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A full quantum mechanical approach is extended to a coupled waveguide-ring resonator interacting with a three-level quantum dot (QD). The transmission and reflection amplitudes, as well as the resonator and the QD responses, are solved exactly via a real-space approach, which shows the single-photon transport properties. One feature of the system is the coupling between the two degenerate whispering- gallery modes (WGMs) of the resonator at rate β due to backscattering caused by surface roughness of the cavity. Another feature is describing the coupling between QD and the cavity by two parameters g1 and g2. From the analytic numerical results we can see the difference from two-level system.It may better interpret the experiment of a quantum dot strongly coupled to WGMs in a cavity.
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Keywords:
- mode coupling /
- microdisc cavity /
- three-level quantum dot /
- full quantum mechanical approach
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[2] O’Brien J L, Pryde G J, White A G, Ralph T C, Branning D 2003 Nature (London) 426 264
[3] Zhang S, Wang J, Zhang Q, Tang C J 2009 Acta Phys.Sin. 58 73 (in Chinese) [张 盛、王 剑、张 权、唐朝京 2009 58 73]
[4] Mattle K, Weinfurter H, Kwiat P G, Zeilinger A 1996 Phys.Rev. Lett. 76 4656
[5] Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature (London) 390 575
[6] Shen J T, Fan S H 2009 Phys. Rev. A 79 023838
[7] Shen J T, Fan S H 2007 Phys. Rev. A 76 062709
[8] Shen J T, Fan S H 2005 Opt. Lett. 30 2001
[9] Shen J T, Fan S H 2005 Phys. Rev. Lett. 95 213001
[10] Aoki T, Dayan B, Wilcut E, Bowen W P, Parkins A S, Kippenberg T J, Vahala K J, Kimble H J 2006 Nature (London) 443 671
[11] Peter E, Senellart P, Martrou D, Lematre A, Hours J, Gérard J M, Bloch J 2005 Phys. Rev. Lett. 95 067401
[12] Reithmaier J P, Sek G, Lffler A, Hofmann C, Kuhn S,Reitzenstein S, Keldysh L,Kulakovskii V, Reinecke T L, Forchel A 2004 Nature 432 197
[13] Braginsky V B,Gorodetsky M L, Ilchenko S V 1989 Phys.Lett. A 57 R2293
[14] Yoshie T, Scherer A, Hendrickson J, Khitrova G, Gibbs H M,Rupper G, Ell C, Shekin O B, Deppe D G 2004 Nature 432 200
[15] Srinivasan K, Painter O 2007 Phys. Rev. A 75 023814
[16] Srinivasan K, Painter O 2007 Nature (London) 450 862
[17] Mazzei A, Gotzinger S, Menezes L de S, Zumofen G, Benson O, Sandoghdar V 2007 Phys. Rev. Lett. 99 173603
[18] Zheng S B,Guo G C 2000 Phys. Rev. Lett. 85 2392
[19] Zhao H M, Lou Q H, Zhou J, Dong J X, Wei Y R, Wang Z J 2008 Acta Phys.Sin. 57 3525 (in Chinese) [赵宏明、楼祺洪、周 军、董景星、魏运荣、王之江 2008 57 3525]
[20] Wang N, Lu Y T, Li Y L, Jiao Z Y 2008 Acta Phys.Sin. 57 5632(in Chinese) [王 宁、陆雨田、李晓莉、焦志勇 2008 57 5632]
[21] Dong C H, Zou C L, Cui J M, Han Z F, Guo G C 2009 Appl. Phys. Lett. 94 231119
[22] Zou C L, Sun F W, Dong C H, Wu X W, Cui J M, Yang Y, Guo G C, Han Z F, arXiv:0908.3531
[23] Turchette Q A, Hood C J, Lange W, Mabuchi H, Kimble H J 1995 Phys. Rev. Lett. 75 4710
[24] Rice P R, Carmichael H J 1988 IEEE J. Quantum Electron. 24 1351
[25] Savage C M, Carmichael H J 1988 IEEE J. Quantum Electron. 24 1495
[26] Alsing P, Carmichael H J 1991 Quantum Opt. 3 13
[27] Armen M A, Mabuchi H 2006 Phys. Rev. A 73 063801
[28] Carmichael H J 2003 Statistical Methods in Quantim Optics I: Master Equations and Fokker-Planck Equations (Springer-Verlag, Berlin)
[29] Ajiki H, Ishihara H, Edamatsu K 2009 New J. Phys. 11 033033
[30] Hu X P, Guo H 2009 Acta Phys.Sin. 58 272 (in Chinese) [胡孝平、郭 红 2009 58 272]
[31] Radmore P M, Knight P L 1982 J. Phys. B: At. Mol. Phys. 15 561
[32] Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press)
[33] Hiroshi A, Hajime I 2008 Journal of Applied Phys. 104 123105
[34] Shen J T, Fan S H 2009 Phys. Rev. A 79 023837
[35] Taylor J R 1972 Scattering Theory: The Quantum Theory on Nonrelativistic Collisions (Wiley, New York)
