LAUSR

Abstract The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are symmetric with respect to the initial and final states. Here we extend time-dependent perturbation theory into the non-Hermitian realm and consider the transitions in a stationary Hermitian system, described by a self-adjoint Hamiltonian H ˆ 0 , induced by a time-dependent non-Hermitian interaction f ( t ) H ˆ 1 . In the weak interaction (perturbative) limit, the transition probabilities generally turn out to be asymmetric for exchange of initial and final states. In particular, for a temporal shape f ( t ) of the perturbation with one-sided Fourier spectrum, i.e. with only positive (or negative) frequency components, transitions are fully unidirectional, a result that holds even in the strong interaction regime. Interestingly, we show that non-Hermitian perturbations can be tailored to be transitionless, i.e. the perturbation leaves the system unchanged as if the interaction had not occurred at all, regardless the form of H ˆ 0 and H ˆ 1 . As an application of our results, we provide important physical insights into the asymmetric (chiral) behavior of dynamical encircling of an exceptional point in two- and three-level non-Hermitian systems.