Adiabatic Shortcut In Nonlinear Two-Level System

Quantum adiabatic evolution is not only an important subject in quantum mechanics theory,but also plays an important role in quantum information processing and quantum computing schemes.How to keep the eigenstate probability of each energy constant during the evolution process has become an important research direction.Generally,it requires a long evolution time to keep the adiabaticity of a quantum system.However,in practical applications,the evolution time should be as short as possible to avoid decoherence effect.Therefore,how to balance the fidelity of the target state and the time accumulated decoherence has become a central issue for the application of the adiabatic quantum processing.To address this issue,Berry proposed a“transitionless quantum driving”(TQD)method based on reverse engineering to accelerate adiabatic evolution in a short time.By canceling the effects of the off-diagonal elements in the time-dependent Hamiltonian under the adiabatic basis,this method provides an natural way to accelerate the adiabatic evolution without any perturbations.Consequently,this method rapidly meets the increasing interest in the quantum information and computation and other methods to accelerate adiabatic process,such as Lewis-Riesenfeld invariant,are also developed.In this paper,we study the adiabatic shortcuts of nonlinear two-level systems by adding a linear anti-adiabatic field to the nonlinear LZ protocol based on the idea of a quantum-free transition-driven scheme.This thesis consists of four parts,of which the third chapter is our main work.The first and second chapters briefly introduce the background and significance of this research topic,and review the research history of quantum mechanics,quantum informatics,geometric phases,and quantum adiabatic shortcuts.The concepts and principles of quantum adiabatic theorem,geometric phase and quantum adiabatic shortcuts are introduced in detail.The third chapter studies the transitionless quantum driving theory of nonlinear systems.The transitionless quantum drive theory is applied to the two-level Landau–Zener model to realize the transitionless quantum drive of a two-level linear system.The results show that by using the TQD method,the adiabatic shortcuts can be perfectly realized in a linear two-level system.Since it is difficult to pass the analytic solution of the eigenvalues and eigenstates of the nonlinear two-level system,the linear TQD scheme is used to achieve the adiabatic shortcuts when the nonlinear strength is weak.It is discussed how the additional TQD Hamiltonian affects the nonlinear dynamics when the nonlinear strength is stronger than the critical point.The last chapter summarizes and prospects the content of this article.