光子晶体中量子纠缠和量子关联的动力学研究
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摘要
量子信息学是量子力学与信息科学和计算机科学相结合而发展起来的新型交叉学科。量子信息科学的发展不仅具有巨大的商业价值，而且在国防安全方面有着潜在的应用前景。在量子信息学的主要研究内容中，量子纠缠无疑是最重要的物理资源，它的发展决定着量子信息技术能否打开广阔的应用前景。然而，系统与环境之间的相互作用将破坏整个量子系统的量子纠缠。这是实现量子计算机的主要障碍，所以我们要关注量子开放系统理论。在开放量子系统理论中，选择的热库不同，对量子系统的影响也是不一样的。在本文中，我们研究光子晶体热库中量子纠缠和量子关联的动力学性质，研究在光子晶体热库中如何避免或者控制纠缠破坏，这对于实际量子信息过程与量子计算具有潜在的应用价值。本论文的结构如下：
在论文的第一章，介绍了本文的研究背景。第二章和第三章介绍了与本文研究工作密切相关的基本概念与基本方法。在第二章中，介绍了量子信息学中的一些基本概念。第三章介绍了光子晶体的基本理论，包括光子晶体的性质、制备及光子晶体热库的基本理论。本论文的第四、五、六章详细介绍了我们的研究工作以及取得的成果，具体如下:
在第四章中，我们讨论了结构振幅阻尼信道中量子信息保真度随时间的演化，研究光子晶体中光子的局域效应对单量子比特信息保真度和纠缠保真度的影响，并分析了它与原子的0→1共振跃迁频率和光子晶体带隙边缘频率之间的失谐的关系。经过研究发现共振频率与带隙边缘的相对位置对保真度有很大的影响：当原子的跃迁频率在禁带里的时候，量子信息能够得到很好的保护，流失的很少，并且保真度能够长时间的处于一个稳态的值。最后我们还讨论了这种信道中，两体系统的纠缠保真度随时间的演化。
在第五章中，我们研究了置于同一个光子晶体中的两个二能级原子之间的纠缠动力学演化。并详细讨论了原子共振跃迁频率与光子晶体带隙边缘频率之间的失谐条件和原子之间的偶极-偶极相互作用对纠缠演化的影响。研究发现当原子的跃迁频率在光子禁带里，也就是失谐δ <0时，光子晶体热库可以很好的抑制置于其中的两原子系统的退相干效应，使它们之间的纠缠保持在一个很大的稳态值。并且对于不同的纠缠初态，光子晶体热库对它们的影响也不同。同时，原子之间的偶极-偶极相互作用DDI也可以起到操控原子间量子纠缠的作用。因此，光子晶体热库能够很好的操控置于其中的原子或量子点间的纠缠。
在第六章中，我们研究了置于同一个光子晶体热库中的两体系统量子关联的动力学演化。并详细讨论了量子系统的初始状态和原子上能级与禁带带边的相对位置对量子关联的影响。经过研究发现，量子谐错在光子晶体热库中能保持长时间的稳态值，并且在出现纠缠突然死亡的区域不会出现量子谐错的突然死亡，说明量子谐错抵御外界退相干的能力比量子纠缠要强。对于初态是可分离态的情况，光子晶体可以诱导两体系统之间产生很大的量子谐错值，并能通过调控频率失谐的值来操控原子之间的量子关联。因此，光子晶体热库能够很好的操控置于其中的原子或量子点间的量子关联。
在第七章中，我们对全文做了一个总结和展望。
Quantum information is a new cross subject，which is the combination of thequantum mechanics, information science and computer science. The developmentof quantum information not only has great commercial value but also has a greatprospect of application in our national security system. Quantum entanglement isan important resource in quantum information science, and its developmentdetermines whether the quantum information science has a widen applicationforeground. However the inevitable interaction between the quantum system andenvironment will eventually destroy the quantum entanglement of the wholequantum system. This is the main obstacle in the realization of the quantumcomputer. So we should study on the quantum information in open quantumsystems. In open quantum system theory, entanglement dynamics will presentdifferently because of different reservoir. This dissertation study the entanglementand quantum correlation dynamics of atoms in photonic crystals, concerning onhow to avoid or control entanglement decay in PBG reservoir. This work haspotential application values in quantum information processing and quantumcomputing. The structure of this dissertation is arranged as follows.
Chapter1gives the research background of this dissertation. In chapters2and3, we introduce the fundamental conceptions and methods which are relative to ourwork. Chapter2introduces the basic concepts in quantum information science. InChapter3we introduce the fundamental theory of photonic crystals, including theproperty and preparation of photonic crystal and the elementary theory of PBGreservoir. Chapter4,5and6introduce our research achievements in detail.Including:
In chapter4, we study the properties of the fidelity of one-qubit operations in amplitude damping channels and reveal their properties as a function of coupling tothe photonic crystal environment. We show that there is a direct connectionbetween the information fidelity and the detuning of the atomic frequency from thephotonic band gap (PBG). When the atomic transition frequency is far inside theband gap, the time evolution of the fidelity maintains asymptotically a steady-statevalue and can be controlled by the controllable PBG environment. We finally studythe entanglement fidelity of the two-qubit system in this quantum channel.
In chapter5, we have analyzed the dynamics of two-qubit entanglement withthe two qubits separated at an arbitrary distance and interacting with an isotropicphotonic crystal. Special attention is paid to the effects of the detuning conditionsand the DDI on the entanglement dynamics of the two-qubit system. It has beenfound that, the deeper the atomic transition frequency is in the band gap, the higheris the preserved entanglement; for some initial states, where entanglement isalready constant, the effect of detuning can be to trigger a maximal entanglement.We also find that, the entanglement can also be modified by the DDI between thetwo atoms. Concretely, when the frequency detuning is negative, the entanglementdecreases with the increase of the strength of the DDI. For a positive detuning,however, the strong DDI leads to the increase of the entanglement. Hance, thequbits may be coherently manipulated by the controllable PBG environment toperform some quantum information protocol in nanostructured materials.
In chapter6, we have presented a non-Markovian model describing the exactquantum correlation dynamics of two qubits interacting with a common PBGenvironment. Special attention is paid to the effects of detuning conditions and theinitial states on quantum correlation dynamics of the two-qubit system. We haveobserved that, the quantum discord can survive for a long time in PBGenvironment. Concretely, the discord is immune to a “sudden death” and evolvesasymptotically to a definite steady value in the long-time limit. We have also foundthat, the quantum discord can be created on demand in PBG reservoir. The result here gives a clear way on how to control and manipulate the dynamics of quantumcorrelation by the controllable PBG materials. This is quite significant inperforming some quantum information protocol in nanostructured materials.
Chapter7denotes the conclusion and prospect.
在论文的第一章，介绍了本文的研究背景。第二章和第三章介绍了与本文研究工作密切相关的基本概念与基本方法。在第二章中，介绍了量子信息学中的一些基本概念。第三章介绍了光子晶体的基本理论，包括光子晶体的性质、制备及光子晶体热库的基本理论。本论文的第四、五、六章详细介绍了我们的研究工作以及取得的成果，具体如下:
在第四章中，我们讨论了结构振幅阻尼信道中量子信息保真度随时间的演化，研究光子晶体中光子的局域效应对单量子比特信息保真度和纠缠保真度的影响，并分析了它与原子的0→1共振跃迁频率和光子晶体带隙边缘频率之间的失谐的关系。经过研究发现共振频率与带隙边缘的相对位置对保真度有很大的影响：当原子的跃迁频率在禁带里的时候，量子信息能够得到很好的保护，流失的很少，并且保真度能够长时间的处于一个稳态的值。最后我们还讨论了这种信道中，两体系统的纠缠保真度随时间的演化。
在第五章中，我们研究了置于同一个光子晶体中的两个二能级原子之间的纠缠动力学演化。并详细讨论了原子共振跃迁频率与光子晶体带隙边缘频率之间的失谐条件和原子之间的偶极-偶极相互作用对纠缠演化的影响。研究发现当原子的跃迁频率在光子禁带里，也就是失谐δ <0时，光子晶体热库可以很好的抑制置于其中的两原子系统的退相干效应，使它们之间的纠缠保持在一个很大的稳态值。并且对于不同的纠缠初态，光子晶体热库对它们的影响也不同。同时，原子之间的偶极-偶极相互作用DDI也可以起到操控原子间量子纠缠的作用。因此，光子晶体热库能够很好的操控置于其中的原子或量子点间的纠缠。
在第六章中，我们研究了置于同一个光子晶体热库中的两体系统量子关联的动力学演化。并详细讨论了量子系统的初始状态和原子上能级与禁带带边的相对位置对量子关联的影响。经过研究发现，量子谐错在光子晶体热库中能保持长时间的稳态值，并且在出现纠缠突然死亡的区域不会出现量子谐错的突然死亡，说明量子谐错抵御外界退相干的能力比量子纠缠要强。对于初态是可分离态的情况，光子晶体可以诱导两体系统之间产生很大的量子谐错值，并能通过调控频率失谐的值来操控原子之间的量子关联。因此，光子晶体热库能够很好的操控置于其中的原子或量子点间的量子关联。
在第七章中，我们对全文做了一个总结和展望。
Quantum information is a new cross subject，which is the combination of thequantum mechanics, information science and computer science. The developmentof quantum information not only has great commercial value but also has a greatprospect of application in our national security system. Quantum entanglement isan important resource in quantum information science, and its developmentdetermines whether the quantum information science has a widen applicationforeground. However the inevitable interaction between the quantum system andenvironment will eventually destroy the quantum entanglement of the wholequantum system. This is the main obstacle in the realization of the quantumcomputer. So we should study on the quantum information in open quantumsystems. In open quantum system theory, entanglement dynamics will presentdifferently because of different reservoir. This dissertation study the entanglementand quantum correlation dynamics of atoms in photonic crystals, concerning onhow to avoid or control entanglement decay in PBG reservoir. This work haspotential application values in quantum information processing and quantumcomputing. The structure of this dissertation is arranged as follows.
