Adaptive correction of phase estimation with time based on weak measurement.

An adaptive correction algorithm is demonstrated based on weak measurement, which introduces a feedback and an additional interaction to the system and can dynamically adjust the operating point in accordance with the condition of the estimated phase change. Two schemes, fast adaptive correction and slow adaptive correction, are proposed for different conditions of the modulation device. Fast adaptive correction scheme can realize a real-time correction and maintain the high sensitivity. Slow adaptive correction scheme, as a supplement, can correct the distortion of the measured parameter by changing the measuring period. These two schemes are useful for high precision phase estimation with time in modern physics and practical applications, including, but not limited to, timing synchronization, accurate distance measurement, and gravity wave detection. Moreover, we discuss the deviation of the adaptive correction for considering system noise in practical measurement.