腔QED系统连续变量纠缠态的动量表象描述
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摘要
建立于20世纪初叶,发展至今的量子力学显著地深化了我们对自然界的认知。一方面,它的理论所涵盖的一些基本问题,如量子力学基础、原理等最根本的问题,在学术界至今仍然没有得到定论；另一方面,作为一门强有力的工具量子力学的现实应用却日益广泛。其在原子物理、固体物理、核物理及量子信息等涉及研究微观尺度物质结构的领域发挥着重要的作用。作为一门刚诞生不久却备受瞩目的学科—量子信息学以其广阔的研究领域和重要的应用前景吸引着大批学者们的关注。同时也是量子理论与现有电信科学技术交叉而形成的新学科。它的诞生与发展极大地扩充了量子理论的内涵,并有助于我们加深对量子性质本质的理解。在量子理论支配下的量子信息所描述的信息世界,呈现出了与我们熟知的经典信息全然不同的特点。其中,量子纠缠作为一种非局域的关联现象,在理论和实验上成为了人们研究的重点。关于连续变量量子纠缠态的制备更是目前量子光学研究的前沿领域,这主要得益于连续变量量子通讯在探测效率、比特速率以及通讯带宽三个方面的出色表现。因此,基于连续变量的量子通讯网络应用的研究具有明亮的前景。本文在无量纲动量表象下讨论了V位型系统的非旋波效应,研究了带有分束器(BS)与参量下转换(NDPC)类型算符项的哈密顿量的动力学以及纠缠行为,并且给出了波函数形式的纯态解。通过对环境自由度取迹,体系的主方程显示了原子跃迁通道上的量子相干效应可以导致自发辐射的淬灭现象。如果腔的损耗非常小且自发辐射淬灭的条件能够满足,那么就能回归到纠缠纯态解的情况。即使在腔损耗无法忽略的情况下,自发辐射淬灭仍然可以帮助我们减少环境对体系的损耗。
本文共分为四章。第一章介绍了量子光学和量子信息的基本理论,其中包括腔QED系统、量子纠缠及其度量等。第二章给出了原子与场相互作用的的基本规律,包括电磁场的量子化以及原子-光场相互作用的全量子理论。第三章简要介绍了IWOP技术(即正规序下的积分技术)的理论基础。第四章是我们主要的研究工作。这章首先介绍了运用V型原子-腔体系产生双模纠缠相干态的方案。当采用非旋波近似时,我们发现非旋波项尽管很小却对体系的纠缠性质有着关键的影响,并且给出了该体系的波函数纯态解。随后,考虑当原子和腔场的损耗都存在时,在适当条件下,我们发现原子的自发辐射能被彻底淬灭,从而减少因退相干而造成的对系统纠缠的破坏。
Established in the beginning of the twentieth century, still in development, quantum mechanics is significantly deepening the understanding of our natural. One aspect is that the basic problems of the theory, such as foundations and principles of quantum mechanics, have no conclusion accepted by academia so far. On the other hand, the application of quan-tum mechanics are increasing widely. As we know, quantum mechanics occupies a leading role in the world of micro scale material structure, especially in the area of atomic physics, solid physics, nuclear physics and quantum information. As an emerging discipline attracted significant interest, quantum information theory has got much attention from scholars for it has wide research field and important application prospect, and it is also a new cross subject of quantum theory and information science. Meanwhile, it widely enriches the research field of quantum theory and helps us to have a better understanding of the essence of quantum theory. Dominated by quantum mechanics, the world of quantum information takes a new look and shows some distinguished advantages compared with classical information. Quan-tum entanglement is a nonlocal correlation, it is becoming an important research field both in theory and experiment. The preparation of continuous-variable (CV) entanglement states are acting on a frontier field in quantum optics, this is mainly because CV quantum commu-nication have excellent performance in detection efficiency, bit rate and communication band. Therefore, the research on CV communication network has wide application in the future. This thesis mainly discuss the effect of nonsecular terms of a V-type system in momentum representation, the Hamiltonian of which both beam splitter (BS) and nondegenerate para-metric down conversion (NPDC) terms appear. The pure state solution of wave function enables us to fully discuss the dynamics and entanglement properties of our system. By tracing over the environment degrees, we obtain a master equation of the system and show that the effect of the quantum interference resulted from the two atomic decay pathways can lead to spontaneous emission quenching. If the loss of the cavity is extremely small, the pure entangled state can be obtained under the condition of spontaneous emission quenching. Even if the cavity loss cannot be ignored, the quenching of spontaneous emission can help us to decrease the dissipation from the environment.
