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In this paper, we discuss the transport properties of a single photon, which is in a coupled cavity array system where the two nearest cavities nonlocally couple to a -type three-level atom, under the condition of ideal and dissipation, respectively. By employing the quasi-boson picture, the transmission amplitude of the single photon in an open system is investigated analytically. The system where the coupled cavity array nonlocally couples with the three-level atom demonstrates several advantages. Compared with other systems, this system has many parameters to manipulate the single photon transport properties. Moreover, the system of the coupled cavity array that nonlocally couples with the three-level atom may have a wider range of application because the single photon transmission spectrum in this system has three peaks. Furthermore, it has characteristics of its own. At the same value of Rabi frequency , changing the coupling strength between the atom and one cavity of the coupled cavity array shows that there exists an fixed point where the transmission rate is always 1, and the point is corresponding to the frequency of the photon c-. In the nonideal case, it is shown that the dissipations of the cavity and the atom affect distinctively the transmission of photons in the coupled cavity arrays. When considering only the dissipation of the atom, the atomic dissipation increases the dips of the single photon transport spectrum, while the peaks have no observable changes. When considering only the dissipation of the cavity, the peaks of the single photon transmission amplitude are diminished deeply, while the cavity dissipation does not have any effect on the dips. In addition, with both the cavity dissipation rate and the number of the cavity increasing, the photon transmission spectrum peaks decrease. A comparison of the dissipative cavity case with the dissipative atom case shows that the incomplete reflect near the peak is mostly caused by the cavity dissipation, and that the incomplete reflect near the dip is mostly caused by the three-level atom dissipation. Specifically, when considering both the atom and the cavity dissipation at the same time, the dips of the single photon transport spectrum are affected by both the atomic and the cavity dissipation. Instead, with the cavity dissipation rate increasing, the photon transmission spectrum dips are reduced. But for the peaks of the single photon transport spectrum, the dips are always determined by the cavity dissipation rate and the number of the cavity, while the atomic dissipation has no significant influence on them.
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Keywords:
- coupled cavity array /
- three-level atom /
- nonlocally coupling
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[1] Hartmann M J, Brando F G S L, Plenio M B 2008 Laser Photon. Rev. 2 527
[2] Sun C P, Wei L F, Liu Y X, Nori F 2006 Phys. Rev. A 73 022318
[3] Zhou L, Gong Z R, Liu Y X, Sun C P, Nori F 2008 Phys. Rev. Lett. 101 100501
[4] Gong Z R, Ian H, Zhou L, Sun C P 2008 Phys. Rev. A 78 053806
[5] Biella A, Mazza L, Carusotto I, Rossini D, Rosario F 2015 Phys. Rev. A 91 053815
[6] Cheng M T, Song Y Y, Ma X S 2016 J. Mod. Opt. 63 881
[7] Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E, Kimble H J 2005 Nature 436 87
[8] Aoki T, Dayan B, Wilcut E, Bowen W P, Parkins A S, Kippenberg T J, Vahala K J, Kimble H J 2006 Nature 443 671
[9] Srinivasan K, Painter O 2007 Nature 450 862
[10] Dayan B, Parkins A S, Aoki T, Ostby E P, Vahala K J, Kimble H J 2008 Science 319 1062
[11] Rosenblit M, Horak P, Helsby S, Folman R 2004 Phys. Rev. A 70 053808
[12] Zang X F, Jiang C 2010 J. Phys. B: At. Mol. Opt. Phys. 43 215501
[13] Zhou T, Zang X F, Liu Y S, Zheng L, Gao T 2015 J. Mod. Opt. 62 32
[14] Cheng M T, Song Y Y, Luo Y Q, Ma X S, Wang P Z 2011 J. Mod. Opt. 58 1233
[15] Cheng M T, Zong W W, Ye G L, Ma X S, Zhang J Y, Wang B 2016 Commun. Theor. Phys. 65 767
[16] Shi Y Q, Kong W L, Wu R C, Zhang W X, Tan L 2017 Acta Phys. Sin. 66 054204 (in Chinese) [石永强, 孔维龙, 吴仁存, 张文轩, 谭磊 2017 物理学报 66 054204]
[17] Shen J T, Fan S 2009 Phys. Rev. A 79 023837
[18] Shen J T, Fan S 2009 Phys. Rev. A 79 023838
[19] Rephaeli E, Shen J T, Fan S 2010 Phys. Rev. A 82 033804
[20] Zhou L, Yang S, Liu Y X, Sun C P, Nori F 2009 Phys. Rev. A 80 062109
[21] Hai L, Tan L, Feng J S, Bao J, L C H, Wang B 2013 Eur. Phys. J. D 67 173
[22] Cheng M T, Ma X S, Ting M T, Luo Y Q, Zhao G X 2012 Phys. Rev. A 85 053840
[23] Cheng M T, Luo Y Q, Song Y Y, Zhao G X 2011 Commun. Theor. Phys. 55 501
[24] Schmid S I, Evers J 2011 Phys. Rev. A 84 053822
[25] Witthaut D, Srensen A S 2010 New. J. Phys. 12 043052
[26] Zhou L, Chang Y, Dong H, Kuang L M, Sun C P 2012 Phys. Rev. A 85 013806
[27] Lang J H 2010 Chin. Phys. Lett. 28 104210
[28] del Valle E, Hartmann M J 2013 J. Phys. B: At. Mol. Opt. Phys. 46 224023
[29] Creatore C, Fazio R, Keeling J, Treci H E 2014 Proc. R. Soc. A 470 20140328
[30] Liu K, Tan L, L C H, Liu W M 2011 Phys. Rev. A 83 063840
[31] Bao J, Tan L 2014 Acta Phys. Sin. 63 084201 (in Chinese) [鲍佳, 谭磊 2014 物理学报 63 084201]
[32] Tan L, Hai L 2012 J. Phys. B: At. Mol. Opt. Phys. 45 035504
[33] Hai L, Tan L, Feng J S, Xu W B, Wang B 2014 Chin. Phys. B 23 024202
[34] Notomi M, Kuramochi E, Tanabe T 2008 Nat. Photon. 2 741
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