光在一维耦合波导阵列中的量子传输行为与相关特性

发布时间：2018-06-23 07:08

本文选题：一维波导阵列 + 光子　；参考：《南开大学》2014年博士论文

【摘要】：光在波导阵列中的传播特性使得波导阵列在光信号处理、光通信、光计算等领域有巨大的应用前景。同时,由于光在波导阵列中的传播方程与薛定谔方程具有相同的形式,所以可以通过光在波导阵列中的传播行为直观地研究量子力学的一些基本效应。由于波导阵列在应用和理论研究中的重要作用,基于波导阵列的光的传播特性的研究成为光学研究中的一个很活跃的领域。不过,之前主要是研究经典光在波导中的传播,此时光的传播遵从麦克斯韦方程组,主要是利用了光的波动性。最近,非经典光在波导阵列中的传输行为吸引了广泛关注。在本论文中,我们在一维耦合波导阵列中通过引入缺陷、结构无序以及构造准PT对称结构,研究了光子在波导阵列中的传输行为,即通过特定结构的波导阵列来操控光子的传输和相干行为。在第一章中,我们主要介绍了研究背景。首先介绍了在波导阵列中使用经典光来研究量子力学基本原理和效应的情况,并简单介绍了几个例子；随后介绍了关于非经典光在波导阵列中的研究进展。最后阐述了本论文的研究立意和内容安排。在第二章中,我们主要介绍了本论文研究工作中所用到的基本理论和相关知识。分别介绍了一维波导阵列结构和耦合模理论,算符所满足的海森堡运动方程,以及经典相关和量子相关函数,最后介绍了PT对称非厄米体系。在第三章中,我们首先研究了单光子在周期及具有缺陷的波导阵列中的传输行为,然后进一步研究了双光子路径纠缠态在一维耦合波导阵列中的传输行为。结果表明,当引入负的非对角缺陷时,缺陷波导的作用类似于光子反射镜,使得双光子路径纠缠态在波导阵列中传输时总是表现出聚束特性。之后,我们研究了引入非对角缺陷及对角缺陷的波导阵列中光子的局域现象,以及光子在波导阵列中传输时其双光子相关函数的振荡行为,发现由于量子干涉效应,不同的双光子相关矩阵元具有不同的振荡周期,与经典光波振荡周期一致或者是经典光波振荡周期的一半。通过对两种缺陷本征态的理论分析,我们发现缺陷态对双光子路径纠缠态在波导阵列中的量子相关特性起着非常重要的作用。在第四章中,我们在非对角无序波导阵列中引入对角和非对角缺陷,研究了光在其中的传输行为和量子相关特性。在非对角无序波导阵列中,由于安德森局域效应,光子在波导阵列中的传输会出现局域现象。而当引入对角缺陷和非对角缺陷时,我们发现缺陷的引入可以改变光子在传输过程中的局域程度,不但可以增强或者减弱局域程度,甚至可以完全破坏光子局域效应。对应地,我们研究了费米子在周期调制势场中随时间演化的行为,发现某些玻色子路径纠缠态在波导阵列中的传输行为与费米子在周期势场中的时间演化行为类似,或许以后可以通过选取适当的光子入射态在波导阵列中的传输行为来研究和表征费米子在势场中随时间演化的行为。在第五章中,我们构造了一个新型的准PT对称波导阵列。在该结构中,我们只引入吸收波导,而无需引入增益波导,这种准PT对称波导阵列在实验上能够较容易地实现。我们研究了光子在这种准PT对称波导阵列中的传输行为和量子相关特性。研究表明,随着吸收系数的增强,PT对称会被破坏,即体系对应着一个相变点。通过计算,我们发现非对角无序的引入会使得体系的相变点提前。我们进一步研究了在这种PT对称波导阵列中总光子数的变化,发现在这样的准PT对称波导体系中同样存在着吸收增强透过效应,并且非对角无序度的增大会增强这种效应。在第六章中,我们对本论文的工作进行了总结,并且对后期工作进行了展望。
[Abstract]:The propagation characteristics of light in the waveguide array make the waveguide array have a great application prospect in the fields of optical signal processing, optical communication and optical computing. At the same time, because the propagation equation of light in the waveguide array has the same form as the Schrodinger equation, quantum mechanics can be intuitively studied by the propagation behavior of light in the waveguide array. Some basic effects. Due to the important role of waveguide array in the application and theoretical research, the study of the propagation characteristics of light based on the waveguide array has become a very active field in the optical research. However, the propagation of the classical light in the waveguide was mainly studied before. The propagation of the time is based on the Maxwell equation, which is mainly used. Recently, the propagation behavior of non classical light in waveguide arrays has attracted wide attention.
In this paper, we study the propagation behavior of photons in a waveguide array by introducing defects, structural disorder and constructing quasi PT symmetric structures in a one-dimensional coupled waveguide array, that is, to manipulate the transmission and coherence of the photon through a specific structure of waveguide array.
In the first chapter, we mainly introduce the research background. First, we introduce the use of classical light to study the basic principles and effects of quantum mechanics in the waveguide array, and briefly introduce several examples, and then introduce the research progress on the non classical light in the waveguide array. Finally, the purpose and content of this research are discussed. Arrangement.
In the second chapter, we mainly introduce the basic theory and related knowledge used in this research work. We introduce the one-dimensional waveguide array structure and coupled mode theory, the Heisenberg equation of motion satisfied by the operator, and the classical correlation and quantum correlation functions. Finally, the PT symmetric non Hermite system is introduced.