Chapter1gives the research background of this dissertation. In chapters2and3, we introduce the fundamental conceptions and methods which are relative to ourwork. Chapter2introduces the basic concepts in quantum information science. InChapter3we introduce the fundamental theory of photonic crystals, including theproperty and preparation of photonic crystal and the elementary theory of PBGreservoir. Chapter4,5and6introduce our research achievements in detail.Including:
In chapter4, we study the properties of the fidelity of one-qubit operations in amplitude damping channels and reveal their properties as a function of coupling tothe photonic crystal environment. We show that there is a direct connectionbetween the information fidelity and the detuning of the atomic frequency from thephotonic band gap (PBG). When the atomic transition frequency is far inside theband gap, the time evolution of the fidelity maintains asymptotically a steady-statevalue and can be controlled by the controllable PBG environment. We finally studythe entanglement fidelity of the two-qubit system in this quantum channel.
In chapter5, we have analyzed the dynamics of two-qubit entanglement withthe two qubits separated at an arbitrary distance and interacting with an isotropicphotonic crystal. Special attention is paid to the effects of the detuning conditionsand the DDI on the entanglement dynamics of the two-qubit system. It has beenfound that, the deeper the atomic transition frequency is in the band gap, the higheris the preserved entanglement; for some initial states, where entanglement isalready constant, the effect of detuning can be to trigger a maximal entanglement.We also find that, the entanglement can also be modified by the DDI between thetwo atoms. Concretely, when the frequency detuning is negative, the entanglementdecreases with the increase of the strength of the DDI. For a positive detuning,however, the strong DDI leads to the increase of the entanglement. Hance, thequbits may be coherently manipulated by the controllable PBG environment toperform some quantum information protocol in nanostructured materials.
In chapter6, we have presented a non-Markovian model describing the exactquantum correlation dynamics of two qubits interacting with a common PBGenvironment. Special attention is paid to the effects of detuning conditions and theinitial states on quantum correlation dynamics of the two-qubit system. We haveobserved that, the quantum discord can survive for a long time in PBGenvironment. Concretely, the discord is immune to a “sudden death” and evolvesasymptotically to a definite steady value in the long-time limit. We have also foundthat, the quantum discord can be created on demand in PBG reservoir. The result here gives a clear way on how to control and manipulate the dynamics of quantumcorrelation by the controllable PBG materials. This is quite significant inperforming some quantum information protocol in nanostructured materials.
Chapter7denotes the conclusion and prospect.
引文
[1] Moore G E, Cramming more Components onto integrated circuits [M]Proceedings of the IEEE,1998.
[2] Nielsen M A and Chuang1L，Quantum computation and quantuminformation [M] Cambridge: Cambridge University Press,2000.
[3] Shor P W, Polynomial-time algorithms for prime factorization and discretelogarithms on a quantum computer [M] SIAM J Comput,1996.
[4] Grover L K, A fast quantum mechanics algorithm of database search In:Proceedings of the28thAnnual ACM Symposium on Theory ofComputation [M] Philadelphia PA USA,1996.
[5] Knill E, Laamme R, Martinez R, et al, An algorithmic benchmark forquantum information processing [J] Nature,2000,404:368-370.
[6]范洪义，从量子力学到量子光学[M].上海：上海交通大学出版社，2005.
[7]苏汝铿等，量子力学[M].北京：高等教育出版社，2002.
[8] Lee J Y, Kim M. S, Entanglement teleportation via werner states [J] Phys.Rev. Lett.,2000,84(18):4236-4239.
[9] Akio M, Teleportation without resorting to Bell measurement [J] Phys. Lett.A.,2000,270:293-295.
[10]曾谨言，量子力学[M].北京：科学出版社，2007.
[11] Artur K. Ekert, Quantum cryptography based on Bell’s theorem [J] Phys.Rev. Lett.,1991,67:661-664.
[12] Knill E and Laflamme R, Power of one bit of quantum information [J]Phys. Rev. Lett.,1998,81(25):5672-5675.
[13] Datta A, Flammia S T and Caves C M, Entanglement and the power of onequbit [J] Phys. Rev.A,2005,72(4):042316-042318.
[14] Datta A, Anil S J and Carlton M Caves, Quantum discord and the power ofone qubit [J] Phys. Rev. Lett.,2008,100(5):050502-050505.
[15] Henderson L and Vedral V, Classical, quantum and total correlations [J]Phys. A: Math. Gen,2001,34:6899-6905.
[16] Ollivier H and Zurek W H, Quantum discord: A measure of thequantumness of correlations [J] Phys. Rev. Lett.,2001,88(1):017901-017905.
[17] Breuer H P and Petruccione F, The theory of open quantum systems [M]New York: Oxford University Press,2002.
[18] Breuer H P, Laine E M and Piilo J, Measure for the degree ofnon-markovian behavior of quantum processes in open systems [J] Phys.Rev. Lett.,2009,103(21):210401-210405.
[19] Grabert H, Schramm P and Ingold G L, Quantum Brownian motion: Thefunctional integral approach [J] Phys. Rep.,1988,168:115-207.
[20] Stelmachovic J and Buzek V, Dynamics of open quantum systems initiallyentangled with environment: Beyond the Kraus representation [J]Phys.Rev.A,2001,64:062106.
[21] Schilemann J, Khaetskii A and Loss D, Electron spin dynamics in quantumdots and related nanostructures due to hyperfine interaction with nuclei [J] J.Phys.: Condens. Matter,2003,15: R1809-R1833.
[22] Haake F and Reibold R, Strong damping and low-temperature anomaliesfor the harmonic oscillator [J] Phys.Rev.A,1985,32:2462-2475.
[23] Hu B L, Paz J P and Zhang Y, Quantum Brownian motion in a generalenvironment: Exact master equation with nonlocal dissipation and colorednoised [J] Phys.Rev. D,1992,45:2843-2861.
[24] Michel M, Mahler G and Gemmer J, Fourier’s law from Schrodingerdynamics [J] Phys. Rev. Lett.,2005,95:180602-180605.
[25] Bellomo B, Lofranco R and Compagno G, Entanglement dynamics of twoindependent qubits in environments with and without memory [J] Phys.Rev. A,2008,77:032342.
[26] Yablonovitch E. Inhibited Spontaneous Emission in Solid-State Physics andElectronics [J]. Phys. Rev. Lett.1987,58:2059–2062.
[27] Sajeev J. Strong localization of photons in certain disordered dielectricsuper lattices [J]. Phys. Rev. Lett.1987,58:2486–2489.
[28] Jie G, Sun F W, and Wong C W. Implementation scheme for quantumcontrolled phase-flip gate through quantum dot in slow-light photoniccrystal waveguide [J]. App. Phys. Lett.2008,93:151108-1511011.
[29] Entezar S R. Entanglement of a two-level atom and its spontaneousemission near the edge of a photonic band gap [J]. Phys. Lett. A2009,373:3413-3418.
[30] Entezar S R. Controllable atom–photon entanglement near a3D anisotropicphotonic band edge [J]. J. Phys. B: At. Mol. Opt. Phys.2010,43:085503-085510.
[31] Cirac J I, et al, Quantum computation with cold trapped ions [J] Phys. Rev.Lett.1995,74:4091–4094.
[32] Buzek V and Hillery M, Quantum copying: Beyond the no-cloning theorem[J] Phys. Rev. A1996,54:1844–1852.
