進階搜尋


 
系統識別號 U0026-0812200914301250
論文名稱(中文) 開放系統中的量子退相干
論文名稱(英文) Quantum Decoherences in Open Systems
校院名稱 成功大學
系所名稱(中) 物理學系碩博士班
系所名稱(英) Department of Physics
學年度 96
學期 2
出版年 97
研究生(中文) 涂維元
研究生(英文) Wei-Yuan Tu
電子信箱 l2695402@mail.ncku.edu.tw
學號 l2695402
學位類別 碩士
語文別 英文
論文頁數 96頁
口試委員 指導教授-張為民
口試委員-陳岳男
口試委員-陳柏中
口試委員-周忠憲
中文關鍵字 退相干  波包  開放量子系統  量子點 
英文關鍵字 quantum dots  open quantum systems  wave packets  Decoherence 
學科別分類
中文摘要 在此論文中我們探討在開放系統中的量子退相干現象。我們採用費曼維儂的影響泛涵理論,分別在兩個不同的物理系統中探討量子退相干的機制與作用。首先我們考慮一個在離散譜環境影響下的量子諧振子的波包運動,探究其量子相干性消退之表現所在。我們也考量由於波包和環境交互作用所引起波包內部結構的不穩定性。該波包運動的馬可夫與非馬可夫行為之轉換與環境條件的關係也在此
工作中被指出。接著我們擴展費曼維儂的影響泛涵理論到費米子相干態表象來研究雙量子點在耦合到週遭電極的情況下的電子動力學的退相干問題。藉由最小動作量的路徑方法我們可以得到一組描述複雜馬可夫電子動力學的方程式,並從中推導一個精確的主方程,來刻劃雙量子點在週遭電極影響下的退相干行為。從中我們探討由於和電極交換電子所引起的雙兩子點內部能量結構的動態變化過程
以及奈秒尺度下電子態分布權重的複雜轉移,來加深我們對量子退相干在此典型奈米結中構的機制的了解與掌握。
英文摘要 In this thesis we explore decoherence in open quantum systems. We approach this problem using Feynman-Vernon’s influence functional theory in two very distinct systems. We consider first a wave packet of a particle in a harmonic trap interacting with an environment with discrete
spectra where the reduced dynamics of the wave packet is studied. Instability due to the interaction between the system and its quantum environment is investigated and Markovian to non-Markovian transition is discussed. We then extend the theory to the fermion coherent state representation to study the decoherent dynamics of electrons in a double quantum dot under the influence of electron reservoirs connected to the dots. There we derived an exact master equation for arbitrary spectral densities for dot-lead tunneling via the stationary path
equations which fully manifests the complex non-Markovian charge dynamics. Real time fluctuations of the double dot parameters are explored and decoherence are closely analyzed based on our exact solutions from Markovian to non-Markovian regimes.
論文目次 1 Introduction 1
1.1 From Open Systems to Quantum Decoherence . . . . . . . . . . . . . . . . . . . 2
1.2 Path Integral Approach to Open Quantum Systems . . . . . . . . . . . . . . . . . 7
1.2.1 The coordinate representation . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 The coherent state representation . . . . . . . . . . . . . . . . . . . . . . . 9
2 Wave Packet Decoherence in a Few-Mode Environment 12
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Time Evolution of Open Quantum Systems . . . . . . . . . . . . . . . . . . . . . 13
2.3 Analytical Solution to the Dissipation Dynamics . . . . . . . . . . . . . . . . . . 15
2.4 Non-Markovian Wave Packet Dynamics . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Conclusions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Coherent Electron Dynamics in a Double Quantum Dot 25
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Fermion Coherent State Path Integral Approach to an Isolated Double Quantum
Dot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 The Master Equation for a Double Quantum Dot Gated by Electrodes . . . . . . 28
3.3.1 Rate equations and the corresponding Markovian limits . . . . . . . . . . 32
3.4 The Coherent Dynamics of Electrons in a Double Quantum Dot . . . . . . . . . 35
3.4.1 The time dependent transport matrices . . . . . . . . . . . . . . . . . . . 36
3.4.2 Charge qubit decoherence under various manipulation conditions . . . . . 40
3.5 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

A Some detailed derivations of Chapter 2 69
A.1 Derivation of the solution to the dissipation dynamical equation . . . . . . . . . . 69
A.2 Verification of the solution to the dissipation dynamical equation . . . . . . . . . 70
A.2.1 Root property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
A.2.2 Verification of the solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
B The basics of a double quantum dot and some detailed derivations of Chapter
3 73
B.1 A short note on a double quantum dot . . . . . . . . . . . . . . . . . . . . . . . . 73
B.2 Derivation of the influence functional . . . . . . . . . . . . . . . . . . . . . . . . . 74
B.3 The stationary pathes and the master equation . . . . . . . . . . . . . . . . . . . 76
Bibliography 77
參考文獻 [1] W. H. Zurek, Phys. Today 44 (10), 36 (1991); Rev. Mod. Phys. 75, 715 (2003).
