TY - JOUR

T1 - Action formalism for geometric phases from self-closing quantum trajectories

AU - Romito, Alessandro

AU - Shea, Dominic

PY - 2024/8/2

Y1 - 2024/8/2

N2 - 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.

AB - 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.

U2 - 10.1088/1751-8121/ad5e4b

DO - 10.1088/1751-8121/ad5e4b

M3 - Journal article

VL - 57

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 31

M1 - 315303

ER -