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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 管希聖(Hsi-Sheng Goan) | |
dc.contributor.author | Kuan-Liang Liu | en |
dc.contributor.author | 劉冠良 | zh_TW |
dc.date.accessioned | 2021-06-13T04:29:31Z | - |
dc.date.available | 2007-07-24 | |
dc.date.copyright | 2006-07-24 | |
dc.date.issued | 2006 | |
dc.date.submitted | 2006-07-20 | |
dc.identifier.citation | [1] Gerardo Adesso, Alessio Serafini, and Fabrizio Illuminati. Extremal entanglement
and mixedness in continuous variable systems. Phys. Rev. A, 70:022318, (2004). [2] H. J. Carmichael. Statistical Methods in Quantum Optics 1. Springer. [3] Andrea Donarini. Dynamics of Shuttle Devices. PhD thesis, Technical University of Denmark, (2004). [4] Lu-Ming Duan, G. Giedke, J. I. Cirac, and P. Zoller. Inseparability criterion for continuous variable systems. Phys. Rev. Lett., 84(12):12, (2000). [5] J. Eisert and M. B. Plenio. Introduction to the basics of entanglement theory in continuous-variable systems. Int. J. Quant. Inf., 1:479, (2003). [6] A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik. Unconditional quantum teleportation. Science, 282:706, (1998). [7] M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner. Distribution functions in physcis: fundamentals. Phys. Rep., 106:121, (1984). [8] B. L. Hu, Juan Pablo Paz, and Yuhong Zhang. Quantum brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise. Phys. Rev. D, 45(8):2843, (1992). [9] Juan Pablo Paz and Wojciech Hubert Zurek. Environment-induced decoherence and the transition from quantum to classical. e-Print quant-ph/0010011. [10] M. B. Plenio, J. Hartley, and J. Eisert. Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedon. New Journal of Physics, 6(36), (2004). [11] Jakub S Prauzner-Bechcicki. Two-mode squeezed vacuum state coupled to the common thermal reservoir. J. Phys. A, 37:L173–L181, (2004). [12] J. J. Sakurai. Modern Quantum Mechanics. Addison-Wesley, (1994). [13] Wolfgang P. Schleich. Quantum Optics in Phase Space. WILEY-VCH, (2001). [14] R. Simon. Peres-horodecki separability criterion for continuous variable systems. Phys. Rev. Lett., 84(12):2726, (2000). [15] G. Vidal and R. F. Werner. Computable measure of entanglement. Phys. Rev. A, 65:032314, (2002). [16] R. F. Werner. Quantum states with einstein-podolsky-rosen correlations admitting a hidden-variable model. Phys. Rev. A, 40:4277, (1989). [17] E. Wigner. On the quantum correction for thermodynamics equilibrium. Phys. Rev., 40:749, (1932). [18] William K. Wootters. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett., 80:10, (1998). | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/33212 | - |
dc.description.abstract | 量子糾纏態在量子傳輸及量子通訊上扮演極為重要的角色。因此探討開放系統之量子糾纏態隨時間的動力演變是現今一個重要的課題。我們假設四個相關之奈米力學開放系統模型, 並僅使用微擾法導出各別量子系統之non-Markovian master equation。然而在之前的文獻中大都使用Markovian 或rotating-wave 近似法來處理問題, 但non-Markovian 對於真實系統的描述更貼近於實驗觀察。
因此我們採用non-Markovian 來處理我們的問題。從此些方程出發, 我們使用two-mode squeezed vacuum state 為我們的初始態並引用logarithmic negativity來定義量子糾纏的程度。我們發現在完全沒有環境作用的情況下, 量子糾纏隨時間的演變為週 期性振盪或維持定值。但若考慮環境的影響, 量子糾纏將會隨時間而遞減且週期性現象會逐漸消失。當環境與系統間的作用越強時, 量子糾纏存在的時間越短。我們發現當兩個系統與同一環 境作用下之情況量子糾纏態存在的時間遠比兩個系統各自與不同的環境作用來得久。我們也發現原本沒有糾纏性質的量子態可透過系統間的交互作用或與同一環境作用而產生量子糾纏。此 外, 在我們所採用的參數條件下(低溫及低系統振盪頻率下), Markovian 及rotating-wave 近似法不能獲得良好的近似結果, 因此以non-Markovian 來處理此類系統是必需且必要的。 | zh_TW |
dc.description.abstract | Quantum entangled states play a crucial role in the quantum teleportation and quantum information science, hence the research of the dynamics of entanglement has
become an important topic and has attracted much attention recently. We use perturbative method to derive non-Markovian master equations, which were derived in the literature before by other extra approximations such as rotating-wave and Markovian approximations, of four different but related models of the open nanomechanical systems respectively. Markovian approximation is close to physical phenomena only under the long time regime so we use the non-Markovian instead of Markovian approximation to deal with our models. We use two-mode squeezed vacuum state as our initial entangled state and use the definition of logarithmic negativity to quantify the degree of entanglement. We find that the dynamics of quantum entanglement varies periodically or maintains constant under environment free condition. However, under the influence of environment, entanglement will decrease with time and the periodic or revival behaviors dies out gradually. As the interaction between the environment and system increases, the time span during which entanglement exists decrease. We find that the entanglement can be sustained much longer when two subsystems are coupled to a common bath than respectively to independent reservoirs. Furthermore, we find that a separable state can become entangled through the interaction of two subsystems or coupling to a common bath. We also find that under some conditions (e.g. at low temperature or low system vibration frequency) Markovian and rotatingwave approximations are not the good approximations. So non-Markovian case is essential in order to obtain the accurate results of the system's entanglement time evolution. