Weak measurement with the peak-contrast-ratio pointer

Abstract

Weak measurement as a nonperturbative theory has been shown to be powerful in the fundamentals of quantum mechanics and high-precision metrology, in which the pointer is of great importance to parameter estimation and experimental design. In this work, we find that under the conditions of weak coupling and Gaussian meter, the probability distribution after the postselection follows a bimodal function and the peak contrast ratio (PCR) can be applied as a special pointer, which is different from the shift of mean value. To obtain the PCR, only two values corresponding to the two peaks in the distribution function are required. We theoretically present the relation of the PCR and parameters to be estimated, and then demonstrate it in an experiment. Weak measurement with the PCR pointer has the advantages of reducing the requirements of the apparatus and suppressing noise, which also provides a heuristic approach for studying weak measurement when the weak value is very large.