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In this paper, a new kind of quasi-boson method is used to eliminate the coordinates of the environment and redescribe the dissipative system by using an effective Hamiltonian; the localized mode and the interaction between cavities can be renormalized. Based on the quasi-boson approach, the single photon transport in one-dimensional coupled cavity array, with a driven cascade-type three-level atom embedded in one of the cavity, is investigated under the influence of the environment. The single-photon transmission and the reflection amplitudes are obtained analytically. And the additional effective potential induced by the interaction between the atom and the cavity is also derived. The effects of the controlling parameters on the reflection and transmission amplitudes are discussed with considering the dissipation. It is shown that the decay rates of the atoms and the cavity both reduce the reflection spectrum. But the dissipation of the atom has a significant influence on the reflection amplitude compared with the cavity decay under the same conditions. Due to the irreversible loss of energy, the photon number is non-conservative. Furthermore, the single-photon can be almost reflected by the three-level atom in the dissipative case when one adjusts the detuning and photon number of the quantized cavity field. The investigation will be of benefit to the realization of photon transport in a real experiment, which is also helpful for manipulating the photons in quantum information and quantum simulation.
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Keywords:
- environment effect /
- coupled cavity array /
- quasi-boson approach /
- single-photon transport
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[1] Raimond J M, Brune M, Haroche S 2001Rev.Mod.Phys. 73 565
[2] Mabuchi H, Doherty A C 2002Science 298 1372
[3] Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M, Schoelkopf R J 2004Nature 431 162
[4] Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E, Kimble H J 2005Nature 436 87
[5] Xia F, Sekaric L, Vlasov Y 2007Nat.Photonics 1 65
[6] Notomi M, Kuramochi E, Tanabe T 2008Nat.Photonics 2 741
[7] Hartmann M J, Brandao F G S L, Plenio M B 2008Laser Photonics Rev. 2 527
[8] Rosenblit M, Horak P, Helsby S, Folman R 2004Phys.Rev.A 70 053808
[9] Bermel P, Rodriguez A, Johnson S G, Joannopoulos J D, Soljacic M 2006Phys.Rev.A 74 043818
[10] Romero G, Garca-Ripoll J J, Solano E 2009Phys.Rev.Lett. 102 173602
[11] Aoki T, Dayan B, Wilcut E, Bowen W P, Parkins A S, Kippenberg T J, Vahala K J, Kimble H J 2006Nature 443 671
[12] Srinivasan K, Painter O 2007Nature 450 862
[13] Rakher M T, Ma L, Slattery O, Tang X, Srinivasan K 2010Nat.Photonics 4 786
[14] Zhou L, Gong Z R, Liu Y X, Sun C P, Nori F 2008Phys.Rev.Lett. 101 100501
[15] Gong Z R, Lan H, Zhou L, Sun C P 2008Phys.Rev.A 78 053806
[16] Zhou L, Yang L P, Li Y, Sun C P 2013Phys.Rev.Lett. 111 103604
[17] Lu J, Zhou L, Kuang L M, Nori F 2014Phys.Rev.A 89 013805
[18] Yan W B, Fan H 2014Phys.Rev.A 90 053807
[19] Diehl S, Micheli A, Kantian A, Kraus B, Bchler P H, Zoller P 2008Nat.Phys. 4 878
[20] Gerace D, Treci H E, Imamolu A, Giovannetti V, Fazio R 2009Nat.Phys. 5 281
[21] Karasik I R, Wiseman M H 2011Phys.Rev.Lett. 106 020406
[22] Hur K L 2008Ann.Phys. 323 2208
[23] Szymaska H M, Keeling J, Littlewood B P 2006Phys.Rev.Lett. 96 230602
[24] Dalidovich D, Kennett P M 2009Phys.Rev.A 79 053611
[25] Carusotto I, Gerace D, Tureci H E, DeLiberato S, Ciuti C, Imamolu A 2009Phys.Rev.Lett. 103 033601
[26] Diehl S, Tomadin A, Micheli A, Fazio R, Zoller P 2010Phys.Rev.Lett. 105 015702
[27] Schmidt S, Gerace D, Houck A A, Blatter G, Treci H E 2010Phys.Rev.B 82 100507
[28] Tomadin A, Giovannetti V, Fazio R, Gerace D, Carusotto I, Treci H E, Imamolu A 2010Phys.Rev.A 81 061801
[29] Hartmann J M 2010Phys.Rev.Lett. 104 113601
[30] Morrison S, Parkins S A 2008Phys.Rev.Lett. 100 040403
[31] Kiffner M, Hartmann J M 2010Phys.Rev.A 81 021806
[32] Ferretti S, Andreani C L, Treci H E, Gerace D 2010Phys.Rev.A 82 013841
[33] Han J Y, Chan H Y, Yi W, Daley J A, Diehl S, Zoller P, Duan M L 2009Phys.Rev.Lett. 103 070404
[34] Knap M, Arrigoni E, Linden W, Cole H J 2011Phys.Rev.A 83 023821
[35] Liu K, Tan L, Lv C H, Liu W M 2011Phys.Rev.A 83 063840
[36] Tan L, Hai L 2012J.Phys.B:At.Mol.Opt.Phys. 45 035504
[37] Hai L, Tan L, Feng J S, Bao J, Lv C H, Wang B 2013Eur.Phys.J.D 67 173
[38] Cheng M T, Ma X S, Ding M T, Luo Y Q, Zhao G X 2012Phys.Rev.A 85 053840
[39] Flgge S 1999Practical Quantum Mechanics(Berlin:Springer-Verlag) pp64-68
[40] Sachiko K, Masashi B, Fumiaki S 2013J.Phys.B:At.Mol.Opt.Phys. 46 224004
[41] Sandberg M, Wilson C M, Persson F, Bauch T, Johansson G, Shumeiko V, Duty T, Delsing P 2008Appl.Phys.Lett. 92 203501
[42] Majumdar A, Rundquist A, Bajcsy M, Vuckovic J 2012Phys.Rev.B 86 045315
[43] Liao J Q, Huang J F, Liu Y X, Kuang L M, Sun C P 2009Phys.Rev.A 80 014301
[44] Houck A A, Schuster D I, Gambetta J M, Schreier J A, Johnson B R, Chow J M, Schoelkopf R J 2007Nature 449 328
[45] Kuramochi E, Notomi M, Mitsugi S, Shinya A, Tanabe T, Watanabe T 2006Appl.Phys.Lett. 88 041112
[46] Noda S, Fujita M, Asano T 2007Nat.Photonics 1 449
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