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Applied Physics Letters

Retaining high precision and sensitivity for an extended range of phase estimation via modulated weak measurement

Zhaoxue Li, Jiangdong Qiu, Linguo Xie, Lan E Luo, Xiong Liu, Zhiyou Zhang, Changliang Ren, Jinglei Du

Published Nov 5, 2018• 14 citations
Publisher

Abstract

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.

DOI
10.1063/1.5055652

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Applied Physics Letters•Mar 18, 2019•25 citations
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.
Phase estimation has attracted much attention in the field of sensing, where weak measurement has become an effective solution for the study of small physical quantities because of its anomalous amplification property. However, it is difficult for weak measurement to cope with large low-frequency noise signals in the environment due to its extremely narrow linear range, which makes the extension of weak measurement to practical applications a challenging task. In order to solve this issue, we propose and experimentally verify a phase demodulation scheme based on weak measurement, which solves the problem of working point offset caused by the noise through artificially introducing a high-frequency carrier and performing demodulation operations on the output light. The experimental results show that the scheme can improve the signal-to-noise ratio by 17 dB compared to standard weak measurement and ensures low distortion in phase demodulation. Moreover, the scheme is not limited to a specific modulation depth, which greatly improves the robustness of the scheme.
Pre- and post-selected (PPS) measurement, especially the weak PPS measurement, has been proved to be a useful tool for measuring extremely tiny physical parameters. However, it is difficult to retain both the attainable highest measurement sensitivity and precision with the increase of the parameter to be measured. Here, a modulated PPS measurement scheme based on coupling-strength-dependent modulation is presented with the highest sensitivity and precision retained for an arbitrary coupling strength. This idea is demonstrated by comparing the modulated PPS measurement scheme with the standard PPS measurement scheme in the case of unbalanced input meter. By using the Fisher information metric, we derive the optimal pre- and post-selected states, as well as the optimal coupling-strength-dependent modulation without any restriction on the coupling strength. We also give the specific strategy of performing the modulated PPS measurement scheme, which may promote practical application of this scheme in precision metrology.
Weak measurement enables the amplification of weak physical effects via post-selection and has become an important tool in precision optical metrology; however, conventional schemes based on mean-pointer shifts suffer from response saturation, limited linear range, and stringent stability requirements. Here, we propose and experimentally demonstrate a weak-measurement scheme based on spectral-interference trough shifts, where the zero-intensity points of the post-selected spectrum act as the measurement pointer, establishing an analytical mapping between the trough displacement and the target phase or time delay. Theoretical analysis shows that, under detector resolution limits, the measurement resolution depends solely on the frequency of extinction point and is independent of weak-value singular amplification or bias-phase modulation, thereby maintaining high sensitivity while avoiding pointer saturation. Experiments demonstrate that the trough-shift scheme achieves significantly better agreement between measured and theoretical sensitivities than biased weak measurement and provides a stable linear response without additional bias-compensation structures, reaching a minimum resolvable phase variation at the 10−7 level. Moreover, the approach intrinsically supports multi-period traceable measurements and exhibits strong robustness against intensity fluctuations and spectral distortions, offering a promising route toward high-sensitivity, large-dynamic-range, and stable weak measurement-based optical sensing.
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 High-precision temperature measurement with adjustable operating range is investigated and experimentally demonstrated based on weak measurement in the frequency domain. The operating range of measurement is precisely modulated by introducing a dynamic extra time delay to the post-selection pumped by a femtosecond laser. By choosing appropriate nonlinear materials and the attenuation, the resolution of the optimized extra time delay can be improved by two orders of magnitude over that of a traditional phase delay compensator. Considering the influence of noise in the experiment, the highest precision of 8.03 × 10 −7 °C can be achieved by using a currently available spectrometer. Moreover, the average sensitivity can reach to 38 nm/°C. Taking advantage of the high precision and adjustable operating range, the proposed method has great potential applications in high-precision temperature measurements.
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.