[33] John von Neumann, Mathematical foundations of quantum mechanics [M]Princeton University Press,1996.
[34] Landau L D and Lifshita E M, Quantum Mechanics (Non-RelativisticTheory)[M] Brtterworth-Heinemann,1981.
[35] Fano U, Description of states in quantum mechanics by density matrix andoperator techniques [J] Rev. Mod. Phys.,1957,29(1):74-93.
[36] Reinhard F. W, Quantum states with Einstein-Podolsky-Rosen correlationsadmitting a hidden-variable model [J] Phys. Rev. A1989,40:4277–4281.
[37] Gu S J, Fidelity approach to quantum phase transitions [J] InternationalJournal of Modern Physics B,2010,24(23):4371-4458.
[38]张永德,量子信息物理原理.[M]科学出版社,2006.
[39] Einstein A, Podolsky B and Rosen N, Can quantum mechanical descriptionof physical reality be considered dcomplete?[J] Phys. Rev.,1935,47:777-779.
[40] Roseilde T., Verrueeh P, Fubin A, Haas S and Tognett V, Entanglement andFactorized Ground States in Two-Dimensional Quantum Antiferromagnets[J] Phys. Rev. Lett.,2005,94:147208(4).
[41] Osborn T J and Nielsen M A, Entanglement in a simple quantum phasetransition [J] Phys. Rev. A,2002,66:032110(12).
[42] Vidal G, Latorre J L, Rieo E and Kitae A, Entanglement in QuantumCritical Phenomena [J] Phys. Rev. Lett.,2003,90:227902(4).
[43] Cavaleanti D et al., Entanglement versus energy in the entanglementtransfer Problem·[J] Phys. Rev. A，2006,74:042328-042330.
[44]周正威，郭光灿，量子信息讲座续讲第三讲量子纠缠态[J]物理，2000.
[45] Greenberger D M，Horne M A and Zeilinger A, In Bell’s Theorem,Quantum Theory and Conceptions of the Universe [M] The Netherlands:Kluwer Academics, Dordrecht,1989.
[46] Vedral V, Plenio M B, Rippin M A and Knight P L, QuantifyingEntanglement [J] Phys. Rev. Lett.,1997,78:2275-2278.
[47] Wootters W K, Entanglement of formation of an Arbitrary State of twoqubits [J] Phys. Rev. Lett.,1998,80:2245-2248.
[48] Bennett C H, Divincenzo D P, Smolin J A and Wootters W K, Mixed-stateentanglement and quantum error correction [J] Phys. Rev. A,1996,54:3824-3851.
[49] Peres A, Separability Criterion for Density Matrices [J] Phys. Rev. Lett.,1998,77(8):1413-1415.
[50] Vidal G and Werner R F, Computable measure of entanglement [J] Phys.Rev. A,2002,65(3):032314-032318.
[51] Vedral V, Plenio M B, Entanglement measures and purification procedures[J]. Phys. Rev. A,1998,57(3):1619-1633.
[52] Vedral V, The role of relative entropy in quantum information theory [J].Rev. Mod.Phys.,2002,74(1):197-234.
[53] Raimond J M, Brune M and Haroche S， Manipulating quantumentanglement with atoms and photons in a cavity.[J] Rev. Mod. Phys.,2001,73(3):565–582.
[54] Pellizzari T, Gardiner S A, Cirac J I and Zoller P，Decoherence, continuousobservation and quantum computing: A Cavtity QED Model.[J] Phys. Rev.Lett.,1995,75(21):3788–3791.
[55] Cirac J I, Zoller P, Kimble H and Mabuchi H，Quantum state transfer andentanglement distribution among distant nodes in a quantum network.[J]Phys. Rev. Lett.,1997,78(16):3221–3224.
[56] Li G X, Wu S P and Huang G M. Generation of entanglement andsqueezing in the system of two ions trapped in a cavity.[J] Phys. Rev. A,2005,71(6):063817.
[57] Rempe G, Thompson R J, Kimble R J and Lalezari R. Measurement ofultralow losses in an optical interferometer.[J] Opt. Lett.,1992,17(5):363–365.
[58] Wallraff A, Schuster D I, Blais A et al. Strong coupling of a single photonto a superconducting qubit using circuit quantum electrodynamics.[J]Nature,2004,431(7005):162–167.
[59] Sillanpaa M A, Park J I and Simmonds R W，Coherent quantum statestorage and transfer between two phase qubits via a resonant cavity.[J]Nature,2007,449(7161):438–442.
[60] Majer J, Chow J M, Gambetta J M et al., Coupling super conducting qubitsvia a cavity bus.[J] Nature,2007,449(7161):443–447.
[61] Nogues G, Rauschenbeutel A, Osnaghi S et al. Seeing a single photonwithout destroying it.[J] Nature,1999,400(6741):239–242.
[62] Rauschenbeutel A, Nogues G, Osnaghi S et al. Step-by-step engineeredmulti-particle entanglement.[J] Science,2000,288(5473):2024
[63] Brune M, Bernu J, Guerlin C et al. Process tomography of field dampingand measurment of Fock state lifetimes by quantum nondemolition photoncounting in a cavity.[J] Phys. Rev. Lett.,2008,101(24):240402-240405.
[64] Loss D and DiVincenzo D P. Quantum computation with quantum dots.[J]Phys.Rev. A,1998,57(1):120–126.
[65] Reimann S M and Manninen M. Electronic structure of quantum dots.[J]Rev.Mod. Phys.,2002,74(4):1283–1342.
[66] Hanson R, Kouwenhoven L P, Petta J R et al. Spins in few-electronquantumdot.[J] Rev. Mod. Phys.,2007,79(4):1217-1220.
[67] Feng M, An J H and Zhang W M. Generation of entangled photon pairs bysemiconductor quantum dots in a structure of quantum cellular automata.[J]J. Phys. C,2007,19(7):326215.
[68] Josephson B D, Possible new effects in superconductive tunnelling.[J]Phys. Lett.,1962,1(7):251–253
[69] Makhlin Y, Scho¨n G and Shnirman A. Quantum state engineering withJosephson-junction devices [J] Rev. Mod. Phys.,2001,73(2):357–400.
[70] Deng Z J, Gao K L and Feng M. Generation of N-qubit W states withSQUID qubits by adiabatic passage.[J] Phys. Rev. A,2006,74(6):064303
[71] Zhang X L, Gao K L and Feng M. Preparation of cluster states and W stateswith superconducting quantum-interference-device qubits in cavity QED.[J]Phys.Rev. A,2006,74(2):024303.
[72] Vandersypen L M K and Chuang I L，NMR techniques for quantum controland computation.[J] Rev. Mod. Phys.,2004,76(4):1037–1069.
[73] Dur W, Vidal G, and Cirac J I，Three qubits can be entangled in twoinequivalent way.[J] Phys. Rev. A,2000,62(6):062314.
[74] Shih Y H, Alley C O, New type of Einstein-Podolsky-Rosen experimentusing pairs of produced by optical parametric down-conversion [J] Phys.Rev. Lett.,1987,61(26):2921-2924.
[75] Arnesen M C, Bose S, Vedral V, Natural thermal and magneticentanglement in1D Heisenberg [J] Phys. Rev. Lett.,2001,87(1):017901-017904.
[76] Davidovich L, Zagury N, Brune M et al, Teleportation of an atomic statebetween two cavities using non-local microvave fields [J] Phys. Rev. A,1994,50(2):R895-R898.
[77] Cirac J I, Parkins A S, Schemes for atomic-state teleportation [J]. Phys. Rev.A,1994,50(6):R4441-R4444.
[78] Turchette Q A, Wood C S, King B E, Myatt C J, Leibfried D, Itano W M,Monroe C and Wineland D J, Deterinistic entanglement of two trapped ions[J].Phys. Rev. Lett.,1998,81(17):3631-3634.
[79] Zhao Z, Chen Y A, Zhang A N, Yang T, Briegel H J and Pan J W,Experimental demonstration of five-photon entanglement andopen-destination teleportation [J] Nature,2004,430:54-58.
[80] Pan J W, Daniell MM Gasparoni S, Weihs G and Zeilinger A, Experimentaldemonstration of four-photon entanglement and high-fidelity teleportation[J] Phys. Rev. Lett.,2001,86(20):4435-4438.
[81] Yu T and Eberly J H, Finite-time disentanglement Via Spontaneousemission [J] Phys. Rev. Lett.,2004,93:140404-104048.
[82] Yu T and Eberly J H, Quantum open system theory: bipartite aspects [J].Phys. Rev. Lett.,2006,97:140403-104047.
[83] DiVincenzo D. P, Horodecki M, Leung D W, Smolin J A., and. Terha B. M,Locking Classical Correlations in Quantum States [J]. Phys. Rev. Lett.,2004,92:067902-067905.