[2] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge
Univ. Press, Cambridge, 2000).
[3] R. Brown, Phil. Mag. 4, 161 (1828).
[4] A. Einstein, Ann. Phys. (Leipzig) 17 549 (1905).
[5] P. Langevin, CR Acad. Sci. 146 530 (1908).
[6] M. Smoluchowski, Phys. Z. 13 1069 (1912).
[7] S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
[8] I. R. Seniztky, Phys. Rev. 119 670 (1960).
[9] G.W. Gardiner and P. Zoller, Quantum Noise : A Handbook of Markovian and Non-
Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer,
Berlin, 2004).
[10] H. B. Callen, T. A. Welton, Phys. Rev. 83, 34 (1951).
[11] R. H. Koch, D. J. Van Harlingen, and J. Clarke, Phys. Rev. Lett. 45, 2132 (1980).
[12] P. Caldirola, Nuovo Cim. 18, 393 (1941).
[13] E. Kanai, Prog. Thoer. Phys. 3, 440 (1948).
[14] H. Dekker, Phys. Rev. A 16, 2126 (1977).
[15] W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973).
[16] S. Nakajima, Prog. Theor. Phys. 20, 948 (1958).
[17] H. Mori, Prog. Theor. Phys. 33, 423 (1965).
[18] R. Zwanzig, J. Chem. Phys. 33, 1338 (1960).
[19] H. Haken, Rev. Mod. Phys. 47, 67 (1975).
78
[20] G. W. Ford, M. Kac and P. Mazur, J. Math. Phys. 6, 504 (1965); G. W. Ford, J. T. Lewis
and R. F. O’Connell, Phys. Rev. A 37, 4419 (1988).
[21] F. Haake, Statistical Treatment of Open Systems by Generalized Master Equation (Springer,
Berlin, 1973).
[22] L. Mandel and E. Wolf, Quantum Coherence and quantum optics (Cambridge University
Press, Cambridge, 1995).
[23] H. Risken, The Fokker Planck Equation (Springer, Berlin, 1984).
[24] A. D. Fokker, Ann. Phys. (Leipzig), 43, 310 (1915).
[25] M. Planck, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl., 325 (1917)
[26] E. P. Wigner, Phys. Rev. 40, 749 (1932).
[27] J. R. Oppenheimer, Phys. Rev. 31, 66 (1928).
[28] G. Gamow, Z. Physik 51, 204 (1928).
[29] R. W. Gurney and E. U. Condon, Nature (London), 122, 439 (1928).
[30] T. Holstein, Ann. Phys. (New York) 8, 325 (1959); D. Emin and T. Holstein,ibid 53, 439
(1969).
[31] C. P. Flynn and A. M. Stoneham, Phys. Rev. B 1, 3966 (1970).
[32] N. Takigawa and M. Abe, Phys. Rev. C 41, 2451 (1990).
[33] A.B. Balantekin and N. Takigawa, Rev. Mod. Phys. 70, 77 (1998).
[34] A. N. Cleland, J. M. Martinis, and J. Clarke, Phys. Rev. B 37, 5950 (1988).
[35] P. W. Anderson, B. I. Halperin and C. M. Varma, Phil. Mag. 25, 1 (1972).
[36] W. A. Phillips, J. Low Temp. Phys. 7, 351 (1972).
