Geometric phase in weak measurements

Graciana Puentes

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 ($φ$), 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 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.

J H Hannay

Jean-Marc Lévy-Leblond

Graciana Puentes

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.

Graciana Puentes

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 ( 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 makes a |π| discrete jump. 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.

Arno Böhm