Majorana Representation for the Mutilevel Adiabatic-impluse Model

The Landau-Zener-Stückelberg-Majorana (LZSM) transition, which denotes the transition between energy levels at an avoided crossing, has drawn much attention since it was first studied by Landau, Zener, Stückelberg and Majorana in 1932. It has been studied for many years while it is still worthwhile to be studied. In this work, we study the dynamics and stokes phase in multi-level LZSM transition. We reviewed the method given by Zener and Majorana. By comparing the method given by Zener and Majorana in the simulation of the two-level and three-level system’s transition probability, we verified the validity of the adiabatic-impulse model. Then we derive the transition matrix for the multi-level system to predict the multi-level system’s transition probability and Stokes phase and consequently give out the simulation of transition probability and Stokes phase associated with these multi-level transitions. Our results provide a method to study multi-level LZSM interferometry and applications in studying the parameters of multilevel systems.