Quantum phase transition in arrays of dissipative cavities with two-photon process

Xiong Fang; Feng Xiao-Qiang; Tan Lei

doi:10.7498/aps.65.044205

Abstract

In this paper, we employ a new kind of quasi-boson approach and the mean field theory to study analytically the Hamiltonian of an array of cavities with a three-level atom embedded in each cavity in the process of two-photon resonant transition under the influence of a bosonic bath. The superfluid order parameter of the system is obtained analytically and then analyzed numerically to investigate the effects of dissipation on the quantum phase transition from the superfluid to the Mott-insulator phase. It is shown that when the two-photon resonance is achieved one can have the superfluid phase at (ZJ/)= (ZJ/)c' 0.34 in the related ideal case. Furthermore, the system while in the two-photon resonant process has a larger dissipation rate as compared with that in the one-photon resonant process, thus leading to the suppression of the long-range coherence time and enhancement of the critical hopping rate for restoring coherence.

Keywords:

two-photon process /
coupled cavity arrays /
superfluid-Mott-insulator phase transition /
quasiboson

Authors and contacts

1.
Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China

Corresponding author: Tan Lei, tanlei@lzu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11274148).

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[46]	Christian N 2010 Ph. D. Dissertation (Berlin: Freie Universitt Berlin)
[47]	Scala M, Militello B, Messina A, Piilo J, Maniscalco S 2007 Phys. Rev. A 75 013811
[48]	Schtzhold R, Uhlmann M, Xu Y, Fischer R U 2006 Phys. Rev. Lett. 97 200601

Cited By

[1]	Raimond M J, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565
[2]	Mabuchi H, Doherty C A 2002 Science 298 1372
[3]	Wallraff A, Schuster I D, Blais A, Frunzio L, Huang S R, Majer J, Kumar S, Girvin M S, Schoelkopf J R 2004 Nature 431 162
[4]	Birnbaum M K, Boca A, Miller R, Boozer D A, Northup E T, Kimble J H 2005 Nature 436 87
[5]	Xia F, Sekaric L, Vlasov Y 2007 Nat. Photon. 1 65
[6]	Notomi M, Kuramochi E, Tanabe T 2008 Nat. Photon. 2 741
[7]	Hartmann J M, Brando L S G F, Plenio B M 2006 Nat. Phys. 2 849
[8]	Greentree D A, Tahan C, Cole H J, Hollenberg L C L 2006 Nat. Phys. 2 856
[9]	Angelakis G D, Santos F M, Bose S 2007 Phys. Rev. A 76 031805(R)
[10]	Hartmann J M, Brando L S G F, Plenio B M 2008 Laser Photon. Rev. 2 527
[11]	Yanik F M, Fan S 2004 Phys. Rev. Lett. 92 083901
[12]	Zhou L, Gong R Z, Liu X Y, Sun P C, Nori F 2008 Phys. Rev. Lett. 101 100501
[13]	Longo P, Schmitteckert P, Busch K 2010 Phys. Rev. Lett. 104 023602
[14]	Liew H C T, Savona V 2010 Phys. Rev. Lett. 104 183601
[15]	Ji A C, Sun Q, Xie X C, Liu W M 2009 Phys. Rev. Lett. 102 023602
[16]	Ji A C, Xie X C, Liu W M 2007 Phys. Rev. Lett. 99 183602
[17]	Diehl S, Micheli A, Kantian A, Kraus B, Bchler P H, Zoller P 2008 Nat. Phys. 4 878
[18]	Gerace D, Treci H E, Imamolu A, Giovannetti V, Fazio R 2009 Nat. Phys. 5 281
[19]	Karasik I R, Wiseman M H 2011 Phys. Rev. Lett. 106 020406
[20]	Hur K L 2008 Ann. Phys. 323 2208
[21]	Szymnska H M, Keeling J, Littlewood B P 2006 Phys. Rev. Lett. 96 230602
[22]	Dalidovich D, Kennett P M 2009 Phys. Rev. A 79 053611
[23]	Carusotto I, Gerace D, Tureci H E, DeLiberato S, Ciuti C, Imamolu A 2009 Phys. Rev. Lett. 103 033601
[24]	Diehl S, Tomadin A, Micheli A, Fazio R, Zoller P 2010 Phys. Rev. Lett. 105 015702
[25]	Schmidt S, Gerace D, Houck A A, Blatter G, Treci H E 2010 Phys. Rev. B 82 100507
[26]	Tomadin A, Giovannetti V, Fazio R, Gerace D, Carusotto I, Treci H E, Imamolu A 2010 Phys. Rev. A 81 061801(R)
[27]	Hartmann J M 2010 Phys. Rev. Lett. 104 113601
[28]	Morrison S, Parkins S A 2008 Phys. Rev. Lett. 100 040403
[29]	Kiffner M, Hartmann J M 2010 Phys. Rev. A 81 021806(R)
[30]	Ferretti S, Andreani C L, Treci H E, Gerace D 2010 Phys. Rev. A 82 013841
[31]	Han J Y, Chan H Y, Yi W, Daley J A, Diehl S, Zoller P, Duan M L 2009 Phys. Rev. Lett. 103 070404
[32]	Knap M, Arrigoni E, von der Linden W, Cole H J 2011 Phys. Rev. A 83 023821
[33]	Liu K, Tan L, L C H, Liu W M 2011 Phys. Rev. A 83 063840
[34]	Bao J, Tan L 2014 Acta Phys. Sin. 63 084201 (in Chinese) [鲍佳, 谭磊 2014 物理学报 63 084201]
[35]	Del E V, Hartmann M J 2013 J. Phys. B: At. Mol. Opt. Phys. 46 224023
[36]	Creatore C, Fazio R, Keeling J, Treci H E 2014 Proc. R. Soc. A 470 20140328
[37]	Hai L, Tan L, Feng J S, Xu W B, Wang B 2014 Chin. Phys. B 23 024202
[38]	Yang X, Tong Z Y, Kuang L M 2007 Acta Phys. Sin. 57 1689 (in Chinese) [杨雄, 童朝阳, 匡乐满 2007 物理学报 57 1689]
[39]	Dong Y L, Zhu S Q, You W L 2012 Phys. Rev. A 85 023833
[40]	Benjamn V C, Andreas K, Juan J G R 2013 J. Phys. B: At. Mol. Opt. Phys. 46 224024
[41]	Zhang H, Zhang S A, Wang Z G, Sun Z R 2010 Chin. Phys. B 19 113208
[42]	Ren X Z, Cong H L, Liao X, Li L 2012 Chin. Phys. B 21 054210
[43]	Tang S Q, Yuan J B, Wang X W, Kuang L M 2015 Chin. Phys. Lett. 32 040303
[44]	Lambropoulos P, Petrosyan D 2007 Fundamentals of Quantum Optics and Quantum Information (Berlin: Springer-Verlag) pp1-197
[45]	Sheshadri K, Krishnamurthy R H, Pandit R, Ramakrishnan V T 1993 Europhys. Lett. 22 257
[46]	Christian N 2010 Ph. D. Dissertation (Berlin: Freie Universitt Berlin)
[47]	Scala M, Militello B, Messina A, Piilo J, Maniscalco S 2007 Phys. Rev. A 75 013811
[48]	Schtzhold R, Uhlmann M, Xu Y, Fischer R U 2006 Phys. Rev. Lett. 97 200601

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Vol. 65, Issue 4 - 2016-02-20

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