Adiabatic Shortcut In Quantum-classical Corresponding Theory

The adiabatic evolution process is crucial in the theory and practice of quantum mechanics.However,maintaining quantum processes adiabatic by controlling the evolution of parameters requires a long time to reach.At the same time,there are often situations of decoherence,noise,loss and so on in the evolution process.Therefore,finding a shortcut for accelerating the adiabatic process has attracted extensive attention in the quantum system driven by a time-dependent Hamiltonian.In this paper,we study the adiabatic shortcut methods in quantum-classical corresponding theory.And how to transform the adiabatic quantum shortcut process into its classical correspondence is discussed.It's not only a new way of thinking about the classical adiabatic shortcut,but also a feasible method for simulating the quantum adiabatic shortcut via a classical system.This paper is divided into 4 chapters which the third chapter is our main work.Firstly,chapter 1 introduces the needed background to study this topic.Next,chapter 2 establishes the significance of this paper on the basis of the first chapter.The concepts of adiabatic evolution,quantum Berry phase,classical geometric angle and three main methods for quantum adiabatic shortcut are presented in detail.In Chapter 3,we introduce the quantum-classical corresponding theory,and transform the quantum adiabatic shortcut into the classical version for two-and three-level atoms.The related theory indicates that additional coupling between the oscillators can be used to accelerate the adiabatic evolution of coupled oscillator.In addition,we find that quantum-classical corresponding theory can apply to couter-adiabatic driving Hamiltonian.In a word,we construct the theoretical framework of the adiabatic shortcut in classical systems and obtain the exact results in specific examples.Finally,the conclusions and discussion are given.