Topological weak-measurement-induced geometric phases revisited

Graciana Puentes

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arXiv · 2406.00176

Topological weak-measurement-induced geometric phases revisited

Graciana Puentes

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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 ($φ$), 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.

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Graciana Puentes. 2024-06-06. Topological weak-measurement-induced geometric phases revisited. https://arxiv.org/abs/2406.00176

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