Interference-based weak-value amplification effects in post-selected weak measurement

Weak measurement (WM) based on post-selection is a useful tool for precision metrology due to the ability of amplifying weak physical effects. In this paper, we reveal the underlying mechanism of the amplification in the post-selected WM based on the weak-value amplification (WVA) and the almost balanced weak-values amplification (ABWVA) strategies. We find that the amplification stems from the interference between the local oscillator and signal components which are respectively associated with the initial system state and the state disturbance induced by the weak coupling. The magnitude of the amplification is proportional to the interference strength which is dominated by the post-selection and the coupling strength. Furthermore, our theory can perfectly explain the amplification limit in the WVA strategy and the anomalous amplification in the ABWVA strategy.

Automated summary

This study investigates the amplification mechanism in weak measurement based on post-selection, revealing that amplification stems from the interference between the local oscillator and signal components. The amplification magnitude is proportional to the interference strength dominated by post-selection and coupling strength. The theory explains the amplification limit in the weak-value amplification strategy and the anomalous amplification in the almost balanced weak-values amplification strategy.