典型量子系统中的纠缠调制及信息处理
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摘要
量子纠缠是量子力学特有的现象,一直是物理学中一个引人注目的研究领域,是实现量子通信的关键要素。量子态是量子信息的载体,量子信息的处理是对编码的量子态进行传输过程,量子态制备和量子信息传输质量的评价,成为量子信息领域中的重要任务。依赖强度耦合双模多光子J-C模型和同时考虑原子运动和光场频率变化相互作用系统是具有典型意义的量子系统,本文研究这两类系统中的纠缠调控、各类量子态的制备及信息保真度的问题,得出了一系列新的有意义的结论:
1、给出了依赖强度耦合双模J-C模型多光子过程的哈密顿量,在强场条件下,分别运用量子约化熵和量子相对熵研究二能级原子与双模相干场依赖强度耦合多光子过程中,原子和场之间的纠缠以及双模场的模间纠缠演化及纠缠态的制备。结果表明,这两类纠缠演化均与原子跃迁时吸收(或发射)的光子数k密切相关。在多光子过程中(k≥2),原子-场之间产生持续的最大纠缠,双模场的模间纠缠演化呈现非线性变化,两类纠缠失去对抗性。分别制备了与时间无关的原子-场EPR态和场的模间纠缠态。
2、在旋波近似下,同时考虑原子运动和光场频率随时间作正弦函数变化,运用量子约化熵研究二能级原子与单模辐射场相互作用系统中场与原子的纠缠演化规律;利用数值计算的方法分别给出了在不考虑与考虑原子的运动的情况下场熵随时间的演化曲线,讨论了原子运动、场模结构、场频率的幅值和角频率变化对场熵的影响;解析制备了光场与原子的纠缠态、光场偶数态及原子相干叠加态,获得了调控和制备上述量子态的系统参数。结果表明场熵的演化受场频率变化的调制;原子的运动导致了场熵演化周期加倍;在场频率变化的角频率一定的情形下,场熵演化规律与场模结构参数的奇偶性有关;无论原子运动与否,都可周期性制备场-原子的近似EPR态。
3、在旋波近似下,同时考虑原子运动和光场频率随时间作正弦函数变化,运用全量子理论研究了二能级原子与单模辐射场相互作用系统中量子态保真度的演化。数值讨论了原子初态、原子运动速度、场模结构参数、场频率变化的幅值和角频率对量子信息保真度的影响。结果表明,通过选择合适的原子初态、原子速度和场模结构及调节场频率变化,可获得原子量子态的完全保真输出。
Quantum entanglement is a strange phenomenon of quantum mechanics, and it is a research field which always be noted in Physics. Quantum entanglement is the key factor of experimental realization of quantum communication. Quantum state is the carrier of quantum information. Quantum information processing is the information transmission of the encoded quantum state. The preparation of quantum state and the evaluation of the quality of information transmission are very important tasks in this research field. The intensity-dependent coupling two-mode multiphoton Jaynes-Cummings model and the system that consists of a moving two-level atom interacting with a frequency variation field are significative typical quantum systems. This thesis has investigated entanglement evolution, preparation of quantum states and the fidelity of quantum information in the two systems. A series of significant results are obtained.
1. The effective Hamiltonian of the two-mode multiphoton Jaynes-Cummings model is given via the intensity-dependent coupling in the rotating wave approximation. Considering strong field, the atom-field entanglement and the entanglement between two modes of coherent field, according to the above model, are investigated using the quantum reduced entropy and quantum relative entropy, respectively. It is showed that properties of these two types of entanglements are considerably relevant to the absorption or emission photon number k, per atomic transition. Different properties of entanglements in the processes of two-photon (k=1) and multiphoton (k>2) are revealed respectively. Given the preparation of entangled states discussed, the EPR states of atom-field irrelevant to time, as well as entangled states between two models of the coherent field are prepared, respectively.
2. In the rotating-wave approximation, considering atomic motion and the field frequency varying with time in the form of sine-function at the same time, the evolution of the field quantum entropy in the system that consists of a two-level atom interacting with a single-mode field are studied. In two cases of neglecting atomic motion and considering atomic motion, figures of the time evolutions of the field entropy are plotted respectively using numerical calculations, and the influences of the atomic motion, the field-model structure parameter, amplitude and angular frequency of the field-frequency variation on the field entropy are discussed. The atom-field entangled states, field fock states and atomic high fidelity states are prepared by analytic method and the related system parameters of these quantum states operation are acquired. The results show that the time evolution behavior of the field entropy is modulated by the frequency variation of field, the interaction between the field and atom will weaken with the increase of the amplitude of variation of the field frequency, the period of the field entropy agrees with the period of field-frequency variation; the atomic motion will result in the period of the field entropy doubled; the evolution of the field entropy is related to the parity of field-mode structure parameter; the approximate EPR states of field-atom can be prepared periodically whether the atom moves or not.
