Signal-recycled weak measurement for ultrasensitive velocity estimation* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11674120 and 11734015), and the Fundamental Research Funds for the Central Universities of the Ministry of Education of China (Grant Nos. CCNU19TS074 and CCNU18CXTD01).

Abstract

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.