We propose a scheme called the weak measurement with two pointers to measure time delays in a large dynamic range with high precision. One pointer with the light frequency and the other pointer with the postselected probability play a complementary role in the dynamic range of the time-delay estimation. By inserting the main systematic errors, we study the antierror capability and the amplification behavior of two types of pointers, where the pointer with the postselected probability shows stronger robustness against systematic errors and larger working range in general. The proof-of-principle experiments together with the Fisher information metric analysis show that high precision can be effectively retained in a large dynamic range of the time-delay estimation. Further implementation strategy of this scheme is also provided, which may promote the precise estimation of other parameters in a large dynamic range.
We propose a scheme called the weak measurement with two pointers to measure time delays in a large dynamic range with high precision. One pointer with the light frequency and the other pointer with the postselected probability play a complementary role in the dynamic range of the time-delay estimation. By inserting the main systematic errors, we study the antierror capability and the amplification behavior of two types of pointers, where the pointer with the postselected probability shows stronger robustness against systematic errors and larger working range in general. The proof-of-principle experiments together with the Fisher information metric analysis show that high precision can be effectively retained in a large dynamic range of the time-delay estimation. Further implementation strategy of this scheme is also provided, which may promote the precise estimation of other parameters in a large dynamic range.
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.
Optical time delays play a pivotal role in modern physics and practical applications. We propose and experimentally validate a weak measurement system with a double-edge filter, which enables the real-time, high-precision estimation of varying time delays, and the effective suppression of technical noise. In the experiment, the postselected probe light is processed by the double-edge filter, which is formed by a pair of fiber Bragg gratings positioned symmetrically about the center frequency of the probe light, and subsequently detected by photodetectors. The experimental results demonstrate a time-delay precision of 1.66 attoseconds (as) and real-time estimation capability. With a postselection angle of ${10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{rad}$ and the system operating within the most sensitive linear dynamic range, the precision can be further improved to ${10}^{\ensuremath{-}4}$ as. The approach benefits from its high sensitivity and rapid detection, which shows great potential applications in real-time and high-precision time-delay measurements.
Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising result that squeezed coherent states of the pointer can give postselected weak measurements a higher signal-to-noise ratio than standard ones while all standard coherent states cannot, which suggests that raising the precision of weak measurements by postselection calls for the presence of "nonclassicality" in the pointer states. For the second strategy, we show that the quantum Fisher information of postselected weak measurements is generally larger than that of standard weak measurements, even without using the failed postselection events, but the gap can be closed with a proper choice of system state.
In quantum weak measurement, a weak value is a quantity related to a pointer shift of a measuring device which is usually determined by pre- and postselection states. For conventional weak measurement, a single weak-value model has been well addressed in precision metrology of time delay, but it only holds for a narrowband light source. To further improve the measurement accuracy, a broad-spectrum light source is needed. We find that the single weak-value model no longer holds, due to the occurrence of modified preselection states. Here, a multiple weak-value model is established by introducing the modified preselection states in the estimation of time delay. For broad-spectrum light source with 50-nm spectral width, the multiple weak-value scheme enables us to achieve a high resolution of $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}\mathrm{as}$. Our proposed multiple weak-value amplification may have important applications in various fields involving precise time-delay detection.
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.
We derive a general theory for the joint weak measurement with arbitrary postselection and employ it in the time-delay measurement. Especially, we study two special cases, i.e., the balanced and unbalanced postselection regimes, and present an experiment to verify the theoretical results. The experimental results show that under similar conditions, the signal-to-noise ratio of using joint weak measurement scheme remains higher than 12 dB when the measured time-delay is smaller the ultimate precision limit of the weak-value amplification scheme. Moreover, the joint weak measurement scheme is robust to the misalignment errors and the wavelength-dependency of optical components, which indicates its advantage of improving the measurement precision with convenient laboratory equipments.