The content of this article can be broadly divided into four chapters. In chapter1, the basic theory of quantum information and quantum optics are introduced, including the measurement of quantum entanglement, the basic of cavity QED system and the concept of CV entanglement which we are especially focused on. chapter2shows the rudiments of the interaction between atom and field, including the quantization of the electromagnetic field, the quantum theory of the interaction between atom and field. In chapter3. the theory of IWOP (integration within an ordered product) technique is introduced. Last chapter is our main work. A scheme generating entangled coherent states by using V-type atom-cavity system is presented in this chapter. When nonsecular approximation is employed, we find that nonsecular terms, although small, can have a significant effect on the entanglement properties, and we also give a pure state solution in wave function to describe it. In the presence of cavity losses and atomic relaxation, we show that complete quenching of spontaneous emission is possible under appropriate conditions. Therefor, reduce an adverse impact from decoherence process.
本文共分为四章。第一章介绍了量子光学和量子信息的基本理论,其中包括腔QED系统、量子纠缠及其度量等。第二章给出了原子与场相互作用的的基本规律,包括电磁场的量子化以及原子-光场相互作用的全量子理论。第三章简要介绍了IWOP技术(即正规序下的积分技术)的理论基础。第四章是我们主要的研究工作。这章首先介绍了运用V型原子-腔体系产生双模纠缠相干态的方案。当采用非旋波近似时,我们发现非旋波项尽管很小却对体系的纠缠性质有着关键的影响,并且给出了该体系的波函数纯态解。随后,考虑当原子和腔场的损耗都存在时,在适当条件下,我们发现原子的自发辐射能被彻底淬灭,从而减少因退相干而造成的对系统纠缠的破坏。
Established in the beginning of the twentieth century, still in development, quantum mechanics is significantly deepening the understanding of our natural. One aspect is that the basic problems of the theory, such as foundations and principles of quantum mechanics, have no conclusion accepted by academia so far. On the other hand, the application of quan-tum mechanics are increasing widely. As we know, quantum mechanics occupies a leading role in the world of micro scale material structure, especially in the area of atomic physics, solid physics, nuclear physics and quantum information. As an emerging discipline attracted significant interest, quantum information theory has got much attention from scholars for it has wide research field and important application prospect, and it is also a new cross subject of quantum theory and information science. Meanwhile, it widely enriches the research field of quantum theory and helps us to have a better understanding of the essence of quantum theory. Dominated by quantum mechanics, the world of quantum information takes a new look and shows some distinguished advantages compared with classical information. Quan-tum entanglement is a nonlocal correlation, it is becoming an important research field both in theory and experiment. The preparation of continuous-variable (CV) entanglement states are acting on a frontier field in quantum optics, this is mainly because CV quantum commu-nication have excellent performance in detection efficiency, bit rate and communication band. Therefore, the research on CV communication network has wide application in the future. This thesis mainly discuss the effect of nonsecular terms of a V-type system in momentum representation, the Hamiltonian of which both beam splitter (BS) and nondegenerate para-metric down conversion (NPDC) terms appear. The pure state solution of wave function enables us to fully discuss the dynamics and entanglement properties of our system. By tracing over the environment degrees, we obtain a master equation of the system and show that the effect of the quantum interference resulted from the two atomic decay pathways can lead to spontaneous emission quenching. If the loss of the cavity is extremely small, the pure entangled state can be obtained under the condition of spontaneous emission quenching. Even if the cavity loss cannot be ignored, the quenching of spontaneous emission can help us to decrease the dissipation from the environment.
