Population transfer at exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields

We study the population transfer between resonance states for a time-dependent loop around exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields. Exceptional points are well-suited for population transfer mechanisms, since a closed loop around these in parameter space commutes eigenstates. We address the question how shape and duration of the dynamical parameter loop affects the transferred population, in order to optimize the latter. Since the full quantum dynamics of the expansion coefficients is time-consuming, we furthermore present an approximation method, based on a $2\times 2$ matrix.