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Applied Physics Letters

Adaptive estimation of time-varying phase via weak value amplification

Chunhui Shi, Qi Song, Hongjing Li, Xiaorui Tan, Zhongyuan Luo, Jingzheng Huang, Guihua Zeng

Published Mar 18, 2024• 5 citations
Publisher

Abstract

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.

DOI
10.1063/5.0187786

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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.
Extending quantum sensing to time-varying parameter estimation is a potential and challenging task in practical application. To achieve this goal, we propose an adaptive method to estimate an unknown time-varying parameter through light-intensity split detection and the insertion of reference phases in the weak measurement. Theoretical analysis and numerical simulation are applied to illustrate the feasibility and practical applications of our method. The results demonstrate that the method has adjustable sensitivity and linear dynamic range, and is robust to nonideal measurement conditions. Moreover, we analyze the precision of our method and show that its precision limit can surpass the standard quantum limit and approach the Heisenberg scaling when using a squeezed light of optimal Gaussian state.
Weak measurement is employed to measure faint signals due to its capability to amplify detection results above technical noise. However, achieving high amplification effects requires accurate adjustment to the experimental system. Estimating unknown time-varying phases, accurately estimating phases, and sensitively perceiving phase changes pose challenges, demanding the system to continuously remain at the appropriate working range. To address this issue, we propose a neural network-based adaptive weak measurement scheme via single-channel light intensity detection. Through machine learning calibrating the experimental system, the reference phase can be dynamically and accurately adjusted, accommodating time-varying phase changes and ensuring the system operates optimally. Compared with traditional dual-channel weak measurement systems, the scheme reduces experimental complexity. Meanwhile, by accurately adjusting the reference phase, the scheme has higher sensitivity and estimation precision compared to the non-modulated scheme. We validate the effectiveness of the scheme in estimating the period and stochastic time-varying phase. The proposed method highlights the advancement of machine learning in weak measurement systems and can also be applied to other quantum-enhanced measurement schemes.
Abstract High precision phase estimation is at the core of modern physics and practical applications. We investigate a method for high precision phase estimation via inserting a reference state which enables weak measurement technique to be used in wide dynamic range. A reference phase is introduced artificially to offset the time delay between preselection state and reference state. The sensitivity of measured phase and the linear dynamic range are controllable by adjusting reference phase. Moreover, an arbitrary postselection in measurement is applicable by choosing appropriate reference phase. This method has merits of controllable sensitivity and wide dynamic range, which shows great potential practical applications in high precision phase measurement.
Abstract Reliable detection of weak phase signals under significant channel loss and complex noise environments is a crucial step for practical applications of optical integrated communication and sensing systems. In this letter, we propose and experimentally demonstrate an enhanced long-distance weak signal transmission method assisted by weak measurement. Performing heterodyne detection and light intensity compensation on two nearly symmetric post-selected paths, the method enables real-time estimation of a time-varying phase while maintaining robustness against technical noises proportional to light intensity or photon number, detector common-mode noise, and significant attenuation over long-distance transmission. Experimental results indicate a potential phase sensitivity at the level of 10 −8 rad even with a signal light intensity attenuation of 48.1 dB. Potentially, combining the adaptive adjustment strategy, the method may provide a viable solution in remote weak signal detection and extraction, thereby contributing to optical integrated communication and sensing.
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.
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.