[37] J. L. Black, Glassy Metlas I, Topics in Applied Physics, Vol. 46, ed. by H.-J. G¨untherodt
and H. Beck (Springer Verlag, Berlin, 1981).
[38] J. Stockburger, U. Weiss and R. G¨orlich, Z. Phys. B 84, 457 (1991).
[39] A. J. Leggett, Directions in Condensed Matter Physics, Vol. 1, ed. by G. Grinstein and G.
Mazenko (World Scientific, Singapore, 1986).
[40] Y. Makhlin, G. Sch¨on, and A. Shnirman, Rev. Mod. Phys. 73, 357 (2001).
[41] F. Guinea, V. Hakim, and A. Muramatsu, Phys. Rev. B 32, 4410(1985).
[42] J. T. Stockburger and H. Grabert, Chem. Phys. 268, 249 (2001); Phys. Rev. Lett. 88,
170407 (2002).
79
[43] M. Grifoni and P. H¨anggi, Phys. Rep. 304, 229 (1998).
[44] F. B. Anders and A. Schiller, Phys. Rev. B 74, 245113 (2006).
[45] A. Warshel, Z.T. Chu, W.W. Parson, Science 246, 112 (1989).
[46] J. M. Martinis, S. Nam, J. Aumentado, K. M. Lang and C. Urbina, Phys. Rev. B 67,
094510 (2003).
[47] L. M. K. Vandersypen and I. L. Chuang, Rev. Mod. Phys. 76, 1037 (2005).
[48] X. Hu and S. Das Sarma, Phys. Rev. Lett. 96, 100501 (2006).
[49] G. C. Ghirardi, A. Rimini and T. Weber, Phys. Rev. D 34, 470 (1986).
[50] G. J. Milburn, Phys. Rev. A 44, 5401 (1991).
[51] R.C. Ashoori, Nature 379, 413 (1996).
[52] L.P. Kouwenhoven, T.H. Oosterkamp, M.W.S. Danoesastro, M. Eto, D.G. Austing, T.
Honda and S. Tarucha, Science 278, 1788 (1997).
[53] D.R. Stewart, D. Sprinzak, C.M. Marcus, C.I. Duruoz and J.S. Harris Jr., Science 278
1784 (1997).
[54] H. Grabert and M.H. Devoret (Ed.), Single Charge Tunneling, NATOASI Series B, vol.
294 (Plenum Press, NewYork, 1991).
[55] S.M. Reimann and M. Manninen, Rev. Mod. Phys. 74 1283 (2002).
[56] M. Tews, Annalen der Physik 13 249 (2004).
[57] E. Schr¨odinger, Naturwiss. 14, 664 (1926).
[58] R. P. Feynman and F. L. Vernon, Ann. Phys. 24, 118 (1963).
[59] A. O. Caldeira and A. J. Leggett, Physica 121A, 587 (1983).
[60] J.W. Negele and H. Orland, Quantum Many-Particle Systems (AddisonWesley, Singapore,
1988).
[61] W. H. Zurek, Phys. Rev. D 26, 1862 (1982).
[62] A. O. Caldeira and A. J. Leggett, Ann. Phys. 149, 374 (1983); 153, 445 (1984).
[63] F. Haake, and R. Reibold, Phys. Rev. A 32, 2462 (1985).
[64] H. Grabert, P. Schramm and P. -L. Ingold, Phys. Rev. Lett. 58, 1285(1987).
[65] W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071 (1989).
[66] B. L. Hu, J. P. Paz, and Y. H. Zhang, Phys. Rev. D 45, 2843 (1992); ibid. 47 1576 (1993).
80
[67] J. P. Paz, S. Habib and W. H. Zurek, Phys. Rev. D 47, 488 (1993).
[68] D. Braun, P. A. Braun, and F. Haake, Opt. Commun. 179, 411 (2000).
[69] G. W. Ford and R. F. O’Connell, Phys. Rev. D 64, 105020 (2001).
[70] W. T. Strunz and F. Haake, Phys. Rev. A 67, 022102 (2003); W. T. Strunz, F. Haake and
D. Braun, ibid. 67, 022101 (2003).
[71] K. Shiokawa and B. L. Hu, Phys. Rev. A 70, 062106 (2004).
