnitude higher than the standard approach while being compatible with practical imperfections. In the proof-of-principle experiment of measuring longitudinal phase change in time domain, sensitivity up to $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ attosecond is exemplified. Our approach can be applied to measure other small parameters with extremely high sensitivity, providing a method for future precision metrology.
Abstract Weak-value amplification employs postselection to enhance the measurement of small parameters of interest. The amplification comes at the expense of reduced success probability, hindering the utility of this technique as a tool for practical metrology. Following other quantum technologies that display a quantum advantage, we formalize a quantum advantage in the success probability and present a scheme based on non-linear collective Hamiltonians that shows a super-extensive growth in success probability while simultaneously displaying an extensive growth in the weak value. We propose an experimental implementation of our scheme.