[84] Piani M., Christandl M., Mora C. E., and Horodecki P, Broadcast CopiesReveal the Quantumness of correlations[J] Phys. Rev. Lett.,2009,102:250503-250506.
[85] Modi K, Paterek T, Son W, Vedral V and Williamson M, Unified view ofquantum and classical correlations [J] Phys. Rev. Lett.,2010,104(8):080501-080504.
[86] Dakic B, Vedral B, and Brukner C, Necessary and suffickient condition fornonzero quantum discord [J] Phys. Rev. Lett.,2010,105(19):090502-090505.
[87] Luo S and Fu S, Geometric measure of quantum discord [J] Phys. Rev.Lett.,2010,82(3):034302-034305.
[88] Dowling J P and Bowden C M. Anomalous Index of Refraction in PhotonicBand Gap Materials [J].Journal of Modern Optics.1994,41:345-351.
[89] Nelson R L and Haus J W.One-dimensional Photonic Crystal in ReflectionGeometry for Optical Applications [J].Appl.Phy.Lett.2003,83:1089-1091.
[90] Li Z Y, Gu B Y and Yang G Z，Large Absolute Band Gap in2D AnisotropicPhotonic Crystals [J]. Phys. Rev. Lett.1998,81:2574-2577.
[91] Winn J N and Meade R D，Two-dimensional Photonic Band-Gap Materials[J]. Journal of Modern Optics.1994,41:257-273.
[92] Li Z Y, Wang J and Gu B Y. Creation of Partial Band Gaps in AnisotropicPhotonic Band Gaps Structures [J]. Phys. Rev. B.1999,60:5751-5758.
[93] Sozuer H S and Dowling J P. Photonic Band calculations for WoodpileStructures [J]. Journal of Modern Optics.1994,41:231-239.
[94] Zakhidov A A, Baughman R H and Iqbal Z. Carbon structures with three-dimensional periodicity at optical wavelengths [J]. Science.1998,282:897-901.
[95] Steven G J, Fan S, Mekis A,et al.Multipole-cancellation mechanism forhigh-Q cavities in the absence of a complete photonic band gap [J]. Appl.Phys. Lett.2001,78:3388-3390.
[96] Scherer A, Doll T, Yablonvitch E, et al. Electromagnetic crystal structures,design, synthesis, and applications (Optical)[J]. J. Lightwave Tech.1999,17(11):1928-1930.
[97] Lee R K, Painter O J, D'Urso B, et al. Measurement of spontaneousemission from a two-dimensional photonic band gap defined microcavity atnear-infrared wavelengths [J]. Appl. Phys. Lett.1999,74(11):1522-1524.
[98] Hougaard K G, Broeng J and Bjarklev A. Low pump power photoniccrystal fibre amplifers [J]. Electron. Lett.2003,39:599-600.
[99] Mazurenko D A, Akimov A V, Pevtsov B A, et al. Ultrafast switching in Si-embedded opals [J]. Physica E.2003,17:410-413.
[100] Mizugruchi J, Tanaka Y, Tamura S, et al. Focusing of light in a three-dimessional cubic photonic crystal [J]. Phys. Rev. B.2003,67:075109-075119.
[101] Yablonovitch E and Gmitter T J. Donor and acceptor modes in photonicband structure [J]. Phys. Rev. Lett.1991,67:3380–3383.
[102] zbay, E. Layer-by-layer photonic crystals from microwave to far-infraredfrequencies [J] J. Opt. Soc. Am. B.1996,13:1945-1955.
[103] Noda S, Yokoyama M, Imada M, et al. Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design [J]. Science.2001,293:1123-1125.
[104] Campbell M and Sharp D N. Fabrication of photonic crystals for the visiblespectrum by holographic lithography [J]. Nature.2000,404:53-56.
[105] Huang C H, Stott J J and Petschek R G. Routes to Self-assembling StablePhotonic B and-gap Phases in E mulsions of Chiral Nematics with IsotropicFluids [J]. Phys. Rev. Lett.1998,80(25):5603-5606.
[106] Feiertag G, Ehrfeld W, Freimuth H, et al. Fabrication of Photonic Crystalsby Deep X-ray Lithography [J]. Appl. Phys. Lett.1997,71(11):1441-1445.
[107] Ballato J.Tailoring. Visible Photonic Bandgaps through MicrostructuralOrder and Coupled Material Effects in Si02Colloidal Crystals [J]. J. Opt.Soc. Am. B.2000,17(2):219-225.
[108] Sajeev J and Wang J. Quantum electrodynamics near a photonic band gap:Photon bound states and dressed atoms Phys. Rev. Lett.1990,64:2418–2421.
[109] Keital C H. Vacuum modified resonance fluorescence in intense laser fields[J] J. Mod. Opt.1996,43:1555-1562.
[110] Woldeyohannes M and Sajeev J. Coherent control of spontaneous emissionnear a photonic band edge: A qubit for quantum computation [J] Phys. Rev.A1999,60,5046-5068.
[111] Bay S, Lambropoulos P and Molmer K. Atom-atom interaction in stronglymodified reservoirs [J] Phys. Rev. A1997,55:1485-1496.
[112] Yang Y P and Zhu Z Y. Spontaneous emission from a three-level atom intwo-band photonic crystals [J] J. Mod. Opt2000,47:1513-1547.
[113] Zhang H Z, Tang S H, Dong P and He J. Quantum interference inspontaneous emission of an atom embedded in a double-band photoniccrystal [J] Phys. Rev. A2002,65:063802-063808.
[114] Paspalakis E, Kylstra N J and Kninght P L. Transparency near a photonicband edge [J] Phys. Rev. A1999,60: R33-R36.
[115] Singh M R. Anomalous electromagnetically induced transparency inphotonic-band-gap materials [J] Phys. Rev. A2004,70:033813-033819.
[116] Singh M R. Photon transparency in metallic photonic crystals doped withan ensemble of nanoparticles [J] Phys. Rev A2009,79:013826-013834.
[117] Singh M R.Transparency and spontaneous emission in a densely dopedphotonic band gap material [J] J. Phys. B: At. Mol. Opt. Phys.2006,39:5131–5141.
[118] Englund D, Faraon A, Zhang B, Yamamoto Y and. Vuckovic J, Generationand transfer of single photons on a photonic crystal chip [J] Opt. Express.,2007,15:5550-5558.
[119] Lin Z L, and Vuckovic J, Enhanced two-photon processes in singlequantum dots inside photonic crystal nanocavities [J]. Phys. Rev. B,2010,81:035301-035305.
[120] Pathak P K and Hughes S., Cavity-assisted fast generation of entangledphoton pairs through the biexciton-exciton cascade [J] Phys. Rev. B,2009,80:155325.
[121] Ten H T, Zhang W M, and Li G X, Entangling two distant nanocavities viaa waveguide [J] Phys. Rev. B,2011,83:062310-062318.
[122] Nielsen M A and Chuang I L, Quantum Computation and QuantumInformation [M] Cambridge, UK: Cambridge University Press2000.
[123] Schumacher B W and Nielsen M A., Quantum data processing and errorcorrection [J] Phys. Rev. A,1996,54:2629-2635.
[124] Reina J H, Quiroga L and Johnson N F, Decoherence of quantum registers[J] Phys. Rev. A,2002,65:032326.
[125] Dajka J, Mierzejewski M and Luczka J, Fidelity of asymmetric dephasingchannels [J] Phys. Rev. A,2009,79:012104(9).
[126] Leibfried D, Blatt R, Monroe C and Wineland D, Quantum dynamics ofsingle trapped ions [J] Rev. Mod. Phys,2005,75:281-324.
[127] Dajka J and Luczka J, Origination and survival of qudit-qudit entanglementin open systems [J] Phys. Rev. A,2008,77:062303(7).
[128] Doll R, Wubs M, Hanggi P and Kohler S, Incomplete pure dephasing ofN-qubit entangled W states [J] Phys. Rev. B,2007,76:045317(15).
[129] Myatt C J, King B E, Turchette Q A, Sackett C A, Kielpinski D, Itano W M,Monroe C and Wineland D J, Decoherence of quantum superpositionsthrough coupling to engineered reservoirs [J] Nature,2000,403:269-273.
[130] Turchette Q A, Myatt C J, King B E, Sackett C A, Kielpinski D, Itano W M,Monroe C and Wineland D J, Decoherence and decay of motional quantumstates of a trapped atom coupled to engineered reservoirs [J] Phys. Rev. A,2000,62:053807(22).
[131] Salles A, de Melo F, Almeida M P, Hor-Meyll M, Walborn S P SoutoRibeiro P H and Davidovich L, Experimental investigation of the dynamicsof entanglement: Sudden death, complementarity, and continuousmonitoring of the environment [J] Phys. Rev. A,2008,78:022322(15).
