Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems

Abstract

In this work, we study the counterdiabatic (CD) driving scheme and population transfer in pseudo- and antipseudo-Hermitian systems. By discussing the adiabatic condition for non-Hermitian system and the relation between the adiabatic evolution and the real energy spectrum, we derive the CD driving scheme for pseudo- and antipseudo-Hermitian systems. Based on these, we derive the condition that an eigenstate of a non-Hermitian Hamiltonian is self-normalized to guarantee the normalized populations of the bare states in non-Hermitian systems. Our results are illustrated by studying the CD driving for a non-Hermitian three-level system. A scheme to realize the perfect population transfer between the bare states is proposed in the antipseudo-Hermitian case.