Action formalism for geometric phases from self-closing quantum trajectories

• URL: http://arxiv.org/abs/2312.14760v1
• Date: Fri, 22 Dec 2023 15:20:02 GMT
• Title: Action formalism for geometric phases from self-closing quantum trajectories
• Authors: Dominic Shea and Alessandro Romito
• Abstract summary: We study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter.
• Score: 55.2480439325792
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: When subject to measurements, quantum systems evolve along stochastic quantum trajectories that can be naturally equipped with a geometric phase observable via a post-selection in a final projective measurement. When post-selecting the trajectories to form a close loop, the geometric phase undergoes a topological transition driven by the measurement strength. Here, we study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We utilize a stochastic path integral that enables the analysis of rare self-closing events using action methods and develop the formalism to incorporate the measurement-induced geometric phase therein. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter. Moreover, the inclusion of Gaussian corrections in the vicinity of the most probable self-closing trajectory quantitatively changes the transition point in agreement with results from numerical simulations of the full set of quantum trajectories.

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