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The influence of phonon on the properties of polaron and qubit in spherical shell quantum dot is studied by solving accurately the time-independent Schrödinger equation, Lee-Low-Pines unitary transformation and variation methods. The numerical results indicate that phonon effect leads to a lower energy of ground (or excited) state of polaron than electronic energy of ground (or excited) state and the increased oscillating period of a qubit, and the phonon effect becomes more obvious with outer radius increasing when inner radius is const. The numerical results also show that the phonon effect cannot influence the amplitude of probability density distribution of electrons in quantum bit, and that the probability density distribution of electrons is dependent on co-ordinate and time and its amplitude is maximal in centre spherical surface and but zero in boundary surface. The probability density of electrons at each position oscillates periodically with time.
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Keywords:
- spherical shell quantum dot /
- polaron /
- qubit /
- probability density
[1] Feynman R P 1982 Int. J. Theor. Phys. 21 467
[2] Feynman R P 1986 Foundations of Physics 16 507
[3] Pellizzari T, Gardiner S A, Cirac J I, Zoller P 1995 Phys. Rev. Lett. 75 3788
[4] Cirac J I, Zoller P 1995 Phys. Rev. Lett. 74 4091
[5] Gershenfeld N A, Chuang I L 1997 Science 275 350
[6] Nakamura Y, Pashkin Y A, Tsai J S 1999 Nature 398 786
[7] Li S S, Long G L, Bai F S, Zheng H Z 2001 Proc. Nat. Acad. Sci. 98 11847
[8] Li X Q, Yan Y J 2002 Phys. Rev. B 65 205301
[9] Gao K Y, Zhao C L 2008 Acta Phys. Sin. 57 4446 (in Chinese) [高宽云, 赵翠兰 2008 物理学报 57 4446]
[10] Cong Y C, Zhao C L 2009 Reseach & Progress of Sclid State Electronic 29 538 (in Chinese) [从银川, 赵翠兰 2009 固体电子学研究与进展 29 538]
[11] Zhang Y F, Jia J F, Han T Z, Tang Z, Shen Q T, Guo Y, Xue Q K 2005 Chin. Phys. 14 1910
[12] Liu X J, Gao K, Li Y, Wei J H, Xie S J 2007 Chin. Phys. 16 2091
[13] Oliveira B P W, Haas S 2009 Phys. Rev. B 79 155102
[14] Stauber T, Vasilevskiy M I 2009 Phys. Rev. B 79 113301
[15] Harouni M B, Roknizadeh R, Naderi M H 2009 Phys. Rev. B 79 165304
[16] Zhao C L, Xiao J L 2010 J. Low. Temp. Phys. 160 209
[17] Xiao J L, Zhao C L 2011 Superlatt. Microstuct. 49 9
[18] Xiao J L, Ding Z H 2011 J. Low. Tem. Phys. 163 302
[19] Ding Z H, Xiao J L 2011 Chin. Phys. B 20 097104
[20] Jiang F S, Zhao C L 2009 Acta Phys. Sin. 58 6786 (in Chinese) [姜福仕, 赵翠兰 2009 物理学报 58 6786]
[21] Zhao C L, Gao K Y 2010 Acta Phys. Sin. 59 4857 (in Chinese) [赵翠兰, 高宽云 2010 物理学报 59 4857]
[22] Mews A, Eychmüller A, Giersig M, Schooss D, Weller H 1994 J. Phys. Chem. 98 934
[23] Eychmüller A, Mews A, Weller H 1993 Chem. Phys. Lett. 208 59
[24] Eychmüller A, Vossmeyer T, Mews A, Weller H 1994 J. Lumin. 58 223
[25] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[26] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
[27] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[28] Chang K, Xiao J B 1998 Phys. Rev. B 57 9780
[29] Chang K, Lou W K 2011 Phys. Rev. Lett. 106 206802
-
[1] Feynman R P 1982 Int. J. Theor. Phys. 21 467
[2] Feynman R P 1986 Foundations of Physics 16 507
[3] Pellizzari T, Gardiner S A, Cirac J I, Zoller P 1995 Phys. Rev. Lett. 75 3788
[4] Cirac J I, Zoller P 1995 Phys. Rev. Lett. 74 4091
[5] Gershenfeld N A, Chuang I L 1997 Science 275 350
[6] Nakamura Y, Pashkin Y A, Tsai J S 1999 Nature 398 786
[7] Li S S, Long G L, Bai F S, Zheng H Z 2001 Proc. Nat. Acad. Sci. 98 11847
[8] Li X Q, Yan Y J 2002 Phys. Rev. B 65 205301
[9] Gao K Y, Zhao C L 2008 Acta Phys. Sin. 57 4446 (in Chinese) [高宽云, 赵翠兰 2008 物理学报 57 4446]
[10] Cong Y C, Zhao C L 2009 Reseach & Progress of Sclid State Electronic 29 538 (in Chinese) [从银川, 赵翠兰 2009 固体电子学研究与进展 29 538]
[11] Zhang Y F, Jia J F, Han T Z, Tang Z, Shen Q T, Guo Y, Xue Q K 2005 Chin. Phys. 14 1910
[12] Liu X J, Gao K, Li Y, Wei J H, Xie S J 2007 Chin. Phys. 16 2091
[13] Oliveira B P W, Haas S 2009 Phys. Rev. B 79 155102
[14] Stauber T, Vasilevskiy M I 2009 Phys. Rev. B 79 113301
[15] Harouni M B, Roknizadeh R, Naderi M H 2009 Phys. Rev. B 79 165304
[16] Zhao C L, Xiao J L 2010 J. Low. Temp. Phys. 160 209
[17] Xiao J L, Zhao C L 2011 Superlatt. Microstuct. 49 9
[18] Xiao J L, Ding Z H 2011 J. Low. Tem. Phys. 163 302
[19] Ding Z H, Xiao J L 2011 Chin. Phys. B 20 097104
[20] Jiang F S, Zhao C L 2009 Acta Phys. Sin. 58 6786 (in Chinese) [姜福仕, 赵翠兰 2009 物理学报 58 6786]
[21] Zhao C L, Gao K Y 2010 Acta Phys. Sin. 59 4857 (in Chinese) [赵翠兰, 高宽云 2010 物理学报 59 4857]
[22] Mews A, Eychmüller A, Giersig M, Schooss D, Weller H 1994 J. Phys. Chem. 98 934
[23] Eychmüller A, Mews A, Weller H 1993 Chem. Phys. Lett. 208 59
[24] Eychmüller A, Vossmeyer T, Mews A, Weller H 1994 J. Lumin. 58 223
[25] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[26] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
[27] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[28] Chang K, Xiao J B 1998 Phys. Rev. B 57 9780
[29] Chang K, Lou W K 2011 Phys. Rev. Lett. 106 206802
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