[132] Raimond J M, Brune M and Haroche S, Manipulating quantumentanglement with atoms and photons in a cavity [J] Rev. Mod. Phys,2001,73:582-565.
[133] Gradshteyn I-S and Ryzhik I M, Table of Integrals, Series, and Products [M]New York: Academic,1980.
[134] Breuer H-P, Kappler B and Petruccione F, Stochastic wave-function methodfor non-Markovian quantum master equations [J] Phys. Rev. A,1999,59:1633-1643.
[135] Braunstein S L and Caves C M, Statistical distance and the geometry ofquantum states [J] Phys. Rev. Lett,,1994,72:3439-3942.
[136] Bellomo B, Franco R-L, Maniscalco S and Compagno G, Entanglementtrapping in structured environments,[J] Phys. Rev. A,1999,78:060302.
[137] Oliveira J.G., Rossi R., Nemes M.C., Protecting, enhancing, and revivingentanglement [J]. Phys. Rev. A,2008,78:044301(3).
[138] Rey A.M., Jiang L., Fleischhauer M., Demler E., Lukin M.D., Many-bodyprotected entanglement generation in interacting spin systems [J]. Phys.Rev. A,2008,77:052305(12).
[139] Mundarain D., Orszag M., Entanglement preservation by continuousdistillation [J]. Phys. Rev. A,2009,79:052333(5).
[140] Alharbi A.F., Ficek Z., Deterministic creation of stationary entangled statesby dissipation [J] Phys. Rev. A,2010,82:054103(4).
[141] Zhang K., Li Z.Y., Transfer behavior of quantum states between atoms inphotonic crystal coupled cavities [J]. Phys. Rev. A,2010,81:033843(10).
[142] Englund D., Majumdar A., Faraon A., Toishi M., Stoltz N., Petroff P.,Vuckovic J., Resonant Excitation of a Quantum Dot Strongly Coupled to aPhotonic Crystal Nanocavity [J]. Phys. Rev. Lett.,2010,104:073904(4).
[143] Craig D.P., Molecular Quantum Electrodynamics: An introduction toRadiation-Molecular Interaction [M] Acamedic Press,1984.
[144] Lehmberg R.H., Radiation from an N-Atom System. II. SpontaneousEmission from a Pair of Atoms [J] Phys. Rev. A,1970,2:889-896.
[145] Paz J.P., Roncaglia A.J., Dynamics of the Entanglement between TwoOscillators in the Same Environment [J] Phys. Rev. Lett.,2008,100:220401.
[146] John S., Wang J., Quantum optics of localized light in a photonic band gap[J]. Phys. Rev. B,1991,43:12772-12789.
[147] Yang Y., Zhu S.-Y., Spontaneous-emission enhancement and populationoscillation in photonic crystals via quantum interference [J] Phys. Rev. A,2000,61:043809(16).
[148] Yang Y., Zhu S.-Y., Spontaneous emission from a two-level atom in athree-dimensional photonic crystal [J] Phys. Rev. A,2000,61:013805(11).
[149] Zanardi P., Rasetti M., Noiseless Quantum Codes [J] Phys. Rev. Lett,1997,79:3306-3309.
[150] Hatef A., Singh M R, Type-I cascaded quadratic soliton compression inlithium niobate: Compressing femtosecond pulses from high-power fiberlasers [J] Phys. Rev. A,2010,81:053815(14).
[151] Niset J, Cerf N J, Multipartite nonlocality without entanglement in manydimensions [J] Phys. Rev. A,2006,74:052103(8).
[152] Lanyon B.P., Barbieri M., Almeida M.P., White A.G., ExperimentalQuantum Computing without Entanglement [J] Phys. Rev. Lett.,2008,101:200501-200504.
[153] Horodecki M., Horodecki P., Horodecki R., Oppenheim J., Sen A., Sen U.,Synak-Radtke B., Local versus nonlocal information inquantum-information theory: Formalism and phenomena [J] Phys. Rev. A.,2005,71:062307(25).
[154] Zurek W.H., Quantum discord and Maxwell’s demons [J] Phys. Rev. A.,2003,67:012320(6).
[155] Datta A., Shaji A., Caves C.M., Quantum Discord and the Power of OneQubit [J] Phys. Rev. Lett.,2008,100:050502-050505.
[156] DeVoe R.G., Brewer R.G., Observation of Superradiant and SubradiantSpontaneous Emission of Two Trapped Ions [J] Phys. Rev. Lett.,1996,76:2049-2052.
[157] Mazzola L., Maniscalco S., Piilo J., Suominen K.-A., Garraway B.M.,Sudden death and sudden birth of entanglement in common structuredreservoirs [J] Phys. Rev. A,2009,79:042302(4).
[158] Ficek Z., Tana R., Dark periods and revivals of entanglement in atwo-qubit system [J] Phys. Rev. A,2006,74:024304(4).
[159] Jiang X., Jiang Y., Wang Y., Sun X., Non-Markovian decay of a three-levelΛ-type atom in a photonic-band-gap reservoir [J] Phys. Rev. A,2006,73:033802(6).
[160] Garraway B.M., Nonperturbative decay of an atomic system in a cavity [J].Phys. Rev. A,1997,55:2290-2303.
[161] Nikolopoulos G.M., Bay S., Lambropoulos P., Quantum systems coupled toa structured reservoir with multiple excitations [J] Phys. Rev. A,1999,60:5079-5082.
[162] Nikolopoulos G.M., Lambropoulos P., Beyond single-photon localization atthe edge of a photonic band gap [J] Phys. Rev. A,2007,61:053812(7).
[163] Natali S., Ficek Z., Temporal and diffraction effects in entanglementcreation in an optical cavity [J] Phys. Rev. A,2007,75:042307(10).
[164] Ficek Z., Tana R., Delayed sudden birth of entanglement,[J]. Phys. Rev. A,2008,77:054301(4).
[165] Benatti F., Floreanini R., Piani M., Environment Induced Entanglement inMarkovian Dissipative Dynamics [J]. Phys. Rev. A,2003,91:070402(4).
[166] Schneider S., Milburn G.J., Entanglement in the steady state of acollective-angular-momentum (Dicke) model [J] Phys. Rev. A,2002,65:042107(5).
[2] Nielsen M A and Chuang1L，Quantum computation and quantuminformation [M] Cambridge: Cambridge University Press,2000.
[3] Shor P W, Polynomial-time algorithms for prime factorization and discretelogarithms on a quantum computer [M] SIAM J Comput,1996.
[4] Grover L K, A fast quantum mechanics algorithm of database search In:Proceedings of the28thAnnual ACM Symposium on Theory ofComputation [M] Philadelphia PA USA,1996.
[5] Knill E, Laamme R, Martinez R, et al, An algorithmic benchmark forquantum information processing [J] Nature,2000,404:368-370.
[6]范洪义，从量子力学到量子光学[M].上海：上海交通大学出版社，2005.
[7]苏汝铿等，量子力学[M].北京：高等教育出版社，2002.
[8] Lee J Y, Kim M. S, Entanglement teleportation via werner states [J] Phys.Rev. Lett.,2000,84(18):4236-4239.
[9] Akio M, Teleportation without resorting to Bell measurement [J] Phys. Lett.A.,2000,270:293-295.
[10]曾谨言，量子力学[M].北京：科学出版社，2007.
[11] Artur K. Ekert, Quantum cryptography based on Bell’s theorem [J] Phys.Rev. Lett.,1991,67:661-664.
[12] Knill E and Laflamme R, Power of one bit of quantum information [J]Phys. Rev. Lett.,1998,81(25):5672-5675.
[13] Datta A, Flammia S T and Caves C M, Entanglement and the power of onequbit [J] Phys. Rev.A,2005,72(4):042316-042318.
[14] Datta A, Anil S J and Carlton M Caves, Quantum discord and the power ofone qubit [J] Phys. Rev. Lett.,2008,100(5):050502-050505.
[15] Henderson L and Vedral V, Classical, quantum and total correlations [J]Phys. A: Math. Gen,2001,34:6899-6905.
[16] Ollivier H and Zurek W H, Quantum discord: A measure of thequantumness of correlations [J] Phys. Rev. Lett.,2001,88(1):017901-017905.
[17] Breuer H P and Petruccione F, The theory of open quantum systems [M]New York: Oxford University Press,2002.
[18] Breuer H P, Laine E M and Piilo J, Measure for the degree ofnon-markovian behavior of quantum processes in open systems [J] Phys.Rev. Lett.,2009,103(21):210401-210405.
[19] Grabert H, Schramm P and Ingold G L, Quantum Brownian motion: Thefunctional integral approach [J] Phys. Rep.,1988,168:115-207.
