量子力学中的Jaynes-Cummings模型态演化分析(胡丽红)

量子力学中的Jaynes-Cummings模型态演化分析专业：光信息科学与技术学号：20080810090205

学生姓名：胡丽红指导老师：熊狂炜

摘要

Jaynes—Cummings(J-C)模型是由单个二能级原子（或分子）与一个单模量子化光场组成的相互作用系统，反映的是单原子和单模辐射场之间的相互作用的两能级量子力学模型。它基于偶极近似和旋转波近似，着重处理电磁场与原子的近共振作用。J-C模型形式简单，是个精确可解的量子系统，并蕴含了丰富的物理内涵，能广泛的应用到许多领域中去，是量子光学、激光物理、核磁共振等问题中常用的一种模型。

本文主要通过两种不同的方法：待定系数法和矩阵法对Jaynes—Cummings 模型的态演化进行理论计算。主要考虑在共振情况下，我们求得态函数系数的变化图。在光场初始态处于真空态或相干态等不同情况下，系统会呈现出不同的量子特征如：真空拉比震荡、崩塌与复原现象。为了进一步完善光场与原子相互作用的量子理论，本文还介绍了几种推广的Jaynes—Cummings模型。

关键词：Jaynes—Cummings模型；态演化；共振

The state evolution analysis of Jaynes-Cummings model in

quantum mechanics

Abstract

Jaynes-Cummings (J-C) model is up to the individual two-level atoms (or molecular) and a single-mode optical field of quantization interaction system.It reflects a two-level quantum mechanical model of the interaction between a single atom and the Single-mode radiation field. It is based on dipole approximation and the rotating wave approximation, mainly deal with the near resonance effect between the electromagnetic field and the atomic. J-C model is simple in form and it is a quantum systems that can be solved precisely.It contains rich connotation of physical, which can widely used to many fields.It’s a model commonly used in the study of quantum optics, laser physics, nuclear magnetic resonance (NMR) and many other problems. This paper mainly uses two different methods: the method of undetermined coefficients and matrix method to perform the theoretical calculation of the state evolution of the Jaynes-Cummings mode. Mainly considering in the condition of resonance, We can obtain the variation diagrams of the coefficients to the corresponding normal function. In the different initial states of light field like in vacuum state or coherent states and so on the different cases, the system will be present different quantum characteristics such as vacuum rabbi shocks, collapse and restoration phenomenon. In order to further perfect the quantum theory of the interaction between the light field and the atoms , this paper introduces several kinds of promotion Jaynes-Cummings models.

Keywords: Jaynes-Cummings model; State evolution; resonanc

目录

引言 (1)

第一章JAYNES-CUMMINGS模型 (2)

1.1J-C模型的相关介绍 (2)

1.1.1 标准J-C模型的物理内涵，重要性和局限性 (2)

1.1.2 标准J-C模型的线性与非线性推广 (3)

1.2J-C模型的基本原理 (4)

第二章用待定系数法计算J-C模型的态函数随时间演化规律 (8)

第三章用矩阵法计算J-C模型的态函数随时间演化规律 (17)

3.1光与原子的相互作用-缀饰原子态 (17)

3.1.1 光场中原子的波函数 (17)

3.1.2 互作用哈密顿量的对角化 (19)

3.1.3 缀饰原子态 (22)

3.2光与原子的相互作用J-C模型 (25)

3.2.1 量子拉比振荡 (25)

3.2.2 单模自发发射 (28)

3.2.3崩塌和复原 (29)

第四章几种推广的J-C模型 (33)

4.1双光子J-C模型 (33)

4.2 型三能级原子与光场R AMAN相互作用 (33)