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The influences of detuning on the duperfluid-nsulator phase transition in coupled dissipative cavity arrays

Bao Jia Tan Lei

The influences of detuning on the duperfluid-nsulator phase transition in coupled dissipative cavity arrays

Bao Jia, Tan Lei
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  • In this paper, based on the effective Jaynes-Cummings-Hubbard model Hamiltonian in the presence of detuning, we use the mean-field and the perturbation theory to figure out the superfluid order parameter of the system. By which we find that detuning from resonance allows one to drive the system from the superfluid into the insulator state of the polaritons and the reverse. In addition, combining with the properties of transportation of coupled dissipative cavity arrays with detuning, we discuss the influence of detuning on the number of superfluid polaritons and the lifetime of superfluid states. It suggests that the number of the superfluid polaritons will increase to its maximum and then reduce again along the negative part of detuning, which is similar to the spectrum of the transmission.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11274148).
    [1]

    Raimond J M, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565

    [2]

    Mabuchi H, Doherty A C 2002 Science 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 2004 Nature 431 162

    [4]

    Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E, Kimble H J 2005 Nature 436 87

    [5]

    Xia F, Sekaric L, Vlasov Y 2007 Nature Photon. 1 65

    [6]

    Notomi M, Kuramochi E, Tanabe T 2008 Nature Photon. 2 741

    [7]

    Hartmann M J, Brandao F G S L, Plenio M B 2008 Laser Photon. Rev. 2 527

    [8]

    Greentree A D, Tahan C, Cole J H, Hollenberg L C L 2006 Nat. Phys. 2 856

    [9]

    Hartmann M J, Brandao F G S L, Plenio M B 2006 Nat. Phys. 2 849

    [10]

    Schmidt S, Blatter G 2009 Phys. Rev. Lett. 103 086403

    [11]

    Diehl S, Micheli A, Kantian A, Kraus B, Bchler H P, Zoller P 2008 Nat. Phys. 4 878

    [12]

    Gerace D, Treci H E, Imamolu A, Giovannetti V, Fazio R 2009 Nat. Phys. 5 281

    [13]

    Karasik R I, Wiseman H M 2011 Phys. Rev. Lett. 106 020406

    [14]

    Hur K L 2008 Ann. Phys. (NY) 323 2208

    [15]

    Leib M, Hartmann M J 2010 New J. Phys. 12 093031

    [16]

    Knap M, Arrigoni E, von der Linden W, Cole J H 2011 Phys. Rev. A 83 023821

    [17]

    Nissen F, Schmidt S, Biondi M, Blatter G, Treci H E, Keeling J 2012 Phys. Rev. Lett. 108 233603

    [18]

    Carusotto I, Gerace D, Tureci H E, De Liberato S, Ciuti C, Imamolu A 2009 Phys. Rev. Lett. 103 033601

    [19]

    D’Souza A G, Sanders B C, Feder D L 2013 Phys. Rev. A 88 063801

    [20]

    Hartmann M J 2010 Phys. Rev. Lett. 104 113601

    [21]

    Tomadin A, Giovannetti V, Fazio R, Gerace D, Carusotto I, Treci H E, Imamolu A 2010 Phys. Rev. A 81 061801(R)

    [22]

    Liu K, Tan L, L C H, Liu W M 2011 Phys. Rev. A 83 063840

    [23]

    Marcos D, Tomadin A, Diehl S, Rabl P 2012 New J. Phys. 14 055005

    [24]

    Schetakis N, Grujic T, Clark S, Jaksch D, Angelakis D G 2013 J. Phys. B: At. Mol. Opt. Phys. 46 224025

    [25]

    Grujic T, Clark S R, Jaksch D, Angelakis D G 2013 Phys. Rev. A 87 053846

    [26]

    Grujic T, Clark S R, Jaksch D, Angelakis D G 2012 New J. Phys. 14 103025

    [27]

    Nissen F, Schmidt S, Biondi M, Blatter G, Treci H E, Keeling J 2012 Phys. Rev. Lett. 108 233603

    [28]

    Kulaitis G, Krger F, Nissen F, Keeling J 2013 Phys. Rev. A 87 013840

    [29]