[72] G. W. Ford and R. F. O’Connell, Phys. Rev. A 73, 032103 (2006).
[73] J. H. An and W. M. Zhang, Phys. Rev. A 76, 042127 (2007).
[74] C. H. Chou, T. Yu, and B. L. Hu, Phys. Rev. E 77, 011112 (2008).
[75] B. H. Bransden, and C. J. Joachen, Physics of Atoms and Molecules (Longman, London,
1983)
[76] R. Bl¨ume, R. Graham, L. Sirko, U. Smilansky, H. Walther, and K. Yamada, Phys. Rev.
Lett. 62, 341 (1991).
[77] C. Brif, H. Rabitz, A. Wallentowitz, I. A. Walmsley, Phys. Rev. A 63, 063404 (2001)
[78] M. Spanner, E. A. Shapiro and M. Ivanov, Phys. Rev. Lett. 92, 093001 (2004); E. A.
Shapiro, I. A. Walmsley, and M. Y. Ivanov, ibid. 98, 050501 (2007)
[79] S. Yoshida, C. O. Reinhold, J. Burgdorfer, W. Zhao, J. J. Mestayer, J. C. Lancaster, and
F. B. Dunning, Phys. Rev. A 75, 013414 (2007).
[80] R. F. O’Connell, Physica E19, 77 (2003).
[81] J. J. Halliwell, Phys. Rev. D 63, 085013 (2001).
[82] G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mancal, Y. C. Cheng, R. E.
Blankenship, and G. R. Fleming, Nature, 446, 782 (2007); H. Lee, Y.-C. Cheng, G. R.
Fleming, Science 316, 1462 (2007).
[83] A. J. Legget, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. Zwerger,
Rev. Mod. Phys. 59, 1 (1987).
[84] H. Grabert, P. Schramm, and G.-L. Ingold, Phys. Rep. 168, 115 (1988).
[85] H. Carmichael, An open systems approach to quantum optics (Springer-Verlag, New York,
1993).
[86] U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1999).
[87] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University
Press, Oxford, New York, 2002).
81
[88] J. J. Halliwell and T. Yu, Phys. Rev. D 53, 2012 (1996).
[89] K. Lindenberg and B. J. West, Phys. Rev. A30, 568 (1984); H. Callen and T. Weldon,
Phys. Rev. 83, 34 (1951); R. Kubo, Lectures in Theoretical Physics Vol. 1(Interscience, New
York, 1959), pp. 120-203.
[90] See the discussion in Ref. [62] on page 388-391, also in private communications with A. J.
Leggett.
[91] R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New
York, 1965).
[92] K. Shiokawa and R. Kapral, J. Chem. Phys. 117, 7852 (2002).
[93] W. M. Zhang, D. H. Feng and R. Gilmore, Rev. Mod. Phys. 62, 867 (1990).
[94] E. Sch¨odinger, Ber. Kgl. Akad. Wiss. Berlin, 296 (1930).
[95] J. H. An, M. Feng and W. M. Zhang, Phys. Rev. A 76, 042127 (2007).
[96] R. H. Brandenberger, Rev. Mod. Phys. 57, 1 (1985); A. Linde, Particle Physics and Infla-
tionary Cosmology (Harwood Academic, Chur, 1990) and references therein.
[97] J. P. Sethna, Phys. Rev. B 24, 698 (1981); ibid. B 25, 5050 (1982).
[98] L. Santos, G. V. Shlyapnikov, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. 85, 1791
(2000).
[99] L. D. Landau and E. M. Lifschitz, Statistical Physics (Pergamon, London, 1969).
[100] F. Bloch, Z. Phys. 74, 295 (1932).
[101] W. G. van der Wiel, S. DeFranceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha, and L.
P. Kouwenhoven, Rev. Mod. Phys. 75, 1 (2003).
[102] T. Brandes, Phys. Rep. 408, 315 (2005).
[103] R. H. Blick and H. Lorenz, Proceedings of the IEEE International Symposium on Circuits
and Systems, II245 (2000).
[104] T. Tanamoto, Phys. Rev. A 61, 022305 (2000)
[105] L. Fedichkin and A. Fedorov, Phys. Rev. A 69, 032311 (2004); L. Fedichkin, M.
