Dynamical approach to shortcuts to adiabaticity for general two-level non-Hermitian systems

¹ Center for Quantum Sciences and School of Physics, Northeast Normal University - Changchun 130024, China
² Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University - Changchun 130024, China

^(a) E-mail: shenhz458@nenu.edu.cn (corresponding author)

Received: 19 March 2023
Accepted: 15 May 2023

Abstract

In this Letter, we apply a class of general two-level non-Hermitian Hamiltonians whose off-diagonal elements are neither equal nor conjugate of each other to study the dynamical approach to shortcut to adiabaticity which is based on engineering the Hamiltonian and dynamical properties of the system to remove any unwanted probability amplitude or implant the desired probability amplitude. Using the special characteristics that one of the eigenvalues of the general two-level non-Hermitian Hamiltonian is real and the other is complex, we can decay (amplify) the population exponentially in the undesired (desired) eigenstate, and maintain the conservation of probability amplitude of the other eigenstate. Applying this approach to general two-level non-Hermitian systems, we find that the efficient population transfer can be achieved by our method, which works even in almost instantaneous manner and has a lower cost compared with the common approach of shortcut to adiabaticity.