[20] Stelmachovic J and Buzek V, Dynamics of open quantum systems initiallyentangled with environment: Beyond the Kraus representation [J]Phys.Rev.A,2001,64:062106.
[21] Schilemann J, Khaetskii A and Loss D, Electron spin dynamics in quantumdots and related nanostructures due to hyperfine interaction with nuclei [J] J.Phys.: Condens. Matter,2003,15: R1809-R1833.
[22] Haake F and Reibold R, Strong damping and low-temperature anomaliesfor the harmonic oscillator [J] Phys.Rev.A,1985,32:2462-2475.
[23] Hu B L, Paz J P and Zhang Y, Quantum Brownian motion in a generalenvironment: Exact master equation with nonlocal dissipation and colorednoised [J] Phys.Rev. D,1992,45:2843-2861.
[24] Michel M, Mahler G and Gemmer J, Fourier’s law from Schrodingerdynamics [J] Phys. Rev. Lett.,2005,95:180602-180605.
[25] Bellomo B, Lofranco R and Compagno G, Entanglement dynamics of twoindependent qubits in environments with and without memory [J] Phys.Rev. A,2008,77:032342.
[26] Yablonovitch E. Inhibited Spontaneous Emission in Solid-State Physics andElectronics [J]. Phys. Rev. Lett.1987,58:2059–2062.
[27] Sajeev J. Strong localization of photons in certain disordered dielectricsuper lattices [J]. Phys. Rev. Lett.1987,58:2486–2489.
[28] Jie G, Sun F W, and Wong C W. Implementation scheme for quantumcontrolled phase-flip gate through quantum dot in slow-light photoniccrystal waveguide [J]. App. Phys. Lett.2008,93:151108-1511011.
[29] Entezar S R. Entanglement of a two-level atom and its spontaneousemission near the edge of a photonic band gap [J]. Phys. Lett. A2009,373:3413-3418.
[30] Entezar S R. Controllable atom–photon entanglement near a3D anisotropicphotonic band edge [J]. J. Phys. B: At. Mol. Opt. Phys.2010,43:085503-085510.
[31] Cirac J I, et al, Quantum computation with cold trapped ions [J] Phys. Rev.Lett.1995,74:4091–4094.
[32] Buzek V and Hillery M, Quantum copying: Beyond the no-cloning theorem[J] Phys. Rev. A1996,54:1844–1852.
[33] John von Neumann, Mathematical foundations of quantum mechanics [M]Princeton University Press,1996.
[34] Landau L D and Lifshita E M, Quantum Mechanics (Non-RelativisticTheory)[M] Brtterworth-Heinemann,1981.
[35] Fano U, Description of states in quantum mechanics by density matrix andoperator techniques [J] Rev. Mod. Phys.,1957,29(1):74-93.
[36] Reinhard F. W, Quantum states with Einstein-Podolsky-Rosen correlationsadmitting a hidden-variable model [J] Phys. Rev. A1989,40:4277–4281.
[37] Gu S J, Fidelity approach to quantum phase transitions [J] InternationalJournal of Modern Physics B,2010,24(23):4371-4458.
[38]张永德,量子信息物理原理.[M]科学出版社,2006.
[39] Einstein A, Podolsky B and Rosen N, Can quantum mechanical descriptionof physical reality be considered dcomplete?[J] Phys. Rev.,1935,47:777-779.
[40] Roseilde T., Verrueeh P, Fubin A, Haas S and Tognett V, Entanglement andFactorized Ground States in Two-Dimensional Quantum Antiferromagnets[J] Phys. Rev. Lett.,2005,94:147208(4).
[41] Osborn T J and Nielsen M A, Entanglement in a simple quantum phasetransition [J] Phys. Rev. A,2002,66:032110(12).
[42] Vidal G, Latorre J L, Rieo E and Kitae A, Entanglement in QuantumCritical Phenomena [J] Phys. Rev. Lett.,2003,90:227902(4).
[43] Cavaleanti D et al., Entanglement versus energy in the entanglementtransfer Problem·[J] Phys. Rev. A，2006,74:042328-042330.
[44]周正威，郭光灿，量子信息讲座续讲第三讲量子纠缠态[J]物理，2000.
[45] Greenberger D M，Horne M A and Zeilinger A, In Bell’s Theorem,Quantum Theory and Conceptions of the Universe [M] The Netherlands:Kluwer Academics, Dordrecht,1989.
[46] Vedral V, Plenio M B, Rippin M A and Knight P L, QuantifyingEntanglement [J] Phys. Rev. Lett.,1997,78:2275-2278.
[47] Wootters W K, Entanglement of formation of an Arbitrary State of twoqubits [J] Phys. Rev. Lett.,1998,80:2245-2248.
[48] Bennett C H, Divincenzo D P, Smolin J A and Wootters W K, Mixed-stateentanglement and quantum error correction [J] Phys. Rev. A,1996,54:3824-3851.
[49] Peres A, Separability Criterion for Density Matrices [J] Phys. Rev. Lett.,1998,77(8):1413-1415.
[50] Vidal G and Werner R F, Computable measure of entanglement [J] Phys.Rev. A,2002,65(3):032314-032318.
[51] Vedral V, Plenio M B, Entanglement measures and purification procedures[J]. Phys. Rev. A,1998,57(3):1619-1633.
[52] Vedral V, The role of relative entropy in quantum information theory [J].Rev. Mod.Phys.,2002,74(1):197-234.
[53] Raimond J M, Brune M and Haroche S， Manipulating quantumentanglement with atoms and photons in a cavity.[J] Rev. Mod. Phys.,2001,73(3):565–582.
[54] Pellizzari T, Gardiner S A, Cirac J I and Zoller P，Decoherence, continuousobservation and quantum computing: A Cavtity QED Model.[J] Phys. Rev.Lett.,1995,75(21):3788–3791.
[55] Cirac J I, Zoller P, Kimble H and Mabuchi H，Quantum state transfer andentanglement distribution among distant nodes in a quantum network.[J]Phys. Rev. Lett.,1997,78(16):3221–3224.
[56] Li G X, Wu S P and Huang G M. Generation of entanglement andsqueezing in the system of two ions trapped in a cavity.[J] Phys. Rev. A,2005,71(6):063817.
[57] Rempe G, Thompson R J, Kimble R J and Lalezari R. Measurement ofultralow losses in an optical interferometer.[J] Opt. Lett.,1992,17(5):363–365.
[58] Wallraff A, Schuster D I, Blais A et al. Strong coupling of a single photonto a superconducting qubit using circuit quantum electrodynamics.[J]Nature,2004,431(7005):162–167.
[59] Sillanpaa M A, Park J I and Simmonds R W，Coherent quantum statestorage and transfer between two phase qubits via a resonant cavity.[J]Nature,2007,449(7161):438–442.
[60] Majer J, Chow J M, Gambetta J M et al., Coupling super conducting qubitsvia a cavity bus.[J] Nature,2007,449(7161):443–447.
[61] Nogues G, Rauschenbeutel A, Osnaghi S et al. Seeing a single photonwithout destroying it.[J] Nature,1999,400(6741):239–242.
[62] Rauschenbeutel A, Nogues G, Osnaghi S et al. Step-by-step engineeredmulti-particle entanglement.[J] Science,2000,288(5473):2024
[63] Brune M, Bernu J, Guerlin C et al. Process tomography of field dampingand measurment of Fock state lifetimes by quantum nondemolition photoncounting in a cavity.[J] Phys. Rev. Lett.,2008,101(24):240402-240405.
[64] Loss D and DiVincenzo D P. Quantum computation with quantum dots.[J]Phys.Rev. A,1998,57(1):120–126.
[65] Reimann S M and Manninen M. Electronic structure of quantum dots.[J]Rev.Mod. Phys.,2002,74(4):1283–1342.
[66] Hanson R, Kouwenhoven L P, Petta J R et al. Spins in few-electronquantumdot.[J] Rev. Mod. Phys.,2007,79(4):1217-1220.
[67] Feng M, An J H and Zhang W M. Generation of entangled photon pairs bysemiconductor quantum dots in a structure of quantum cellular automata.[J]J. Phys. C,2007,19(7):326215.
[68] Josephson B D, Possible new effects in superconductive tunnelling.[J]Phys. Lett.,1962,1(7):251–253
[69] Makhlin Y, Scho¨n G and Shnirman A. Quantum state engineering withJosephson-junction devices [J] Rev. Mod. Phys.,2001,73(2):357–400.
[70] Deng Z J, Gao K L and Feng M. Generation of N-qubit W states withSQUID qubits by adiabatic passage.[J] Phys. Rev. A,2006,74(6):064303
[71] Zhang X L, Gao K L and Feng M. Preparation of cluster states and W stateswith superconducting quantum-interference-device qubits in cavity QED.[J]Phys.Rev. A,2006,74(2):024303.