[36] Huang K 1998 Quantum Field Theory (Wiley, New York)
[37] Stevenson R M, Young R J, Atkinson P, Cooper K, Ritchie D A, Shields A J 2006 Nature 439 179
[38] Young R J, Stevenson R M, Atkinson P, Cooper K, Ritchie D A, Shields A J 2006 New J. Phys. 8 29
[39] Akopian N, Lindner N H, Poem E, Berlatzky Y, Avron J, Gershoni D 2006 Phys. Rev. Lett. 96 130501
[40] Aspect A, Grangier P, Roger G 1981 Phys. Rev. Lett. 47 460
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[1] Knill E, Laflamme R, Milburn G J 2001 Nature (London) 409 46
[2] O’Brien J L, Pryde G J, White A G, Ralph T C, Branning D 2003 Nature (London) 426 264
[3] Zhang S, Wang J, Zhang Q, Tang C J 2009 Acta Phys.Sin. 58 73 (in Chinese) [张 盛、王 剑、张 权、唐朝京 2009 58 73]
[4] Mattle K, Weinfurter H, Kwiat P G, Zeilinger A 1996 Phys.Rev. Lett. 76 4656
[5] Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature (London) 390 575
[6] Shen J T, Fan S H 2009 Phys. Rev. A 79 023838
[7] Shen J T, Fan S H 2007 Phys. Rev. A 76 062709
[8] Shen J T, Fan S H 2005 Opt. Lett. 30 2001
[9] Shen J T, Fan S H 2005 Phys. Rev. Lett. 95 213001
[10] Aoki T, Dayan B, Wilcut E, Bowen W P, Parkins A S, Kippenberg T J, Vahala K J, Kimble H J 2006 Nature (London) 443 671
[11] Peter E, Senellart P, Martrou D, Lematre A, Hours J, Gérard J M, Bloch J 2005 Phys. Rev. Lett. 95 067401
[12] Reithmaier J P, Sek G, Lffler A, Hofmann C, Kuhn S,Reitzenstein S, Keldysh L,Kulakovskii V, Reinecke T L, Forchel A 2004 Nature 432 197
[13] Braginsky V B,Gorodetsky M L, Ilchenko S V 1989 Phys.Lett. A 57 R2293
[14] Yoshie T, Scherer A, Hendrickson J, Khitrova G, Gibbs H M,Rupper G, Ell C, Shekin O B, Deppe D G 2004 Nature 432 200
[15] Srinivasan K, Painter O 2007 Phys. Rev. A 75 023814
[16] Srinivasan K, Painter O 2007 Nature (London) 450 862
[17] Mazzei A, Gotzinger S, Menezes L de S, Zumofen G, Benson O, Sandoghdar V 2007 Phys. Rev. Lett. 99 173603
[18] Zheng S B,Guo G C 2000 Phys. Rev. Lett. 85 2392
[19] Zhao H M, Lou Q H, Zhou J, Dong J X, Wei Y R, Wang Z J 2008 Acta Phys.Sin. 57 3525 (in Chinese) [赵宏明、楼祺洪、周 军、董景星、魏运荣、王之江 2008 57 3525]
[20] Wang N, Lu Y T, Li Y L, Jiao Z Y 2008 Acta Phys.Sin. 57 5632(in Chinese) [王 宁、陆雨田、李晓莉、焦志勇 2008 57 5632]
[21] Dong C H, Zou C L, Cui J M, Han Z F, Guo G C 2009 Appl. Phys. Lett. 94 231119
[22] Zou C L, Sun F W, Dong C H, Wu X W, Cui J M, Yang Y, Guo G C, Han Z F, arXiv:0908.3531
[23] Turchette Q A, Hood C J, Lange W, Mabuchi H, Kimble H J 1995 Phys. Rev. Lett. 75 4710
[24] Rice P R, Carmichael H J 1988 IEEE J. Quantum Electron. 24 1351
[25] Savage C M, Carmichael H J 1988 IEEE J. Quantum Electron. 24 1495
[26] Alsing P, Carmichael H J 1991 Quantum Opt. 3 13
[27] Armen M A, Mabuchi H 2006 Phys. Rev. A 73 063801
[28] Carmichael H J 2003 Statistical Methods in Quantim Optics I: Master Equations and Fokker-Planck Equations (Springer-Verlag, Berlin)
[29] Ajiki H, Ishihara H, Edamatsu K 2009 New J. Phys. 11 033033
[30] Hu X P, Guo H 2009 Acta Phys.Sin. 58 272 (in Chinese) [胡孝平、郭 红 2009 58 272]
[31] Radmore P M, Knight P L 1982 J. Phys. B: At. Mol. Phys. 15 561
[32] Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press)
[33] Hiroshi A, Hajime I 2008 Journal of Applied Phys. 104 123105
[34] Shen J T, Fan S H 2009 Phys. Rev. A 79 023837
[35] Taylor J R 1972 Scattering Theory: The Quantum Theory on Nonrelativistic Collisions (Wiley, New York)
[36] Huang K 1998 Quantum Field Theory (Wiley, New York)
[37] Stevenson R M, Young R J, Atkinson P, Cooper K, Ritchie D A, Shields A J 2006 Nature 439 179
[38] Young R J, Stevenson R M, Atkinson P, Cooper K, Ritchie D A, Shields A J 2006 New J. Phys. 8 29
[39] Akopian N, Lindner N H, Poem E, Berlatzky Y, Avron J, Gershoni D 2006 Phys. Rev. Lett. 96 130501
[40] Aspect A, Grangier P, Roger G 1981 Phys. Rev. Lett. 47 460
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