Regular Article

Anomalous dynamical evolution and nonadiabatic level crossing in exactly solvable time-dependent quantum systems

¹ Center of Theoretical Physics, College of Physics, Sichuan University, Chengdu 610065, P.R. China
² School of Material Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R. China

^a Corresponding author: lixiangcen@scu.edu.cn

Received: 19 July 2019
Received in final form: 6 September 2019
Published online: 24 October 2019

Abstract

The anomalous dynamical evolution and the crossing of nonadiabatic energy levels are investigated for exactly solvable time-dependent quantum systems through a reverse-engineering scheme. By exploiting a typical driven model, we elucidate the peculiarities of its dynamics with anomalous behavior: the evolution of the adiabatic states and of the nonadiabatic ones exhibits opposite behavior from their representative vectors evolving from a parallel state to an antiparallel state; the nonadiabatic level crossing is identified as a necessary consequence since the crossing point corresponds exactly to the perpendicular point of the two vectors in the parametric space. In the light of these results, we show that various driven models with anomalous dynamical evolution can be designed and they offer alternative protocols for the quantum state control.