[72] Vandersypen L M K and Chuang I L，NMR techniques for quantum controland computation.[J] Rev. Mod. Phys.,2004,76(4):1037–1069.
[73] Dur W, Vidal G, and Cirac J I，Three qubits can be entangled in twoinequivalent way.[J] Phys. Rev. A,2000,62(6):062314.
[74] Shih Y H, Alley C O, New type of Einstein-Podolsky-Rosen experimentusing pairs of produced by optical parametric down-conversion [J] Phys.Rev. Lett.,1987,61(26):2921-2924.
[75] Arnesen M C, Bose S, Vedral V, Natural thermal and magneticentanglement in1D Heisenberg [J] Phys. Rev. Lett.,2001,87(1):017901-017904.
[76] Davidovich L, Zagury N, Brune M et al, Teleportation of an atomic statebetween two cavities using non-local microvave fields [J] Phys. Rev. A,1994,50(2):R895-R898.
[77] Cirac J I, Parkins A S, Schemes for atomic-state teleportation [J]. Phys. Rev.A,1994,50(6):R4441-R4444.
[78] Turchette Q A, Wood C S, King B E, Myatt C J, Leibfried D, Itano W M,Monroe C and Wineland D J, Deterinistic entanglement of two trapped ions[J].Phys. Rev. Lett.,1998,81(17):3631-3634.
[79] Zhao Z, Chen Y A, Zhang A N, Yang T, Briegel H J and Pan J W,Experimental demonstration of five-photon entanglement andopen-destination teleportation [J] Nature,2004,430:54-58.
[80] Pan J W, Daniell MM Gasparoni S, Weihs G and Zeilinger A, Experimentaldemonstration of four-photon entanglement and high-fidelity teleportation[J] Phys. Rev. Lett.,2001,86(20):4435-4438.
[81] Yu T and Eberly J H, Finite-time disentanglement Via Spontaneousemission [J] Phys. Rev. Lett.,2004,93:140404-104048.
[82] Yu T and Eberly J H, Quantum open system theory: bipartite aspects [J].Phys. Rev. Lett.,2006,97:140403-104047.
[83] DiVincenzo D. P, Horodecki M, Leung D W, Smolin J A., and. Terha B. M,Locking Classical Correlations in Quantum States [J]. Phys. Rev. Lett.,2004,92:067902-067905.
[84] Piani M., Christandl M., Mora C. E., and Horodecki P, Broadcast CopiesReveal the Quantumness of correlations[J] Phys. Rev. Lett.,2009,102:250503-250506.
[85] Modi K, Paterek T, Son W, Vedral V and Williamson M, Unified view ofquantum and classical correlations [J] Phys. Rev. Lett.,2010,104(8):080501-080504.
[86] Dakic B, Vedral B, and Brukner C, Necessary and suffickient condition fornonzero quantum discord [J] Phys. Rev. Lett.,2010,105(19):090502-090505.
[87] Luo S and Fu S, Geometric measure of quantum discord [J] Phys. Rev.Lett.,2010,82(3):034302-034305.
[88] Dowling J P and Bowden C M. Anomalous Index of Refraction in PhotonicBand Gap Materials [J].Journal of Modern Optics.1994,41:345-351.
[89] Nelson R L and Haus J W.One-dimensional Photonic Crystal in ReflectionGeometry for Optical Applications [J].Appl.Phy.Lett.2003,83:1089-1091.
[90] Li Z Y, Gu B Y and Yang G Z，Large Absolute Band Gap in2D AnisotropicPhotonic Crystals [J]. Phys. Rev. Lett.1998,81:2574-2577.
[91] Winn J N and Meade R D，Two-dimensional Photonic Band-Gap Materials[J]. Journal of Modern Optics.1994,41:257-273.
[92] Li Z Y, Wang J and Gu B Y. Creation of Partial Band Gaps in AnisotropicPhotonic Band Gaps Structures [J]. Phys. Rev. B.1999,60:5751-5758.
[93] Sozuer H S and Dowling J P. Photonic Band calculations for WoodpileStructures [J]. Journal of Modern Optics.1994,41:231-239.
[94] Zakhidov A A, Baughman R H and Iqbal Z. Carbon structures with three-dimensional periodicity at optical wavelengths [J]. Science.1998,282:897-901.
[95] Steven G J, Fan S, Mekis A,et al.Multipole-cancellation mechanism forhigh-Q cavities in the absence of a complete photonic band gap [J]. Appl.Phys. Lett.2001,78:3388-3390.
[96] Scherer A, Doll T, Yablonvitch E, et al. Electromagnetic crystal structures,design, synthesis, and applications (Optical)[J]. J. Lightwave Tech.1999,17(11):1928-1930.
[97] Lee R K, Painter O J, D'Urso B, et al. Measurement of spontaneousemission from a two-dimensional photonic band gap defined microcavity atnear-infrared wavelengths [J]. Appl. Phys. Lett.1999,74(11):1522-1524.
[98] Hougaard K G, Broeng J and Bjarklev A. Low pump power photoniccrystal fibre amplifers [J]. Electron. Lett.2003,39:599-600.
[99] Mazurenko D A, Akimov A V, Pevtsov B A, et al. Ultrafast switching in Si-embedded opals [J]. Physica E.2003,17:410-413.
[100] Mizugruchi J, Tanaka Y, Tamura S, et al. Focusing of light in a three-dimessional cubic photonic crystal [J]. Phys. Rev. B.2003,67:075109-075119.
[101] Yablonovitch E and Gmitter T J. Donor and acceptor modes in photonicband structure [J]. Phys. Rev. Lett.1991,67:3380–3383.
[102] zbay, E. Layer-by-layer photonic crystals from microwave to far-infraredfrequencies [J] J. Opt. Soc. Am. B.1996,13:1945-1955.
[103] Noda S, Yokoyama M, Imada M, et al. Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design [J]. Science.2001,293:1123-1125.
[104] Campbell M and Sharp D N. Fabrication of photonic crystals for the visiblespectrum by holographic lithography [J]. Nature.2000,404:53-56.
[105] Huang C H, Stott J J and Petschek R G. Routes to Self-assembling StablePhotonic B and-gap Phases in E mulsions of Chiral Nematics with IsotropicFluids [J]. Phys. Rev. Lett.1998,80(25):5603-5606.
[106] Feiertag G, Ehrfeld W, Freimuth H, et al. Fabrication of Photonic Crystalsby Deep X-ray Lithography [J]. Appl. Phys. Lett.1997,71(11):1441-1445.
[107] Ballato J.Tailoring. Visible Photonic Bandgaps through MicrostructuralOrder and Coupled Material Effects in Si02Colloidal Crystals [J]. J. Opt.Soc. Am. B.2000,17(2):219-225.
[108] Sajeev J and Wang J. Quantum electrodynamics near a photonic band gap:Photon bound states and dressed atoms Phys. Rev. Lett.1990,64:2418–2421.
[109] Keital C H. Vacuum modified resonance fluorescence in intense laser fields[J] J. Mod. Opt.1996,43:1555-1562.
[110] Woldeyohannes M and Sajeev J. Coherent control of spontaneous emissionnear a photonic band edge: A qubit for quantum computation [J] Phys. Rev.A1999,60,5046-5068.
[111] Bay S, Lambropoulos P and Molmer K. Atom-atom interaction in stronglymodified reservoirs [J] Phys. Rev. A1997,55:1485-1496.
[112] Yang Y P and Zhu Z Y. Spontaneous emission from a three-level atom intwo-band photonic crystals [J] J. Mod. Opt2000,47:1513-1547.
[113] Zhang H Z, Tang S H, Dong P and He J. Quantum interference inspontaneous emission of an atom embedded in a double-band photoniccrystal [J] Phys. Rev. A2002,65:063802-063808.
[114] Paspalakis E, Kylstra N J and Kninght P L. Transparency near a photonicband edge [J] Phys. Rev. A1999,60: R33-R36.
[115] Singh M R. Anomalous electromagnetically induced transparency inphotonic-band-gap materials [J] Phys. Rev. A2004,70:033813-033819.
[116] Singh M R. Photon transparency in metallic photonic crystals doped withan ensemble of nanoparticles [J] Phys. Rev A2009,79:013826-013834.
[117] Singh M R.Transparency and spontaneous emission in a densely dopedphotonic band gap material [J] J. Phys. B: At. Mol. Opt. Phys.2006,39:5131–5141.
[118] Englund D, Faraon A, Zhang B, Yamamoto Y and. Vuckovic J, Generationand transfer of single photons on a photonic crystal chip [J] Opt. Express.,2007,15:5550-5558.
