双光子过程耗散耦合腔阵列中的量子相变

熊芳; 冯晓强; 谭磊

doi:10.7498/aps.65.044205

摘要

基于准玻色方法, 利用平均场理论解析求解了环境作用下双光子过程耦合腔阵列体系的哈密顿量, 得到了体系序参量的解析表达式, 并讨论了耗散对体系超流-Mott绝缘相变的影响. 研究结果表明: 双光子共振情况下系统重铸相干的腔间耦合率临界值为(ZJ/)= (ZJ/)c' 0.34;双光子相互作用过程比单光子过程具有更大的耗散率, 系统维持长程相干状态的时间更短, 而实现重铸相干的腔间耦合率的临界值更大.

关键词:

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

作者及机构信息

1.
兰州大学理论物理研究所, 兰州 730000

通信作者: 谭磊, tanlei@lzu.edu.cn

基金项目: 国家自然科学基金(批准号: 11274148)资助的课题.

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).

参考文献

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施引文献

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[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 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 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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