Geometric phases along quantum trajectories

LUDMILA VIOTTI,; FERNANDO C LOMBARDO; ANA LAURA GRAMAJO; ROSARIO FAZIO

Quantum

Quantum Journal

Año: 2023 vol. 7 p. 1029 - 1052

2521-327X

A monitored quantum system undergoing acyclic evolution of the parameters governingits Hamiltonian accumulates a geometric phasethat depends on the quantum trajectory fol-lowed by the system on its evolution. Thephase value will be determined both by theunitary dynamics and by the interaction of thesystem with the environment. Consequently,the geometric phase will acquire a stochas-tic character due to the occurrence of randomquantum jumps. Here we study the distribu-tion function of geometric phases in monitoredquantum systems and discuss when/if dier-ent quantities, proposed to measure geometricphases in open quantum systems, are represen-tative of the distribution. We also consider amonitored echo protocol and discuss in whichcases the distribution of the interference pat-tern extracted in the experiment is linked tothe geometric phase. Furthermore, we unveil,for the single trajectory exhibiting no quantumjumps, a topological transition in the phase ac-quired after a cycle and show how this criti-cal behavior can be observed in an echo pro-tocol. For the same parameters, the densitymatrix does not show any singularity. We il-lustrate all our main results by consideringa paradigmatic case, a spin-1/2 immersed intime-varying a magnetic field in the presence ofan external environment. The major outcomesof our analysis are however quite general anddo not depend, in their qualitative features, onthe choice of the model studied.