Analysis of adiabatic processes in multilevel N-pod quantum systems from the perspective of Riemannian geometry

Abstract: The analysis of problems related to nonlocalized population transfer between quantum levels requires nontraditional mathematical approaches. Here we study the processes of irremovable nonadiabatic transitions in a (N- 1)-dimensional system of completely degenerate so-called dark states, taking as a base model multilevel N-pod systems. It is shown that quantum dynamics of the dark states due to the operator of nonadiabatic coupling can be described in terms of the Riemannian parallel transport of their geometric counterparts in the space of control parameters. The results of mathematical modeling of nonadiabatic effects, presented in the paper for the case of four-level systems interacting with three laser fields (tripod systems), demonstrate full agreement between the quantum and geometric approaches. These results are of interest for experimental and laboratory plasma research and atomic and laser physics. Graphical abstract: [Figure not available: see fulltext.]