Enhancing Phase Sensitivity in Mach–Zehnder Interferometers for Arbitrary Input StatesSupported by the National Natural Science Foundation of China (Grant Nos. 11875231 and 11935012), the National Key Research and Development Program of China (Grant Nos. 2017YFA0304202 and 2017YFA0205700), and the Fundamental Research Funds for the Central Universities (Grant No. 2018FZA3005).

Abstract

To enhance the phase sensitivity of Mach–Zehnder interferometers, we use a tunable phase shift before the light beams are injected into the interferometer. The analytical result of the optimal phase shift is obtained, which only depends on the initial input states. For a non-zero optimal phase shift, the phase sensitivity of the interferometers in the output ports is always enhanced. We can achieve this enhancement for most states, including entangled and mixed states. The optimal phase shift is exhibited in three examples. Compared to previous methods, this scheme provides a general way to improve phase sensitivity and could find wide applications in optical phase estimations.