3. In the rotating-wave approximation, considering atomic motion and the frequency of the field varying with time in the form of sine-function at the same time, the evolution of the fidelity of quantum information in the system that consists of a two-level atom interacting with a single-mode field are studied. The influences of the initial state of the atom, the atomic motion, the field-model structure parameter, amplitude and angular frequency of the field-frequency variation on the fidelity of quantum states are discussed by numerical calculations. The results show that the complete fidelity output of the atomic state can be obtained by choosing appropriate initial atomic state, appropriate atomic velocity and appropriate field-model structure and adjusting field-frequency variation.
1、给出了依赖强度耦合双模J-C模型多光子过程的哈密顿量,在强场条件下,分别运用量子约化熵和量子相对熵研究二能级原子与双模相干场依赖强度耦合多光子过程中,原子和场之间的纠缠以及双模场的模间纠缠演化及纠缠态的制备。结果表明,这两类纠缠演化均与原子跃迁时吸收(或发射)的光子数k密切相关。在多光子过程中(k≥2),原子-场之间产生持续的最大纠缠,双模场的模间纠缠演化呈现非线性变化,两类纠缠失去对抗性。分别制备了与时间无关的原子-场EPR态和场的模间纠缠态。
2、在旋波近似下,同时考虑原子运动和光场频率随时间作正弦函数变化,运用量子约化熵研究二能级原子与单模辐射场相互作用系统中场与原子的纠缠演化规律;利用数值计算的方法分别给出了在不考虑与考虑原子的运动的情况下场熵随时间的演化曲线,讨论了原子运动、场模结构、场频率的幅值和角频率变化对场熵的影响;解析制备了光场与原子的纠缠态、光场偶数态及原子相干叠加态,获得了调控和制备上述量子态的系统参数。结果表明场熵的演化受场频率变化的调制;原子的运动导致了场熵演化周期加倍;在场频率变化的角频率一定的情形下,场熵演化规律与场模结构参数的奇偶性有关;无论原子运动与否,都可周期性制备场-原子的近似EPR态。
3、在旋波近似下,同时考虑原子运动和光场频率随时间作正弦函数变化,运用全量子理论研究了二能级原子与单模辐射场相互作用系统中量子态保真度的演化。数值讨论了原子初态、原子运动速度、场模结构参数、场频率变化的幅值和角频率对量子信息保真度的影响。结果表明,通过选择合适的原子初态、原子速度和场模结构及调节场频率变化,可获得原子量子态的完全保真输出。
Quantum entanglement is a strange phenomenon of quantum mechanics, and it is a research field which always be noted in Physics. Quantum entanglement is the key factor of experimental realization of quantum communication. Quantum state is the carrier of quantum information. Quantum information processing is the information transmission of the encoded quantum state. The preparation of quantum state and the evaluation of the quality of information transmission are very important tasks in this research field. The intensity-dependent coupling two-mode multiphoton Jaynes-Cummings model and the system that consists of a moving two-level atom interacting with a frequency variation field are significative typical quantum systems. This thesis has investigated entanglement evolution, preparation of quantum states and the fidelity of quantum information in the two systems. A series of significant results are obtained.
1. The effective Hamiltonian of the two-mode multiphoton Jaynes-Cummings model is given via the intensity-dependent coupling in the rotating wave approximation. Considering strong field, the atom-field entanglement and the entanglement between two modes of coherent field, according to the above model, are investigated using the quantum reduced entropy and quantum relative entropy, respectively. It is showed that properties of these two types of entanglements are considerably relevant to the absorption or emission photon number k, per atomic transition. Different properties of entanglements in the processes of two-photon (k=1) and multiphoton (k>2) are revealed respectively. Given the preparation of entangled states discussed, the EPR states of atom-field irrelevant to time, as well as entangled states between two models of the coherent field are prepared, respectively.
2. In the rotating-wave approximation, considering atomic motion and the field frequency varying with time in the form of sine-function at the same time, the evolution of the field quantum entropy in the system that consists of a two-level atom interacting with a single-mode field are studied. In two cases of neglecting atomic motion and considering atomic motion, figures of the time evolutions of the field entropy are plotted respectively using numerical calculations, and the influences of the atomic motion, the field-model structure parameter, amplitude and angular frequency of the field-frequency variation on the field entropy are discussed. The atom-field entangled states, field fock states and atomic high fidelity states are prepared by analytic method and the related system parameters of these quantum states operation are acquired. The results show that the time evolution behavior of the field entropy is modulated by the frequency variation of field, the interaction between the field and atom will weaken with the increase of the amplitude of variation of the field frequency, the period of the field entropy agrees with the period of field-frequency variation; the atomic motion will result in the period of the field entropy doubled; the evolution of the field entropy is related to the parity of field-mode structure parameter; the approximate EPR states of field-atom can be prepared periodically whether the atom moves or not.
3. In the rotating-wave approximation, considering atomic motion and the frequency of the field varying with time in the form of sine-function at the same time, the evolution of the fidelity of quantum information in the system that consists of a two-level atom interacting with a single-mode field are studied. The influences of the initial state of the atom, the atomic motion, the field-model structure parameter, amplitude and angular frequency of the field-frequency variation on the fidelity of quantum states are discussed by numerical calculations. The results show that the complete fidelity output of the atomic state can be obtained by choosing appropriate initial atomic state, appropriate atomic velocity and appropriate field-model structure and adjusting field-frequency variation.
引文
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