    Toyoda K, Matsuno Y, Noguchi A, Haze S, Urabe S 2013 Phys. Rev. Lett. 111 160501

    [30]

    Valle E D, Hartmann M J 2013 J. Phys. B: At. Mol. Opt. Phys. 46224023

    [31]

    Tan L, Hai L 2012 J. Phys. B: At. Mol. Opt. Phys. 45 035504

    [32]

    Hai L, Tan L, Feng J S, Bao J, L C H, Wang B 2013 Eur. Phys. J. D 67 173

    [33]

    Hai L, Tan L, Feng J S, Xu W B, Wang B 2014 Chin. Phys. B 23 024202

    [34]

    Zhou L, Liu Z J, Yan W B, Mu Q X 2011 Chin. Phys. B 20 074205

    [35]

    Imamo\=glu A, Schmidt H, Woods G, Deutsch M 1997 Phys. Rev. Lett. 79 1467

    [36]

    Grangier P, Walls D F, Gher K M 1998 Phys. Rev. Lett. 81 2833

    [37]

    Imamo lu A, Schmidt H, Woods G, Deutsch M 1998 Phys. Rev. Lett. 81 2836

    [38]

    Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E, Kimble H J 2005 Nature 436 87

    [39]

    Du X Y, Zheng W H, Ren G, Wang K, Xing M X, Chen L H 2008 Acta Phys. Sin. 57 571 (in Chinese) [杜晓宇, 郑婉华, 任刚, 王科, 邢名欣, 陈良惠 2008 物理学报 57 571]

    [40]

    Zhou L, Gong Z R, Liu Y X, Sun C P, Nori F 2008 Phys. Rev. Lett. 101 100501

    [41]

    Liao J Q, Gong Z R, Zhou L, Liu Y X, Sun C P, Nori F 2010 Phys. Rev. A 81 042304

    [42]

    Cheng M T, Song Y Y, Yu L B 2012 Chin. Phys. Lett. 29 054211

    [43]

    Gu L M 2012 Chin. Phys. Lett. 29 104206

  • [1]

    Raimond J M, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565

    [2]

    Mabuchi H, Doherty A C 2002 Science 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 2004 Nature 431 162

    [4]

    Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E, Kimble H J 2005 Nature 436 87

    [5]

    Xia F, Sekaric L, Vlasov Y 2007 Nature Photon. 1 65

    [6]

    Notomi M, Kuramochi E, Tanabe T 2008 Nature Photon. 2 741

    [7]

    Hartmann M J, Brandao F G S L, Plenio M B 2008 Laser Photon. Rev. 2 527

    [8]

    Greentree A D, Tahan C, Cole J H, Hollenberg L C L 2006 Nat. Phys. 2 856

    [9]

    Hartmann M J, Brandao F G S L, Plenio M B 2006 Nat. Phys. 2 849

    [10]

    Schmidt S, Blatter G 2009 Phys. Rev. Lett. 103 086403

    [11]

    Diehl S, Micheli A, Kantian A, Kraus B, Bchler H P, Zoller P 2008 Nat. Phys. 4 878

    [12]

    Gerace D, Treci H E, Imamolu A, Giovannetti V, Fazio R 2009 Nat. Phys. 5 281

    [13]

    Karasik R I, Wiseman H M 2011 Phys. Rev. Lett. 106 020406

    [14]

    Hur K L 2008 Ann. Phys. (NY) 323 2208

    [15]

    Leib M, Hartmann M J 2010 New J. Phys. 12 093031

    [16]

    Knap M, Arrigoni E, von der Linden W, Cole J H 2011 Phys. Rev. A 83 023821

    [17]

    Nissen F, Schmidt S, Biondi M, Blatter G, Treci H E, Keeling J 2012 Phys. Rev. Lett. 108 233603

    [18]

    Carusotto I, Gerace D, Tureci H E, De Liberato S, Ciuti C, Imamolu A 2009 Phys. Rev. Lett. 103 033601

    [19]

    D’Souza A G, Sanders B C, Feder D L 2013 Phys. Rev. A 88 063801

    [20]

