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Chinese Physics B

Parameter accuracy analysis of weak-value amplification process in the presence of noise*

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

Published Dec 2, 2020• 2 citations
Publisher

Abstract

We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre- and post-selected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.

DOI
10.1088/1674-1056/abcfa0

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We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre- and post-selected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.
Weak measurements, which offer a significant signal enhancement with pre- and post-selections, have proven to be powerful for precision metrology. However, the measured precision of the parameter of interest is always limited by the post-selection-induced probe loss, especially in the presence of technical noise. In this paper, we investigate the optimal pre- and post-selections of weak measurements for precision metrology in the presence of technical noise. While weak measurements apply more generally, we experimentally measure the spin splitting induced by the spin Hall effect of light (SHEL) to approach this issue. The highest measured precision of the spin splitting can be obtained with the post-selected state in the nonlinear intermediate regime. Surprisingly, the pre- and post-selections for the largest weak-value amplification are incapable of estimation of the spin splitting, since the amplified shift is independent of the spin splitting. Our results are not restricted to the SHEL and could be applied to other parameter estimations with weak measurements.
Abstract There was a long-standing postulation that the precision of weak-value based metrology using post-selection and spectral analysis is limited by the resolution of spectrometer. Current proposals releasing this limitation require either initially Gaussian spectrum or giving up the weak value amplification approximation, both of which make extra restrictions and increase the difficulty of implementation. However, we find that this compromise is unnecessary. Rather than the spectral resolution, the precision of weak-value based metrology mainly relies on how accurate we know about the initial pointer state. Moreover, the relation between knowledge of the initial pointer state and the error-ratio of output is provided and numerically simulated. Our results suggest that the detection devices of weak-value based metrology can be significantly simplified, thus made it a more convenient technique for real-world applications.
Weak-value amplification has been successfully used to amplify the sensitivity of small detector signals, which paved the way towards new developments for precise parameter estimation methods. In general, the scheme is based on the idea that, between pre- and postselection, the measured system and the pointer are coupled in such a way that the interaction depends linearly on the coupling constant, the so-called linear regime. In this article, we propose an improvement to this technique that is based on the quadratic regime of interaction to increase the precision of such measurements. We demonstrate that by employing a purely real (imaginary) weak value in this regime, it is possible to decrease considerably the standard deviation of the final pointer observable in the position (momentum) space, when compared to the traditional linear regime, rendering a precision enhancement. By using an all-optical implementation, we obtained experimental data that confirm our theoretical predictions.
By choosing more orthogonality between preselection and postselection states, one can significantly improve the sensitivity in general optical quantum metrology based on the weak-value amplification (WVA) approach. However, increasing the orthogonality decreases the probability of detecting photons and makes the weak measurement difficult, especially when the weak measurement is disturbed by strong noise and the pointer is drowned in noise with a negative-decibel signal-to-noise ratio (SNR). In this article we introduce and numerically evaluate a modified weak-measurement protocol with a temporal pointer, namely, the autocorrelative weak-value amplification (AWVA) approach. Specifically, a small longitudinal time delay (tiny phase shift) $\ensuremath{\tau}$ of a Gaussian pulse is measured by implementing two simultaneous autocorrelative weak measurements under Gaussian white noise with different SNRs. The small quantities $\ensuremath{\tau}$ are obtained by measuring the autocorrelation coefficient of the pulses instead of fitting the shift of the mean value of the probe in the standard WVA technique. Simulation results show that the AWVA approach outperforms the standard WVA technique in the time domain with smaller statistical errors, remarkably increasing the precision of weak measurement under a strong noise background.
Abstract An exact nonlinear model for pointer shift estimation in phase measurement with weak-value amplification is presented, and the necessary assumptions for the linear approximations are discussed. A realistic experimental weak measurement system with pure imaginary weak-value is demonstrated to verify the nonlinear model, and it is shown that our model is effective over a wide dynamic range. In addition, the influence of several common-type technical noise on the uncertainty of pointer shift estimation in momentum space is analyzed theoretically and verified experimentally, in connection with the relationship between the working condition and the signal-to-noise ratio of the system. This close examination of the impact and ramifications of nonlinearity and technical noise in a realistic experimental phase measurement setting employing weak value amplification provides helpful guidance for its invocation in optical interferometric sensor design.
Improving the phase resolution of interferometry is crucial for high-precision measurements of various physical quantities. Systematic phase errors dominate the phase uncertainties in most realistic optical interferometers. Here, we propose and experimentally demonstrate a weak measurement scheme to considerably suppress the phase uncertainties by the direct amplification of the phase shift in optical interferometry. Given an initial ultrasmall phase shift between orthogonal polarization states, we observe a phase amplification effect with a factor of 388. Our weak measurement scheme provides a practical approach to significantly improve the interferometric phase resolution, which is favorable for precision measurement applications.