Yanchenko, and K. A. Valiev, Nanotechnology 11, 387 (2000).
[106] J. M. Elzerman, R. Hanson, J. S. Greidanus, L. H.Willems van- Beveren, S. DeFranceschi,
L. M. K. Vandersypen, S. Tarucha, and L. P. Kouwenhoven, Phys. Rev. B 67, 161308(R)
(2003)
82
[107] A. K. H¨uttel, S. Ludwig, K. Eberl, and J. P. Kotthaus, Phys. Rev. B 72, 081310(R)
(2005).
[108] T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong and Y. Hirayama, Phys. Rev. Lett.
91, 226084(2003);T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong and Y. Hirayama,
Physica E(Amsterdam) 21, 2046 (2004); T. Fujisawa, T. Hayashi and S. Sasaki, Rep. Prog.
Phys. 69, 759 (2006).
[109] J. R. Petta , A. C. Johnson, J. M. Taylor, E. A. Laird, A Yacoby, M. D. Lukin, C. M.
Marcus, M. P. Hanson, A. C. Gossard. Science 309, 1280 (2005).
[110] J. Gorman, D. G. Hasko, and D. A. Williams, Phys. Rev. Lett. 95, 090502 (2005).
[111] T. Brandes and T. Vorrath, Phys. Rev. B 66, 075341 (2002).
[112] U. Hartmann and F. K. Wilhelm, Phys. Rev. B 69, 161309(R) (2004).
[113] M. J. Storcz, U. Hartmann, S. Kohler, and F. K. Wilhelm, Phys. Rev. B 72, 235321
(2005).
[114] Z. J.Wu, K. D. Zhu, X. Z. Yuan, Y.W. Jiang, and H. Zheng, Phys. Rev. B 71, 205323
(2005).
[115] S. Vorojtsov, E. R. Mucciolo, and H. U. Baranger, Phys. Rev. B 71, 205322 (2005).
[116] V. N. Stavrou and X. Hu, Phys. Rev. B 72, 075362 (2005).
[117] M. Thorwart, J. Eckel and E. R. Micciolo, Phys. Rev. B 72, 235320 (2005).
[118] U. Hohenester, Phys. Rev. B 74, 161307(R) (2006).
[119] S. R. Woodford, A. Bringer and K. M. Indelkofer, Phys. Rev. B 76, 064306 (2007).
[120] Y. Y. Liao, Y. N. Chen, W. C. Chou, and D. S. Chuu, Phys. Rev. B 77, 033303 (2008).
[121] T.H. Stoof and Yu.V. Nazarov, Phys. Rev. B 53, 1050 (1996).
[122] S. A. Gurvitz and Ya. S. Prager, Phys. Rev. B 53, 15932 (1996).
[123] The choice of the energy reference shall not be E1 = E2 = 0 because when the two
localized states are degenerate, E1 = E2, the energy of the dots, EDQD = ((E1+E2)/
2 )(1−ρ00)+
((E1−E2)/)
2 (ρ11 − ρ22) + (ρ12 + ρ21), where the normalization condition 1 − ρ00 = ρ11 + ρ22
is used, becomes EDQD = E1+E2
2 (1 − ρ00) + (ρ12 + ρ21). When there is no electrons in
the dots, ρ00 = 1, the energy of the dots is simply zero. And the choice of E1 = E2 = 0
will cause that the energy of the dots when there is one electron in double dots, ρ11 = 1
or ρ22 = 1 is also 0. In the case where there is no charge leakage this choice of energy
reference is ok. However for the charge qubit being an open system, charge leakage shall be
considered and the choice of energy reference would matter if we look at the time evolution
of the energy of the dots. Otherwise, this choice of energy reference matters nothing as
long as the total energy configuration, the relations between the dot energy levels and the
chemical potentials in the electron reservoirs, remains the same. We can see identical time
evolutions of the density matrix at the energy references E = 0 and E = 0 with the relations
between E and μ1,2 fixed. But the dot energy EDQD given above is of course influenced by
the energy reference.
[124] D.P. DiVincenzo, Science 269, 225(1995).
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2009-08-22起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2009-08-22起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw