运动二能级原子与光场纠缠特性的研究
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摘要
量子纠缠不仅对了解量子力学的基本概念有着重要的意义,而且它更是一种有用的信息“资源”。它在量子隐行传态、量子密集编码、量子密钥分配以及在量子计算的加速、量子纠错、防错等方面都起着关键作用。在实际问题中,原子与场的耦合系数可能是变化的,因此,探究含运动的二能级原子与光场的纠缠特性有一定的创新性和学术价值。
本文应用量子信息熵理论,把标准的Jaynes-Cummings模型扩展到考虑原子运动和不同场模结构以及耦合系数为高斯型的状况,主要对二能级运动原子与光场的纠缠特性进行了研究,并与原子静止时的情况进行了比较。论文主要包括以下五个部分:
第一部分主要介绍了量子纠缠的概念、发展史及其在量子信息中的应用价值,并阐述了本文的选题背景、意义和主要工作。
第二部分介绍了纠缠理论和压缩真空场及其特点,并将场与原子相互作用的理论模型-标准Jaynes-Cummings推广到原子运动的状况,建立了含原子运动的J-C模型的一般动力学基础,为下面的研究工作奠定了理论基础。
第三部分可分为以下三个方面:
1.用量子信息理论研究具有原子运动的双光子Jaynes-Cummings模型中运动原子与光场的纠缠特性。结果表明:当运动原子的场模结构参数p取值较小时,系统的纠缠度不具有周期振荡特性;当p取值较大时,系统的纠缠度有明显的周期振荡特性,且振荡周期是原子静止时的两倍;当在运动原子处于基态或激发态时,系统处于消纠缠状态;当运动原子处于相干叠加态时,原子才与场发生纠缠。
2.用全量子理论研究了原子运动时两纠缠二能级原子与单模真空场相互作用体系的纠缠特性。研究结果表明:当双原子初始处在EPR态时,三体纠缠量最大值与理想W纠缠态纠缠量相同。场模结构参数p影响三体纠缠量随时间演化的振荡特性,随着p值的逐渐增大,三体纠缠量的平均值将越来越小,体系三体纠缠态也会逐渐趋于消纠缠状态。
3.研究了当耦合系数为高斯型分布时运动原子与压缩真空场的纠缠特性,讨论了原子垂直于腔轴的运动、原子初态、压缩参数r对纠缠度的影响。结果发现:原子速度的增大会使原子与光场的有效作用时间变短,纠缠度也将很快达到最大值。压缩参数r对纠缠度的演化曲线有明显的调制作用,当压缩参数取适当值(如r =2)时,系统可长久停留在最大纠缠态、无消纠缠态或持续地处于消纠缠态。
Quantum entanglement not only has important significance in knowing the basic concept of quantum mechanics, but also is one of useful information resources. It is a key problem in quantum teleportation, quantum dense coding, quantum key distribution, quantum computation, quantum error correction and error prevention. In actual problem, the coupling coefficient of atom and field is possibly variational, therefore, to some extent, it is valuable in considering the entangled properties of motorial atom and cavity field.
This paper will expand standard Jaynes-Cummings model to the condition of considering atomic motion, the parameter of field-mode, Gaussian coupling, and mostly investigate the entangled properties of motorial two-level atom and cavity field, and Compare the atoms which are static with that of motion. This paper contants the following five parts:
In the first part, the paper will mainly introduce the quantum entanglement’s concept, development history and applying value in quantum communication, and then elaborate the paper’s subject-selecting background, significance and main work. In the second part, we will present quantum theory, squeezing vacuum field and its character, then expand standard Jaynes-Cummings model to the condition of considering atomic motion, the basic dynamic model with atomic motion will be established, as the theoretical basic of the work in the below.
The third part is made of three facets.
1. The entangled properties of motorial atom and field in the two-photon Jaynes-Cummings model with atomic motion are studied by using the quantum information theory. It is shown that:(1) When the parameter p of the field model structure with atomic motion is smaller, the entanglement of system is not provided with the characteristic of periodic oscillations, when the value of p is greater, the entanglement of system is obviously provided with the characteristic of periodic oscillations, the oscillation period is as much again as atom is resting . when motorial atom is prepared in ground state or excited state ,the system is in the disentangled state; when motorial atom is prepared in coherent superpositions states, the entanglement occurs between motorial atom and field.
2. We investigate the entanglement properties of two entangled two-level atoms that interact resonantly with a single-mode vacuum field with atomic motion using quantum theory. The results show that if the two atoms are prepared in maximum entangled (EPR) state initially, the maximum of three-body entanglement measure is equated with the perfect three-body W entangled state. The parameter of field-mode structure p influences the time evolution oscillation property of three-body entanglement measure, with the gradually increasing of p, the average of three-body entanglement measure will gradually decrease, three-body entangled state will tend to disentangled state inch by inch.
3. The properties of the entanglement between squeezing vacuum state field and moving atom with Gaussian coupling are studied. The influence of atomic motion perpendicularity to the axes of resonant cavity , the initial states of atom, the squeezing parameter on entanglement degree are discussed. The results show that: with the increase of atomic velocity, effective interaction time of the atom and field will shorten, the entanglement degree will also reach the maximum quickly. The squeezing parameter r have a obvious role of concocting the evolution curve of degree of entanglement, if the squeezing parameter is take appropriate value(such as r =2), the system of quantum state will be maximally entangled state for a long time, without disentangled-free state or disentangled state, and the degree of entanglement is stationary.
