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arXiv:1102.4902 · Physical Review A

Ultrasensitive phase estimation with white light

Chuan‐Feng Li, Xiao-Ye Xu, Jian‐Shun Tang, Jin‐Shi Xu, Guang‐Can Guo

Published Apr 19, 2011• 61 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.83.044102

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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.
Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimation. Since many quantities can be converted to phase signal, it is thus interesting and important to consider measuring ultra-small longitudinal phase shifts by using weak measurement. Here, we propose and experimentally demonstrate a novel weak measurement amplification based ultra-small longitudinal phase estimation, which is suitable for polarization interferometry. We realize one order of magnitude amplification measurement of small phase signal directly introduced by Liquid Crystal Variable Retarder and show its robust to finite visibility of interference. Our results may find important applications in high-precision measurements, such as gravitational waves detection.
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.
Standard weak measurement (SWM) has been proved to be a useful ingredient for measuring small longitudinal phase change (LPC) [X. Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C. F. Li, and Guang-Can Guo, Phys. Rev. Lett. 111, 033604 (2013)]. In these SWM proposals, the working regime is selected where the relative phase between orthogonal components is zero, and the LPC can be detected by measuring the shift of the meter state, i.e., the time and frequency domain, which are conjugated observables. Here, we show that an extra bias phase can significantly improve the sensitivity of measuring LPC. This bias phase can be introduced by a precoupling process. Together with a special postselection, a destructive interference can be observed in both the time and frequency domain. Using a broadband source, this conjugated destructive interference occurs in a regime less than 1 as, while the related spectral shift reaches hundreds of THz, resulting in sensitivity outperforming SWM by two orders of magnitude.
Recently, weak measurements were used to measure small effects that are transverse to the propagation direction of a light beam. Here we address the question of whether weak measurements are also useful for measuring small longitudinal phase shifts. We show that standard interferometry greatly outperforms weak measurements in a scenario involving a purely real weak value. However, we also present an interferometric scheme based on a purely imaginary weak value, combined with a frequency-domain analysis, which may have the potential to outperform standard interferometry by several orders of magnitude.
We propose to use weak measurements away from the weak-value amplification regime to carry out precision measurements of time delays of light. Our scheme is robust to several sources of noise that are shown to only limit the relative precision of the measurement. Thus, they do not set a limit on the smallest measurable phase shift, contrary to standard interferometry and weak-value-based measurement techniques. Our idea is not restricted to phase-shift measurements and could be used to measure other small effects using a similar protocol.
Achieving higher sensitivity is an earnest purpose for precision metrology. As a response to this goal, the weak-value amplification approach has been developed for measuring ultrasmall physical effects, realizing sensitivity that had never been reached before. Encouraged by the successes, many efforts have been devoted to obtain ultimate sensitivity of weak-value amplification. However, the benefit would be easily compromised in practice, because the cost of significant reduction on signal intensity leads to an ultralow signal-to-noise ratio. In this work, we bridge this gap by proposing an alternative weak-value amplification approach, which provides sensitivity several orders of magnitude higher than the standard approach while being compatible with practical imperfections. In the proof-of-principle experiment of measuring longitudinal phase change in time domain, sensitivity up to $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ attosecond is exemplified. Our approach can be applied to measure other small parameters with extremely high sensitivity, providing a method for future precision metrology.