Difference Weak Measurement

We propose the difference weak measurement scheme, and illustrate its advantages for measuring small longitude phase-shift in high precision. Compared to the standard interferometry and standard weak measurement schemes, the proposed scheme has much higher resolution in present of various practical imperfections, such as alignment error and light intensity variation error. Moreover, we highlight the advantage of utilizing complex weak value, where its imaginary part can reduce the harmful effect induced by channel decoherence. Finally, we propose closed-loop scenario to solve the narrow dynamic range problem obsessing the current weak measurement schemes. Difference weak measurement scheme simultaneously fulfills the requirements of high precision, wide dynamic range and strong robustness, which makes it a powerfully practical tool for phase-shift measurement and other metrological tasks.