Geometric modulation of transition and survival intensities in non-Hermitian systems

Abstract

The time evolution of non-Hermitian systems is generally nonunitary. Dynamics governed by time-dependent non-Hermitian Hamiltonians lead to a variety of novel phenomena, one of which is state amplification or suppression induced by the complex Berry phase. Here, we extend the framework of geometric modulation to multi-level systems and show that both transition and survival intensities can be modulated. We apply our theory to the non-Hermitian Landau-Zener (LZ) problem. First, we show that, in the half-LZ problem, both the transition and survival probabilities exhibit nonreciprocity due to the complex Berry phase. In the non-Hermitian standard LZ problem, only the survival intensity is known to exhibit nonreciprocity, whereas the transition intensity does not. However, the physical origin of this nonreciprocal behavior remains unclear. In this work, we show that the nonreciprocity originates from the complex Berry phase.