The content of this article can be broadly divided into four chapters. In chapter1, the basic theory of quantum information and quantum optics are introduced, including the measurement of quantum entanglement, the basic of cavity QED system and the concept of CV entanglement which we are especially focused on. chapter2shows the rudiments of the interaction between atom and field, including the quantization of the electromagnetic field, the quantum theory of the interaction between atom and field. In chapter3. the theory of IWOP (integration within an ordered product) technique is introduced. Last chapter is our main work. A scheme generating entangled coherent states by using V-type atom-cavity system is presented in this chapter. When nonsecular approximation is employed, we find that nonsecular terms, although small, can have a significant effect on the entanglement properties, and we also give a pure state solution in wave function to describe it. In the presence of cavity losses and atomic relaxation, we show that complete quenching of spontaneous emission is possible under appropriate conditions. Therefor, reduce an adverse impact from decoherence process.
引文
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[10]苏汝铿.量子力学(第二版)[M].北京：高等教育出版社,2002.
[11]Ekert A. and Jozsa R. Quantum computation and Shor's factoring algorithm [J]. Rev. Mod. Phys., 1996,68(3):733-753.
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[14]Duan L M, Guo G C. A probabilistic cloning machine for replicating two nonorthogonal states [J]. Phys. Lett. A,1998,243:261-264.
[15]Duan L M, Guo G C. Probabilistic cloning and identification of linearly independent quantum states [J]. Phys. Rev. Lett.,1998,80(22):4999-5002.
[16]Einstein A, Podolsky B and Rosen N. Can quantum mechanical description of physical reality be considered complete? [J]. Phys. Rev.,1935,47(10):777-780.
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[19]Ou Z Y, Pereira S F, Kimble H J, et al. Realization of the Einstein-Podolsky-Rosen paradox for continuous variables [J]. Phys. Rev. Lett.,1992,68(25):3663-3666.
[20]Werner R F. Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model [J]. Phys. Rev. A,1989,40(8):4277-4281.
[21]Bell J S. On the problem of hidden variables in quantum mechanics [J]. Rev. Mod. Phys.,1966, 38(3):447-452.
[22]Clauser J F, Horne M A, Shimony A, et al. Proposed experiment to test local hidden-variable theories [J]. Phys. Rev. Lett.,1969,23(15):880-884.
[23]Peres A. Separability criterion for density matrices [J]. Phys. Rev. Lett.,1996,77(8):1413-1415.
[24]Horodecki M. and Horodecki P. Reduction criterion of separability and limits for a class of distil-lation protocols [J]. Phys. Rev. A,1999,59(6):4206-4216.
[25]Vedral V and Plenio M B. Entanglement measures and purification procedures [J]. Phys. Rev. A, 1998,57(3):1619-1633.
[26]Josse V, Dantan A, Vernac L, et al. Polarization squeezing with cold atoms [J]. Phys. Rev. Lett., 2003,91(10):103601(4).
[27]Scully M O. Correlated spontaneous-emission lasers:quenching of quantum fluctuations in the relative phase angle [J]. Phys. Rev. Lett.,1985,55(25):2802-2805.
[28]Solano E, Agarwal G S and Walther H. Strong-driving-assisted multipartite entanglement in cavity QED [J]. Phys. Rev. Lett.,2003,90(2):027903(4).
[29]Xiong H, Scully M O and Zubairy M S. Correlated spontaneous emission laser as an entanglement amplifier [J]. Phys. Rev. Lett.,2005,94(2):023601(4).
[30]Tan H T, Zhu S Y and Zubairy M S. Continuous-variable entanglement in a correlated spontaneous emission laser [J]. Phys. Rev. A,2005,72(2):022305(8).
[31]Wang X and Sanders B C. Multipartite entangled coherent states [J]. Phys. Rev. A,2001,65(1): 012303(7).
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