In the third chapter, we first study the propagation behavior of a single photon in a periodic and defective waveguide array. Then we further study the transmission behavior of the two-photon path entangled state in a one-dimensional coupled waveguide array. The results show that when the negative non diagonal defect is introduced, the effect of the defective waveguide is similar to the photon reflector. The two photon path entangled states always exhibit bunching in the waveguide array. After that, we study the local phenomena of the photons in the waveguide arrays with non diagonal defects and diagonal defects, and the oscillation of the two photon correlation functions when the photon travels in the waveguide array. The photon correlation matrix element has different oscillation periods, which is consistent with the classical light wave oscillation period or half of the classical light wave oscillation period. Through the theoretical analysis of the two kinds of eigenstates, we find that the defect state plays a very important role in the quantum phase characteristics of the two-photon path entangled state in the waveguide array.
In the fourth chapter, we introduce diagonal and non diagonal defects in the non diagonal disorder waveguide array, and study the propagation and quantum correlation of light in it. In the non diagonal disorder waveguide array, due to the local effect of Anderson, the transmission of photons in the waveguide array will be localized, while the diagonal and non diagonal waveguides are introduced. In the case of defects, we find that the introduction of the defect can change the local degree of the photon in the transmission process, not only to enhance or weaken the local degree, but even to completely destroy the local effect of the photon. The propagation behavior in the waveguide array is similar to the time evolution behavior of fermions in the periodic potential field. Perhaps the behavior of the fermions in the potential field can be investigated and characterized by selecting appropriate photon incident states in the waveguide array.
In the fifth chapter, we construct a new quasi PT symmetric waveguide array. In this structure, we only introduce absorption waveguides without introducing gain waveguides. This quasi PT symmetric waveguide array can be easily realized experimentally. We study the transmission behavior and quantum correlation of photons in this quasi PT pair of symmetric waveguide arrays. The study shows that, with the enhancement of the absorption coefficient, the PT symmetry will be destroyed, that is, the system corresponds to a phase transition point. By calculation, we find that the introduction of non diagonal disorder will lead to the advance of the phase transition point of the system. We further study the change of the total number of light in this PT symmetric waveguide array, and find that the quasi PT symmetric wave conductor is found in such a symmetric waveguide array. There is also an enhanced absorption effect in the system, and the increase of non diagonal disorder will enhance this effect.
In the sixth chapter, we summarized the work of this paper and prospected the later work.
【学位授予单位】：南开大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN814

【共引文献】