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Journal of Modern Optics

Enhancing the performance of ultrasensitive velocity weak measurement via dual recycling

Zi-Rui Zhong, Yue Chen, Weijun Tan, Xia-Lin Su, Xiangming Hu, Qing-Lin Wu

Published Apr 23, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1080/09500340.2025.2496713

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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.
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 shown its superiority in measurement of small physical effects. Here we introduce a signal-recycled weak-value-based velocity measurement strategy to decrease the attenuation of detected photons during the post-selection. Like the power-recycled scheme, we can improve the number of detected photons and signal-to-noise ratio of velocity by forming a cavity. However, optimal improvements of number of detected photons and signal-to-noise ratio cannot be obtained simultaneously in our signal-recycled scheme owing to the walk-off effect. Furthermore, we find that the reflected light is relatively strong compared with the power-recycled scheme, which may increase the collection-detection efficiency in prospective relevant experiment.
Weak measurement has been proven to amplify the detection of changes in meters while discarding most photons due to the low probability of postselection. Previous power-recycling schemes enable the failed postselection photons to be repeatedly selected, thus overcoming the inefficient postselection and increasing the precision of detection. In this study, we focus on the polarization-based weak value angular-velocity measurement and introduce three cyclic methods to enhance the accuracy of detecting time shifts in a Gaussian beam: power-recycling, signal-recycling, and dual-recycling schemes. By incorporating one or two partially transmitting mirrors into the system, both the power and the signal-to-noise ratio of the detected light are substantially enhanced. Compared to nonpolarization schemes, polarization-based approaches offer several advantages, including lower optical loss, unique cyclic directions, and a wider optimal region. These features effectively reduce crosstalk among different light paths and theoretically eliminate the walk-off effect, thus yielding improvements in both theoretical performance and application.
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.