[119] Lin Z L, and Vuckovic J, Enhanced two-photon processes in singlequantum dots inside photonic crystal nanocavities [J]. Phys. Rev. B,2010,81:035301-035305.
[120] Pathak P K and Hughes S., Cavity-assisted fast generation of entangledphoton pairs through the biexciton-exciton cascade [J] Phys. Rev. B,2009,80:155325.
[121] Ten H T, Zhang W M, and Li G X, Entangling two distant nanocavities viaa waveguide [J] Phys. Rev. B,2011,83:062310-062318.
[122] Nielsen M A and Chuang I L, Quantum Computation and QuantumInformation [M] Cambridge, UK: Cambridge University Press2000.
[123] Schumacher B W and Nielsen M A., Quantum data processing and errorcorrection [J] Phys. Rev. A,1996,54:2629-2635.
[124] Reina J H, Quiroga L and Johnson N F, Decoherence of quantum registers[J] Phys. Rev. A,2002,65:032326.
[125] Dajka J, Mierzejewski M and Luczka J, Fidelity of asymmetric dephasingchannels [J] Phys. Rev. A,2009,79:012104(9).
[126] Leibfried D, Blatt R, Monroe C and Wineland D, Quantum dynamics ofsingle trapped ions [J] Rev. Mod. Phys,2005,75:281-324.
[127] Dajka J and Luczka J, Origination and survival of qudit-qudit entanglementin open systems [J] Phys. Rev. A,2008,77:062303(7).
[128] Doll R, Wubs M, Hanggi P and Kohler S, Incomplete pure dephasing ofN-qubit entangled W states [J] Phys. Rev. B,2007,76:045317(15).
[129] Myatt C J, King B E, Turchette Q A, Sackett C A, Kielpinski D, Itano W M,Monroe C and Wineland D J, Decoherence of quantum superpositionsthrough coupling to engineered reservoirs [J] Nature,2000,403:269-273.
[130] Turchette Q A, Myatt C J, King B E, Sackett C A, Kielpinski D, Itano W M,Monroe C and Wineland D J, Decoherence and decay of motional quantumstates of a trapped atom coupled to engineered reservoirs [J] Phys. Rev. A,2000,62:053807(22).
[131] Salles A, de Melo F, Almeida M P, Hor-Meyll M, Walborn S P SoutoRibeiro P H and Davidovich L, Experimental investigation of the dynamicsof entanglement: Sudden death, complementarity, and continuousmonitoring of the environment [J] Phys. Rev. A,2008,78:022322(15).
[132] Raimond J M, Brune M and Haroche S, Manipulating quantumentanglement with atoms and photons in a cavity [J] Rev. Mod. Phys,2001,73:582-565.
[133] Gradshteyn I-S and Ryzhik I M, Table of Integrals, Series, and Products [M]New York: Academic,1980.
[134] Breuer H-P, Kappler B and Petruccione F, Stochastic wave-function methodfor non-Markovian quantum master equations [J] Phys. Rev. A,1999,59:1633-1643.
[135] Braunstein S L and Caves C M, Statistical distance and the geometry ofquantum states [J] Phys. Rev. Lett,,1994,72:3439-3942.
[136] Bellomo B, Franco R-L, Maniscalco S and Compagno G, Entanglementtrapping in structured environments,[J] Phys. Rev. A,1999,78:060302.
[137] Oliveira J.G., Rossi R., Nemes M.C., Protecting, enhancing, and revivingentanglement [J]. Phys. Rev. A,2008,78:044301(3).
[138] Rey A.M., Jiang L., Fleischhauer M., Demler E., Lukin M.D., Many-bodyprotected entanglement generation in interacting spin systems [J]. Phys.Rev. A,2008,77:052305(12).
[139] Mundarain D., Orszag M., Entanglement preservation by continuousdistillation [J]. Phys. Rev. A,2009,79:052333(5).
[140] Alharbi A.F., Ficek Z., Deterministic creation of stationary entangled statesby dissipation [J] Phys. Rev. A,2010,82:054103(4).
[141] Zhang K., Li Z.Y., Transfer behavior of quantum states between atoms inphotonic crystal coupled cavities [J]. Phys. Rev. A,2010,81:033843(10).
[142] Englund D., Majumdar A., Faraon A., Toishi M., Stoltz N., Petroff P.,Vuckovic J., Resonant Excitation of a Quantum Dot Strongly Coupled to aPhotonic Crystal Nanocavity [J]. Phys. Rev. Lett.,2010,104:073904(4).
[143] Craig D.P., Molecular Quantum Electrodynamics: An introduction toRadiation-Molecular Interaction [M] Acamedic Press,1984.
[144] Lehmberg R.H., Radiation from an N-Atom System. II. SpontaneousEmission from a Pair of Atoms [J] Phys. Rev. A,1970,2:889-896.
[145] Paz J.P., Roncaglia A.J., Dynamics of the Entanglement between TwoOscillators in the Same Environment [J] Phys. Rev. Lett.,2008,100:220401.
[146] John S., Wang J., Quantum optics of localized light in a photonic band gap[J]. Phys. Rev. B,1991,43:12772-12789.
[147] Yang Y., Zhu S.-Y., Spontaneous-emission enhancement and populationoscillation in photonic crystals via quantum interference [J] Phys. Rev. A,2000,61:043809(16).
[148] Yang Y., Zhu S.-Y., Spontaneous emission from a two-level atom in athree-dimensional photonic crystal [J] Phys. Rev. A,2000,61:013805(11).
[149] Zanardi P., Rasetti M., Noiseless Quantum Codes [J] Phys. Rev. Lett,1997,79:3306-3309.
[150] Hatef A., Singh M R, Type-I cascaded quadratic soliton compression inlithium niobate: Compressing femtosecond pulses from high-power fiberlasers [J] Phys. Rev. A,2010,81:053815(14).
[151] Niset J, Cerf N J, Multipartite nonlocality without entanglement in manydimensions [J] Phys. Rev. A,2006,74:052103(8).
[152] Lanyon B.P., Barbieri M., Almeida M.P., White A.G., ExperimentalQuantum Computing without Entanglement [J] Phys. Rev. Lett.,2008,101:200501-200504.
[153] Horodecki M., Horodecki P., Horodecki R., Oppenheim J., Sen A., Sen U.,Synak-Radtke B., Local versus nonlocal information inquantum-information theory: Formalism and phenomena [J] Phys. Rev. A.,2005,71:062307(25).
[154] Zurek W.H., Quantum discord and Maxwell’s demons [J] Phys. Rev. A.,2003,67:012320(6).
[155] Datta A., Shaji A., Caves C.M., Quantum Discord and the Power of OneQubit [J] Phys. Rev. Lett.,2008,100:050502-050505.
[156] DeVoe R.G., Brewer R.G., Observation of Superradiant and SubradiantSpontaneous Emission of Two Trapped Ions [J] Phys. Rev. Lett.,1996,76:2049-2052.
[157] Mazzola L., Maniscalco S., Piilo J., Suominen K.-A., Garraway B.M.,Sudden death and sudden birth of entanglement in common structuredreservoirs [J] Phys. Rev. A,2009,79:042302(4).
[158] Ficek Z., Tana R., Dark periods and revivals of entanglement in atwo-qubit system [J] Phys. Rev. A,2006,74:024304(4).
[159] Jiang X., Jiang Y., Wang Y., Sun X., Non-Markovian decay of a three-levelΛ-type atom in a photonic-band-gap reservoir [J] Phys. Rev. A,2006,73:033802(6).
[160] Garraway B.M., Nonperturbative decay of an atomic system in a cavity [J].Phys. Rev. A,1997,55:2290-2303.
[161] Nikolopoulos G.M., Bay S., Lambropoulos P., Quantum systems coupled toa structured reservoir with multiple excitations [J] Phys. Rev. A,1999,60:5079-5082.
[162] Nikolopoulos G.M., Lambropoulos P., Beyond single-photon localization atthe edge of a photonic band gap [J] Phys. Rev. A,2007,61:053812(7).
[163] Natali S., Ficek Z., Temporal and diffraction effects in entanglementcreation in an optical cavity [J] Phys. Rev. A,2007,75:042307(10).
[164] Ficek Z., Tana R., Delayed sudden birth of entanglement,[J]. Phys. Rev. A,2008,77:054301(4).
[165] Benatti F., Floreanini R., Piani M., Environment Induced Entanglement inMarkovian Dissipative Dynamics [J]. Phys. Rev. A,2003,91:070402(4).
[166] Schneider S., Milburn G.J., Entanglement in the steady state of acollective-angular-momentum (Dicke) model [J] Phys. Rev. A,2002,65:042107(5).