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Applied Physics Letters

Simultaneously precise estimations of phase and amplitude variations based on weak-value amplification

Lan E Luo, Linguo Xie, Jiangdong Qiu, Xinxing Zhou, Xiong Liu, Zhaoxue Li, Yu He, Zhiyou Zhang, Handong Sun

Published Mar 18, 2019• 25 citations
Publisher

Abstract

In this paper, we theoretically and experimentally present a precision method to simultaneously estimate the phase and amplitude variations of light based on the weak-value amplification. We demonstrate that the imaginary and real components of the weak-value correspond to the amplification of the phase and amplitude variations, respectively. If both the phase and the amplitude are varied, the phase measurement using the imaginary weak-value is not influenced by the amplitude shift and the amplitude measurement using the real weak value is not influenced by the phase shift. Thus, the tiny changes of the phase and amplitude of light can be obtained simultaneously with different post-selections, and the measurement precision reaches ∼10−6 rad. These findings may be favorable for highly sensitive optical polarization-dependent effects, including optical activity and magneto-optic effects.

DOI
10.1063/1.5083995

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In this paper, we theoretically and experimentally present a precision method to simultaneously estimate the phase and amplitude variations of light based on the weak-value amplification. We demonstrate that the imaginary and real components of the weak-value correspond to the amplification of the phase and amplitude variations, respectively. If both the phase and the amplitude are varied, the phase measurement using the imaginary weak-value is not influenced by the amplitude shift and the amplitude measurement using the real weak value is not influenced by the phase shift. Thus, the tiny changes of the phase and amplitude of light can be obtained simultaneously with different post-selections, and the measurement precision reaches ∼10−6 rad. These findings may be favorable for highly sensitive optical polarization-dependent effects, including optical activity and magneto-optic effects.
In this paper, a weak measurement scheme with double pointers (mean value shift and intensity shift of the post-selected light) is presented to simultaneously measure the tiny polarization change (phase and amplitude) of light in a single experimental apparatus. Furthermore, rather than using charge-coupled-device (CCD) to measure the pointer shift, we use the two-channel photoreceiver combined with lock-in amplifier (LIA) to measure the intensities of a split-Gaussian mode in this work. In this way, we introduce two intensity contrast ratios (ICRs) as special pointers to characterize the mean value and intensity shifts. As a result, the measurement precision of the polarization rotation is on the order of magnitude of 10−7rad\,10^{-7}rad10−7radin the experiment. These findings provide a distinctive insight into the weak measurement and have important implications for the accurate measurement of complex optical parameters.
The real-time estimation of a time-varying phase is of great importance in several fields. In order to estimate a time-varying phase with high precision and sensitivity, we propose and experimentally demonstrate an adaptive phase estimation method via weak value amplification by splitting the light into sensing path and monitoring path. In the proposed method, the phase shift can be amplified, an adjustable sensitivity and linear dynamic range can be obtained through the insertion of the reference phase, and a full-range phase estimation could be realized via an appropriate adjustment strategy. Furthermore, detectors with a higher resolution could be selected to detect weak signal by the adjustment of attenuation. Potentially, the phase estimation precision of about 10−8 rad could be achieved with the available equipment.
In this letter, we propose a precision method for phase estimation based on the weak-value amplification (WVA) technique using a monochromatic light source. The anomalous WVA significantly suppresses the technical noise with respect to the intensity difference signal induced by the phase delay when the post-selection procedure comes into play. The phase measured precision of this method is proportional to the weak-value of a polarization operator in the experimental range. Our results compete well with the wide spectrum light phase weak measurements and outperform the standard homodyne phase detection technique.
We propose a modified difference weak measurement scheme that permits precise measurements of the magneto-optical Faraday effect. By making normalized difference processing for a set of post-selected light intensity, a linear-response regime with a significant weak-value amplification effect is established. In the proof-of-principle experiment, we measure the magnetic intensity using the polarization system and achieve precision at the order of ∼10−7 T. Our scheme can be applied to measure other magneto-optical effects, providing a method for future ultra-sensitive sensing and metrology in magnetic physics.
Using the profound interferometric philosophy of weak-value amplification, we propose a simple, general, and robust polarization method for the amplification and quantification of small magnitudes of all possible polarization anisotropy effects in a single experimental embodiment. The approach is experimentally realized by introducing a weak coupling between the polarization degree of freedom of light and the path degree of freedom in a Mach-Zehnder interferometer in the presence of a weak anisotropy effect. Real and imaginary weak-value amplifications of different polarization anisotropy effects are manifested as characteristic changes in the relevant Stokes vector elements at the exit port of the interferometer, which follow orthogonal trajectories in the Poincar\'e sphere. The proof-of-concept experiment demonstrates that by using this scheme, one can faithfully extract and quantify an anisotropy parameter that is smaller than the typical sensitivity of measurement of a given Stokes parameter of a traditional polarimeter by a large weak-value amplification factor. This opens up the possibility of a sample measuring weak-value polarimeter for studying the rich variety of fundamental optical effects and for materials characterization and precision metrology.
We theoretically propose and experimentally demonstrate a modulated weak measurement scheme that permits a precise estimation of the extended phase shift. By choosing the frequency and the total post-selected light intensity as the input and output meter variables, respectively, a linear weak measurement model is established that is especially applicable to precise phase estimation. By performing a time-delay-dependent modulation strategy based on the feedback modulation of the experimental outcome, both the high phase-sensitivity and measurement precision can be retained. We have achieved a precision at the order of ∼10−5 rad that can be effectively retained with an increase in the measured phase.