Topological weak-measurement-induced geometric phases revisited

Abstract

We present an analytic and numerica 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 φ, 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 quasi-continuous limit (N → ∞), 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.