Weak-value metrology and shot-noise limited measurements

Thesis (Ph. D.)--University of Rochester. Dept. of Physics and Astronomy, 2016.This thesis contains a subset of the research in which I have participated in during my studies at the University of Rochester. It contains three projects and one overarching theme of weak-value metrology. We start with chapter 1 where we cover the historical background leading up to quantum optics, which we use for precision metrology. We also introduce the weak-value formulation and give examples of metrological implementations for parameter estimation. Chapter 2 introduces two experiments to measure a longitudinal velocity and a transverse momentum kick. We show that weak-value based techniques are shot-noise limited because we saturate the Cramer-Rao bound for the estimator used, and efficient because we experimentally demonstrate there is virtually no loss of Fisher information of the parameter of interest from the discarded events. In Chapter 3, we present a comparison of two experiments that measure a beam deflection. One experiment is a weak-value based technique, while the other is the standard focusing technique. We set up the two experiments in the presence of simulated technical noise sources and show how the weak-value based technique out performs the standard technique in both visibility and in deviation of the transverse momentum kick. Chapter 4 contains work of the exploration of concatenated postselection for weak-value amplification. We demonstrate an optimization and conditions where postselecting on two degrees of freedom can be beneficial to enhance the weak-value amplification