Eur. Phys. J. D (2017) 71: 14
https://doi.org/10.1140/epjd/e2016-70525-6

Regular Article

Non-Hermitian shortcut to adiabaticity of two- and three-level systems with gain and loss

¹ Department of Applied Physics and Key Laboratory for Quantum Information and Quantum Optoelectronic Devices of Shaanxi Province, Xi’an Jiaotong University, Xi’an 710049, P.R. China
² School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, P.R. China

^a e-mail: liguanqiang@sust.edu.cn

Received: 23 August 2016
Received in final form: 10 November 2016
Published online: 19 January 2017

Abstract

Achieving effectively adiabatic dynamics in finite time is a ubiquitous goal in virtually all fields of modern physics. So-called shortcuts to adiabaticity refer to a set of methods and techniques that allow us to obtain in a short time the same final state that would result from an adiabatic, infinitely slow process. In this paper we generalized the non-Hermitian shortcut method to the situation of the unbalanced gain and loss. We found that the ratio between the gain and loss can control the transfer time and may become a new freedom to speed up the adiabatic transfer process. By using two-level Landau-Zener model and Allen-Eberly model and three-level stimulated Raman adiabatic passage, we investigated the transfer processes and obtained the analytical results about the final transfer time, which are related with the parameters of the corresponding systems. It is pointed out that these processes can be implemented in many systems experimentally such as coupled optical waveguides.