本文应用量子信息熵理论,把标准的Jaynes-Cummings模型扩展到考虑原子运动和不同场模结构以及耦合系数为高斯型的状况,主要对二能级运动原子与光场的纠缠特性进行了研究,并与原子静止时的情况进行了比较。论文主要包括以下五个部分:
第一部分主要介绍了量子纠缠的概念、发展史及其在量子信息中的应用价值,并阐述了本文的选题背景、意义和主要工作。
第二部分介绍了纠缠理论和压缩真空场及其特点,并将场与原子相互作用的理论模型-标准Jaynes-Cummings推广到原子运动的状况,建立了含原子运动的J-C模型的一般动力学基础,为下面的研究工作奠定了理论基础。
第三部分可分为以下三个方面:
1.用量子信息理论研究具有原子运动的双光子Jaynes-Cummings模型中运动原子与光场的纠缠特性。结果表明:当运动原子的场模结构参数p取值较小时,系统的纠缠度不具有周期振荡特性;当p取值较大时,系统的纠缠度有明显的周期振荡特性,且振荡周期是原子静止时的两倍;当在运动原子处于基态或激发态时,系统处于消纠缠状态;当运动原子处于相干叠加态时,原子才与场发生纠缠。
2.用全量子理论研究了原子运动时两纠缠二能级原子与单模真空场相互作用体系的纠缠特性。研究结果表明:当双原子初始处在EPR态时,三体纠缠量最大值与理想W纠缠态纠缠量相同。场模结构参数p影响三体纠缠量随时间演化的振荡特性,随着p值的逐渐增大,三体纠缠量的平均值将越来越小,体系三体纠缠态也会逐渐趋于消纠缠状态。
3.研究了当耦合系数为高斯型分布时运动原子与压缩真空场的纠缠特性,讨论了原子垂直于腔轴的运动、原子初态、压缩参数r对纠缠度的影响。结果发现:原子速度的增大会使原子与光场的有效作用时间变短,纠缠度也将很快达到最大值。压缩参数r对纠缠度的演化曲线有明显的调制作用,当压缩参数取适当值(如r =2)时,系统可长久停留在最大纠缠态、无消纠缠态或持续地处于消纠缠态。
Quantum entanglement not only has important significance in knowing the basic concept of quantum mechanics, but also is one of useful information resources. It is a key problem in quantum teleportation, quantum dense coding, quantum key distribution, quantum computation, quantum error correction and error prevention. In actual problem, the coupling coefficient of atom and field is possibly variational, therefore, to some extent, it is valuable in considering the entangled properties of motorial atom and cavity field.
This paper will expand standard Jaynes-Cummings model to the condition of considering atomic motion, the parameter of field-mode, Gaussian coupling, and mostly investigate the entangled properties of motorial two-level atom and cavity field, and Compare the atoms which are static with that of motion. This paper contants the following five parts:
In the first part, the paper will mainly introduce the quantum entanglement’s concept, development history and applying value in quantum communication, and then elaborate the paper’s subject-selecting background, significance and main work. In the second part, we will present quantum theory, squeezing vacuum field and its character, then expand standard Jaynes-Cummings model to the condition of considering atomic motion, the basic dynamic model with atomic motion will be established, as the theoretical basic of the work in the below.
The third part is made of three facets.
1. The entangled properties of motorial atom and field in the two-photon Jaynes-Cummings model with atomic motion are studied by using the quantum information theory. It is shown that:(1) When the parameter p of the field model structure with atomic motion is smaller, the entanglement of system is not provided with the characteristic of periodic oscillations, when the value of p is greater, the entanglement of system is obviously provided with the characteristic of periodic oscillations, the oscillation period is as much again as atom is resting . when motorial atom is prepared in ground state or excited state ,the system is in the disentangled state; when motorial atom is prepared in coherent superpositions states, the entanglement occurs between motorial atom and field.
2. We investigate the entanglement properties of two entangled two-level atoms that interact resonantly with a single-mode vacuum field with atomic motion using quantum theory. The results show that if the two atoms are prepared in maximum entangled (EPR) state initially, the maximum of three-body entanglement measure is equated with the perfect three-body W entangled state. The parameter of field-mode structure p influences the time evolution oscillation property of three-body entanglement measure, with the gradually increasing of p, the average of three-body entanglement measure will gradually decrease, three-body entangled state will tend to disentangled state inch by inch.
3. The properties of the entanglement between squeezing vacuum state field and moving atom with Gaussian coupling are studied. The influence of atomic motion perpendicularity to the axes of resonant cavity , the initial states of atom, the squeezing parameter on entanglement degree are discussed. The results show that: with the increase of atomic velocity, effective interaction time of the atom and field will shorten, the entanglement degree will also reach the maximum quickly. The squeezing parameter r have a obvious role of concocting the evolution curve of degree of entanglement, if the squeezing parameter is take appropriate value(such as r =2), the system of quantum state will be maximally entangled state for a long time, without disentangled-free state or disentangled state, and the degree of entanglement is stationary.
引文
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