Effects of nonlinearity and technical noise on weak-value amplified phase measurement

Abstract

An exact nonlinear model for pointer shift estimation in phase measurement with weak-value amplification is presented, and the necessary assumptions for the linear approximations are discussed. A realistic experimental weak measurement system with pure imaginary weak-value is demonstrated to verify the nonlinear model, and it is shown that our model is effective over a wide dynamic range. In addition, the influence of several common-type technical noise on the uncertainty of pointer shift estimation in momentum space is analyzed theoretically and verified experimentally, in connection with the relationship between the working condition and the signal-to-noise ratio of the system. This close examination of the impact and ramifications of nonlinearity and technical noise in a realistic experimental phase measurement setting employing weak value amplification provides helpful guidance for its invocation in optical interferometric sensor design.