Eigenstates swapping induced by encircling an exceptional point of the non-hermitian hamiltonian

We propose a scheme to swap the eigenstates of a parameterized non-Hermitian two-state system by encircling an exceptional point (EP) in the parameter space. It is well-known that, in the case of a non-Hermitian system encircling an EP, even if the adiabatic condition is satisfied, the evolution is not necessarily an adiabatic process. As a result, the swapping, which was expected initially, is recognized to be challenging to observe. In this report, we present a scheme to induce the swapping and, for that purpose, we establish the conditions for the non-Hermitian system to evolve adiabatically. The key to inducing the swapping lies in the use of the path including the real axis in the Riemann sheet. Additionally, we propose the polarization convertor using this scheme.