Landau-Zener transitions through a pair of higher-order exceptional points

Abstract

Non-Hermitian quantum systems with explicit time dependence are of ever increasing importance. There are only a handful of models that have been analytically studied in this context. Here, a $\mathcal{PT}$-symmetric non-Hermitian $N$-level Landau-Zener type problem with two exceptional points of $N\mathrm{th}$ order is introduced. The system is Hermitian for asymptotically large times, far away from the exceptional points, and has purely imaginary eigenvalues between the exceptional points. The full Landau-Zener transition probabilities are derived, and found to show a characteristic binomial behavior. In the adiabatic limit the final populations are given by the ratios of binomial coefficients. It is demonstrated how this behavior can be understood on the basis of adiabatic analysis, despite the breakdown of adiabaticity that is often associated with non-Hermitian systems.