在本論文中, 我們研究了有非線性色散關係的表面電漿子在金屬奈米線耦合到量子點時的傳輸性質。利用實空間哈密頓函數得到了表面電漿子的穿透及反射譜線。 在耦合到單量子點的情況下, 我們發現, 由於非線性二次式的色散關係散射譜線可以顯示與一般線性色散關係完全不同的特點。 在耦合到雙量子點的情況下, 我們發現了散射譜線中因干涉行為的產生而有類似量子力學中粒子通過雙勢壘的共振穿隧情形。 此外, 因為非線性的二次式色散關係在相互干涉的散射通道中,Fano-like 譜線在散射譜線中被觀察到。 所有這些奇特的行為表明, 這樣的奈米線系統提供了一個一維的平台, 可以用來驗證光子晶體的能帶特性。 另外我們還研究了在外加磁場下奈米線表面電漿子
耦合到兩個量子點的散射行為。 表面電漿子的色散關係在外加磁場的影響下會被向上移動。 在適當調整量子點的共振能量下, 穿透譜線中因為散射通道的量子干涉而有的對稱雙峰會在磁場的增加下逐漸合併, 而 Fano-like 譜線也將逐漸消失。 進一步的研究也表明兩個量子點之間的糾纏, 也可通過改變外加磁場的大小來加以控制。

In this thesis, the coherent transport of surface plasmons with nonlinear dispersion relations on a metal nanowire coupled to quantum dots is investigated theoretically.
Real-space Hamiltonian is used to obtain the transmission and reflection spectra of the surface plasmons. For the single-dot case, we find that the scattering spectra can show completely different features due to the non-linear quadratic dispersion relation. For the double-dot case, we obtain the interference behavior in transmission and reflection spectra, similar to that in resonant tunneling through a double-barrier potential. More-over, Fano-like lineshape of the transmission spectrum is obtained due to the quadratic dispersion relation in the interfering channels. All these peculiar behaviors indicate that the dot-nanowire system provides a one-dimensional platform to demonstrate the bandgap feature widely observed in photonic crystals. In addition, we also study the effect of the external magnetic field on the scattering properties of the nanowire surface plasmons coupled to two quantum dots. The dispersion relations of the surface plasmon are found to be upwardly displaced in the presence of an external magnetic field. The symmetric double peaks in the transmission spectrum resulting from the interference between two scattering channels of the surface plasmon can combine together, and the associated Fano-like lineshape is smeared out when increasing the magnitude of the magnetic field with suitably tuned quantum-dot transition energies. We further show that the entanglement between the two quantum dots can be controlled by varying the magnitude of the external magnetic field.

[1] D. Pines and D. Bohm, Phys. Rev. 85, 338 (1952).
[2] D. Pines, Rev. Mod. Phys. 28, 184 (1956).
[3] R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[4] C. J. Powell and J. B. Swan, Phys. Rev. 115, 869 (1959) and Phys. Rev. 116, 81 (1959).
[5] E. A. Stern and R. A. Ferrell, Phys. Rev. 120, 130 (1960).
[6] W. Knoll, Annu. Rev. Phys. Chem. 49, 569 (1998).
[7] M. Malmqvist, Nature 361, 186 (1993).
[8] F. -C. Chien and S. -J. Chen, Biosensors Bioelectron. 20, 633 (2004).
[9] R. Berndt, J. K. Gimzewski, and P. Johansson, Phys. Rev. Lett. 67, 3796 (1991).
[10] R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng,
Science 294, 1901 (2001).
[11] R. Jin, C. Y. Cao, E. Hao, G. S. M´etraux, G. C. Schatz, and C. A. Mirkin, Nature
425, 487 (2003).
[12] A. Campion and P. Kambhampati, Chem. Soc. Rev. 27, 241 (1998).
[13] P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[14] R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, Mater. Today 9, 20 (2006).
[15] M. L. Brongersma, J. W. Hartman, and H. H. Atwater, Mater. Res. Soc. Symp. Proc. 582, H10.5 (1999).
[16] S. A. Maier, Current Nanoscience 1, 17 (2005).
[17] D. K. Gramotnev and S. I. Bozhevolnyi Nat. Photon. 4, 83 (2010).
[18] H. J. Kimble, Nature (London) 453, 1023-1030 (2008).
[19] D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nat. Phys. 3, 807-812 (2007).
[20] A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar,
S. M. Girvin, and R. J. Schoelkopf, Nature (London) 431, 162-167 (2004).
[21] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature (London) 436, 87-90 (2005).
[22] K. Srinivasan and O. Painter, Nature (London) 450, 862-865 (2007).
[23] B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble,
Science 319, 1062-1065 (2008).
[24] J. C. F. Matthews, A. Politi, A. Stefanov and J. L. O’Brien, Nature Photonics 3, 346-350 (2009).
[25] M. Rosenblit, P. Horak, S. Helsby, and R. Folman, Phys. Rev. A 70, 053808 (2004).
[26] P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
[27] J. T. Shen and S. Fan, Opt. Lett. 30, 2001 (2005).
[28] J. T. Shen and S. Fan, Phys. Rev. A 79, 023837 (2009).
[29] L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[30] L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, Phys. Rev. A 78, 063827 (2008).
[31] J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, Phys. Rev. A 81, 042304 (2010).
[32] A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer,
H. Park, and M. D. Lukin, Nature (London) 450, 402-406 (2007).
[33] Y. Fedutik, V. V. Temnov, O. Schops, U. Woggon, and M. V. Artemyev, Phys. Rev. Lett. 99, 136802 (2007).
[34] D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[35] G. Y. Chen, Y. N. Chen, and D. S. Chuu, Opt. Lett. 33, 2212-2214 (2008).
[36] Y. N. Chen, G. Y. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. A 79, 033815 (2009).
[37] Y. N. Chen, G. Y. Chen, Y. Y. Liao, N. Lambert, and F. Nori, Phys. Rev. B 79, 245312 (2009).
[38] A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M.
H. Jo, M. D. Lukin and H. Park, Nat. Phys. 5, 475-479 (2009).
[39] K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savel,ev, and F. Nori, Rev. Mod. Phys. 80, 1201 (2008).
[40] W. Chen, G. Y. Chen, and Y. N. Chen, Opt. Exp. 18, 10360 (2010).
[41] W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
[42] J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi Opt. Lett. 22, 475 (1997).
[43] J. T. Shen and S. Fan, Phys. Rev. Lett. 95, 213001 (2005).
[44] L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[45] U. Fano, Phys. Rev. 124, 1866 (1961).
[46] S. Bandopadhyay, B. Dutta-Roy, and H. S. Mani, Am. J. Phys. 72, 1501 (2004).
[47] K. W. Chiu and J. J. Quinn, Phys. Rev. B 5, 4707 (1972).
[48] G. A. Farias, E. F. Nobre, R. Moretzsohn, N. S. Almeida, and M. G. Cottam, J. Opt. Soc. Am. A 19, 2449 (2002).
[49] H. Beutler, Z. Phys. A 93, 177 (1935).
[50] U. Fano, Nuovo Cimento 12, 154 (1935).
[51] E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[52] S. John, Phys. Today 44, 32 (1991).
[53] S. Savel’ev, A. L. Rakhmanov, and F. Nori, Phys. Rev. Lett. 94, 157004 (2005).
[54] A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, Nano Lett. 6, 1822 (2006).
[55] G. Y. Chen, N. Lambert, C. H. Chou, Y. N. Chen, and F. Nori, Phys. Rev. B 84, 045310 (2011).