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arXiv:2309.06832 · Physical Review A

Dual-recycled interference-based weak value metrology

Zi-Rui Zhong, Weijun Tan, Yue Chen, Qing-Lin Wu

Published Sep 18, 2023• 8 citations
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Abstract

Weak value amplification permits small effects to be measured as observable changes at the sacrifice of power due to postselection. The power-recycling scheme has been proven to eliminate this inefficiency of the rare postselection, thus surpassing the limit of the shot noise and improving the precision of the measurement. However, the improvement is strictly limited by the system setup, especially the system loss. Here we introduce a dual-recycling model based on the interferometric weak-value-based deflection measurement. Two mirrors, the power-recycling mirror and signal-recycling mirror, are placed at the bright and dark port of the interferometer, respectively, creating a composite resonator. The results show that both the power and the signal-to-noise ratio (SNR) are greatly enhanced in a wider range of experimental parameters compared to the power-recycling scheme. This work considerably loosens the constraint of the system setup and further explores the real advantage of weak measurement over traditional schemes.

DOI
10.1103/physreva.108.032608

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Weak value amplification permits small effects to be measured as observable changes at the sacrifice of power due to postselection. The power-recycling scheme has been proven to eliminate this inefficiency of the rare postselection, thus surpassing the limit of the shot noise and improving the precision of the measurement. However, the improvement is strictly limited by the system setup, especially the system loss. Here we introduce a dual-recycling model based on the interferometric weak-value-based deflection measurement. Two mirrors, the power-recycling mirror and signal-recycling mirror, are placed at the bright and dark port of the interferometer, respectively, creating a composite resonator. The results show that both the power and the signal-to-noise ratio (SNR) are greatly enhanced in a wider range of experimental parameters compared to the power-recycling scheme. This work considerably loosens the constraint of the system setup and further explores the real advantage of weak measurement over traditional schemes.
Weak-value-amplification has been proven to be advantageous in the detection of small physical effects. However, most of the data are discarded due to the rare post-selection, resulting in a limitation of precision. Here we introduce a dual-recycling cavity based on the interferometric weak-value-based velocity measurement. By properly inserting two partially transmitting mirrors, both the power and signal-to-noise ratio (SNR) are improved, and the peak of the improvement corresponds to two identical matched mirrors. The dual recycling approach also provides a wider optimal range compared to that of the power-recycling scheme. In addition, the practical consideration is discussed to stabilize the lengths of dual-recycling cavity.
The weak-value-based metrology is very promising and has attracted a lot of attention in recent years because of its remarkable ability in signal amplification. However, it is suggested that the upper limit of the precision of this metrology cannot exceed that of classical metrology because of the low sample size caused by the probe loss during postselection. Nevertheless, a recent proposal shows that this probe loss can be reduced by the power-recycling technique, and thus enhance the precision of weak-value-based metrology. Here we experimentally realize the power-recycled interferometric weak-value-based beam-deflection measurement and obtain the amplitude of the detected signal and white noise by discrete Fourier transform. Our results show that the detected signal can be strengthened by power recycling, and the power-recycled weak-value-based signal-to-noise ratio can surpass the upper limit of the classical scheme, corresponding to the shot-noise limit. This work sheds light on higher precision metrology and explores the real advantage of the weak-value-based metrology over classical metrology.
In a quantum-noise limited system, weak-value amplification using postselection normally does not produce more sensitive measurements than standard methods for ideal detectors: the increased weak value is compensated by the reduced power due to the small postselection probability. Here, we experimentally demonstrate recycled weak-value measurements using a pulsed light source and optical switch to enable nearly deterministic weak-value amplification of a mirror tilt. Using photon counting detectors, we demonstrate a signal improvement by a factor of 4.4±0.2 and a signal-to-noise ratio improvement of 2.10±0.06, compared to a single-pass weak-value experiment, and also compared to a conventional direct measurement of the tilt. The signal-to-noise ratio improvement could reach around six for the parameters of this experiment, assuming lower loss elements.
Weak measurement has garnered widespread interest for its ability to amplify small physical effects at the cost of low detection probabilities. Previous entanglement and recycling techniques enhance postselection efficiency and signal-to-noise ratio (SNR) of weak measurement from distinct perspectives. Here, we incorporate a power-recycling cavity into the entanglement-assisted weak measurement system. We obtain an improvement of both detection efficiency and Fisher information, driven by the combined effects of power cycling and entanglement. Furthermore, we analyze three types of errors: cavity power loss, walk-off errors, and readout errors. The conclusions suggest that entanglement is beneficial in mitigating the effects of cavity losses. Moreover, entanglement exacerbates the walk-off effect caused by recycling, but this detriment can be balanced by proper parameter selection. Additionally, power-recycling can complement entanglement in suppressing readout noise, thus enhancing the accuracy of the measurement results and recovering the lost Fisher information. This work delves deeper into the metrological advantages of weak measurement.
We consider the use of cyclic weak measurements to improve the sensitivity of weak-value amplification precision measurement schemes. Previous weak-value experiments have used only a small fraction of events, while discarding the rest through the process of ``postselection.'' We extend this idea by considering recycling of events which are typically unused in a weak measurement. Here we treat a sequence of polarized laser pulses effectively trapped inside an interferometer using a Pockels cell and polarization optics. In principle, all photons can be postselected, which will improve the measurement sensitivity. We first provide a qualitative argument for the expected improvements from recycling photons, followed by the exact result for the recycling of collimated beam pulses, and numerical calculations for diverging beams. We show that beam degradation effects can be mitigated via profile flipping or Zeno reshaping. The main advantage of such a recycling scheme is an effective power increase, while maintaining an amplified deflection.