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arXiv:1306.4768 · Physical Review Letters

Phase Estimation with Weak Measurement Using a White Light Source

Xiao-Ye Xu, Yaron Kedem, Kai Sun, Lev Vaidman A, Chuan-Feng Li, Guang‐Can Guo

Published Jul 17, 2013• 304 citations
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Abstract

We report results of a high precision phase estimation based on a weak measurement scheme using a commercial light-emitting diode. The method is based on a measurement of the imaginary part of the weak value of a polarization operator. The imaginary part of the weak value appeared due to the measurement interaction itself. The sensitivity of our method is equivalent to resolving light pulses of the order of a attosecond and it is robust against chromatic dispersion.

DOI
10.1103/physrevlett.111.033604

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We report results of a high precision phase estimation based on a weak measurement scheme using a commercial light-emitting diode. The method is based on a measurement of the imaginary part of the weak value of a polarization operator. The imaginary part of the weak value appeared due to the measurement interaction itself. The sensitivity of our method is equivalent to resolving light pulses of the order of a attosecond and it is robust against chromatic dispersion.
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.
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 the standard weak measurement, the imaginary part of the weak value is usually constructed with a specific pre- or postselection state to cause a large shift of the frequency-domain pointer. In this paper we demonstrate that the purely real weak value can also shift the frequency-domain pointer when using a broad-spectrum light source. The reason for the deflection of the frequency-domain pointer in this scheme is that the postselection probability of different frequency is different, which causes the rearrangement of the amplitudes of the spectrum. The weak measurement with real weak value can be used for the estimation of time delay, and it is found that it can reach the same high resolution as the standard weak measurement in some sensitive regions.
Weak-value measurement (WVM) technique, especially the linear WVM technique, has been proved to be useful in high precision metrology. However, the phase shift to be measured is strictly dominated by the input meter, such as the light wavelength and the space position, which are the basic elements of the linear WVM regime. In this work, an inverse WVM technique using a monochromatic light source is presented to achieve precise estimation of the wavelength-independent phase shift. The theoretical analysis in sensitivity and precision indicates that the inverse WVM technique is more applicable to wavelength-independent phase estimation, as compared to the typical linear WVM technique. Furthermore, two possible experimental designs based on the inverse WVM technique are proposed, which may promote the practical applications of this technique in precision metrology.
Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimations. Since many physical quantities can be converted into phase signals, it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement. Here, we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation, which is suitable for polarization interferometry. We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference. Besides, we analyze the effect of magnification error which is never considered in the previous works, and find the constraint on the magnification. Our results may find important applications in high-precision measurements, e.g., gravitational wave detection.
An improvement of the scheme by Brunner and Simon [Phys. Rev. Lett. 105, 010405 (2010)] is proposed in order to show that quantum weak measurements can provide a method to detect ultrasmall longitudinal phase shifts, even with white light. By performing an analysis in the frequency domain, we find that the amplification effect will work as long as the spectrum is large enough, irrespective of the behavior in the time domain. As such, the previous scheme can be notably simplified for experimental implementations.