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T04:29:31Z (GMT). No. of bitstreams: 1 ntu-95-R93222048-1.pdf: 2345755 bytes, checksum: ba8a5716d5ebc37e09650ed66d7ba0fa (MD5) Previous issue date: 2006 | en |
dc.description.tableofcontents | 誌謝....................................................iii
摘要.....................................................iv Abstract..................................................v Introduction..............................................1 1 The Basic Concepts......................................3 1.1 Open Quantum System.................................3 1.2 Interaction Picture.................................4 1.3 Wigner Function.....................................5 1.3.1 Mathematical Properties of Quasi-Probability Distribution..................................6 1.3.2 Wigner Distribution . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.3 Properties of Wigner Function . . . . . . . . . . . . . . . . . . 8 1.3.4 Weyl-Wigner Correspondence . . . . . . . . . . . . . . . . . . 10 1.4 Quantum Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 Quantification of Quantum Entanglement . . . . . . . . . . . 13 1.4.2 Concurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4.3 Negativity and Logarithmic Negativity . . . . . . . . . . . . . 14 2 Master Equations for Four Models 16 2.1 The General Form of Perturbative Master equation . . . . . . . . . . 17 2.2 Perturbative Master Equation of Quantum Brownian Motion . . . . . 19 2.3 Model A: Two Systems Couple to Their Respective Reservoirs . . . . 22 2.4 Model B: Two Interactive Systems Couple to Their Respective Reservoirs 25 2.5 Model C: Two Systems Couple to the Same Reservoir . . . . . . . . . 27 2.6 Model D: Two Interactive Systems Couple to the Same Reservoir . . 30 3 Fokker-Planck Equations for Four Models 32 3.1 Fokker-Planck Equation of Quantum Brownian Motion . . . . . . . . 33 3.2 Model A: Two Systems Couple to Respective Reservoirs . . . . . . . 34 3.3 Model B: Two Interactive Systems Couple to Respective Reservoirs . 35 3.4 Model C: Two Systems Couple to the Same Reservoirs . . . . . . . . 37 3.5 Model D: Two Interactive Systems Couple to the Same Reservoir . . 37 4 Discussion 39 4.1 Physical Frequency and Renormalized Frequency . . . . . . . . . . . 39 4.2 The Coefficients of Master Equations for Four Models . . . . . . . . . 41 4.2.1 Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2.2 Numerical Results of Coefficients . . . . . . . . . . . . . . . . 42 4.3 Dynamics of Entanglement for Four Models . . . . . . . . . . . . . . 47 4.3.1 Covariance Matrix and Symplectic Eigenvalues . . . . . . . . . 47 4.3.2 Two-mode Squeezed State . . . . . . . . . . . . . . . . . . . . 49 4.3.3 Numerical Analysis of Dynamics of Entanglement . . . . . . . 50 4.4 Dynamics of Entanglement for Model A and C in the Markovian Approximation and RWA . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.4.1 Model A and C in the Markovian Approximation . . . . . . . 68 4.4.2 Model A and C in the RWA-Markovian Approximation . . . . 71 4.4.3 Numerical Analysis of Dynamics of Entanglement in the Markovian Approximation and RWA . . . . . . . . . . . . . . . . . . 75 5 Conclusions 79 Bibliography 81 | |
dc.language.iso | en | |
dc.title | 環境耦合下奈米力學系統之非馬可夫動力及量子糾纏現象 | zh_TW |
dc.title | NON-MARKOVIAN DYNAMICS AND QUANTUM
ENTANGLEMENT OF NANOMECHANICAL SYSTEMS COUPLED TO THERMAL RESERVOIRS | en |
dc.type | Thesis | |
dc.date.schoolyear | 94-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 蘇正耀,張志義 | |
dc.subject.keyword | 量子糾纏態,量子糾纏, | zh_TW |
dc.subject.keyword | entanglement,non-Markovian,Markovian,RWA,logarithmic negativity,two-mode squeezed vacuum state, | en |
dc.relation.page | 82 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2006-07-21 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 物理研究所 | zh_TW |
顯示於系所單位: | 物理學系 |
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