Signal-recycled weak measurement for ultrasensitive velocity estimation

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.