    Hartmann M J 2010 Phys. Rev. Lett. 104 113601

    [21]

    Tomadin A, Giovannetti V, Fazio R, Gerace D, Carusotto I, Treci H E, Imamolu A 2010 Phys. Rev. A 81 061801(R)

    [22]

    Liu K, Tan L, L C H, Liu W M 2011 Phys. Rev. A 83 063840

    [23]

    Marcos D, Tomadin A, Diehl S, Rabl P 2012 New J. Phys. 14 055005

    [24]

    Schetakis N, Grujic T, Clark S, Jaksch D, Angelakis D G 2013 J. Phys. B: At. Mol. Opt. Phys. 46 224025

    [25]

    Grujic T, Clark S R, Jaksch D, Angelakis D G 2013 Phys. Rev. A 87 053846

    [26]

    Grujic T, Clark S R, Jaksch D, Angelakis D G 2012 New J. Phys. 14 103025

    [27]

    Nissen F, Schmidt S, Biondi M, Blatter G, Treci H E, Keeling J 2012 Phys. Rev. Lett. 108 233603

    [28]

    Kulaitis G, Krger F, Nissen F, Keeling J 2013 Phys. Rev. A 87 013840

    [29]

    Toyoda K, Matsuno Y, Noguchi A, Haze S, Urabe S 2013 Phys. Rev. Lett. 111 160501

    [30]

    Valle E D, Hartmann M J 2013 J. Phys. B: At. Mol. Opt. Phys. 46224023

    [31]

    Tan L, Hai L 2012 J. Phys. B: At. Mol. Opt. Phys. 45 035504

    [32]

    Hai L, Tan L, Feng J S, Bao J, L C H, Wang B 2013 Eur. Phys. J. D 67 173

    [33]

    Hai L, Tan L, Feng J S, Xu W B, Wang B 2014 Chin. Phys. B 23 024202

    [34]

    Zhou L, Liu Z J, Yan W B, Mu Q X 2011 Chin. Phys. B 20 074205

    [35]

    Imamo\=glu A, Schmidt H, Woods G, Deutsch M 1997 Phys. Rev. Lett. 79 1467

    [36]

    Grangier P, Walls D F, Gher K M 1998 Phys. Rev. Lett. 81 2833

    [37]

    Imamo lu A, Schmidt H, Woods G, Deutsch M 1998 Phys. Rev. Lett. 81 2836

    [38]

    Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E, Kimble H J 2005 Nature 436 87

    [39]

    Du X Y, Zheng W H, Ren G, Wang K, Xing M X, Chen L H 2008 Acta Phys. Sin. 57 571 (in Chinese) [杜晓宇, 郑婉华, 任刚, 王科, 邢名欣, 陈良惠 2008 物理学报 57 571]

    [40]

    Zhou L, Gong Z R, Liu Y X, Sun C P, Nori F 2008 Phys. Rev. Lett. 101 100501

    [41]

    Liao J Q, Gong Z R, Zhou L, Liu Y X, Sun C P, Nori F 2010 Phys. Rev. A 81 042304

    [42]

    Cheng M T, Song Y Y, Yu L B 2012 Chin. Phys. Lett. 29 054211

    [43]

    Gu L M 2012 Chin. Phys. Lett. 29 104206

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  • Received Date:  21 July 2013
  • Accepted Date:  18 January 2014
  • Published Online:  05 April 2014

The influences of detuning on the duperfluid-nsulator phase transition in coupled dissipative cavity arrays

  • 1. Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;
  • 2. Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou 730000, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11274148).

Abstract: In this paper, based on the effective Jaynes-Cummings-Hubbard model Hamiltonian in the presence of detuning, we use the mean-field and the perturbation theory to figure out the superfluid order parameter of the system. By which we find that detuning from resonance allows one to drive the system from the superfluid into the insulator state of the polaritons and the reverse. In addition, combining with the properties of transportation of coupled dissipative cavity arrays with detuning, we discuss the influence of detuning on the number of superfluid polaritons and the lifetime of superfluid states. It suggests that the number of the superfluid polaritons will increase to its maximum and then reduce again along the negative part of detuning, which is similar to the spectrum of the transmission.

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