Topological weak-measurement-induced geometric phases revisited

TL;DR

This paper investigates how weak measurements induce geometric phases, analyzing their dependence on measurement parameters through both analytical derivations and numerical simulations, revealing critical points and stability features.

Contribution

It provides a comprehensive analytical and numerical analysis of weak-measurement-induced geometric phases, including their dependence on measurement strength and the number of measurements, with insights into stability and critical behavior.

Findings

Identification of critical measurement-strength parameters where the phase becomes stochastic

Analytical derivation valid in the quasicontinuous limit

Numerical analysis of finite measurement effects and stability

Abstract

We present an analytical and numerical study of a class of geometric phase induced by weak measurements. In particular, we analyze the dependence of the geometric phase on the winding ($W$) of the polar angle ($\varphi$), upon a sequence of $N$ weak measurements of increased magnitude ($c$), resulting in the appearance of a multiplicity of critical measurement-strength parameters where the geometric phase becomes stochastic. Adding to the novelty of our approach, we not only analyze the weak-measurement induced geometric phase by a full analytic derivation, valid in the quasicontinuous limit ($N \rightarrow \infty$), but also we analyze the induced geometric phase numerically, thus enabling us to unravel the finite-$N$ interplay of the geometric phase with the measurement strength parameter, and its stability to perturbations in the measurements protocol.