2023/12/22 by D. G. Shea, Shea, Dominic, Alessandro Romito +1
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2312.14760
openalex publication_date 2023/12/22 · openalex created_date 2023/12/26 · openalex updated_date 2026/07/28
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.