稀薄里德伯原子气体中的两体纠缠

张秦榕; 王彬彬; 张孟龙; 严冬

doi:10.7498/aps.67.20172052

摘要

量子纠缠是量子信息处理和量子计算中不可或缺的物理资源，制备稳定可操控的量子纠缠是研究的热点之一.里德伯原子具有不同于普通中性原子的特点，长寿命和原子之间强烈的偶极相互作用，使得它成为量子信息处理和量子计算的最优候选者.本文在稀薄里德伯原子气体中，构建了空间四面体排布的里德伯原子模型（空间等距的四个原子模型），通过数值求解主方程来研究两体纠缠和里德伯激发的稳态和瞬态动力学性质，发现偶极阻塞机制下的量子纠缠最大，其他满足反偶极阻塞条件的高阶激发引起的纠缠较小，进而从理论上分析了这两种机制下量子纠缠的物理实质.

关键词:

Abstract

Since the establishment of quantum mechanics, quantum entanglement has become one of the most important realms in quantum physics. On the one hand, it reflects some of the most fascinating features, such as quantum coherence, probability and non-locality and so on. On the other hand, it proves to be an indispensable resource of quantum information processing and quantum computation, which is considered to greatly promote the development of human science and technology. In the past decades, inspired by advances in quantum information theory and quantum physics, people have been searching for suitable systems with great enthusiasm to prepare the robust and manipulable quantum entanglement. Recently, Rydberg atoms have been considered to be a good candidate for many quantum information and quantum computation tasks. Compared with general neutral atoms, Rydberg atoms with large principal quantum number have several advantages in the quantum information and computation service. Firstly, they have finite lifetimes much larger than general neutral atoms, which indicates that the long-time entanglement between Rydberg atoms can be achieved. Secondly, due to the high-excitation level, Rydberg-excitation atoms have long-ranged dipole-dipole interaction much stronger than ground state atoms. This strong atomic interaction leads to the so-called blockade effect: when one atom is excited to Rydberg level, the excitation of the neighboring atoms will be strictly suppressed due to the energy shift induced by the strong atomic interaction. On the contrast, if the energy shift is compensated for by the detuning between the energy levels and the driven laser field, these atoms can be excited with higher probability simultaneously. These effects imply that Rydberg atoms provide an excellent platform for investigating the quantum information and quantum computation process, and many important achievements based on them have been achieved. Encouraged by these researches on entanglement and Rydberg atoms, in this paper, we study the steady-state and transient dynamical properties of two-body entanglement and the Rydberg-excitation properties in a dilute gas of Rydberg atoms, which can be represented by a tetrahedrally arranged interacting four-atom model. By solving numerically the master equation of four atoms involving Rydberg level, we investigate the higher-order Rydberg excitations and bipartite entanglement, which is estimated by concurrence. Our results show that the bipartite entanglement can only achieve its maximal value in the strongest dipole blockade regime rather than anti-blockade one (the high-order Rydberg excitations). Furthermore, the physical essence of quantum entanglement is analyzed theoretically in relevant regimes. Our work can naturally extend to more complicated atomic space structures, and might be treated as a good platform for fulfilling many quantum information tasks by employing the quantum entanglement.

Keywords:

作者及机构信息

1.
长春大学理学院, 材料设计与量子模拟实验室, 长春 130022;

2.
东北师范大学量子科学中心, 长春 130117

通信作者: 严冬, ydbest@126.com

基金项目: 国家自然科学基金（批准号：11204019）、吉林省教育厅自然科学基金（批准号：2016287）和博士后基金（批准号：2015M570260）资助的课题.

Authors and contacts

1.
School of Science and Key Laboratory of Materials Design and Quantum Simulation, Changchun University, Changchun 130022, China;

2.
Center for Quantum Sciences, Northeast Normal University, Changchun 130117, China

Corresponding author: Yan Dong, ydbest@126.com

Funds: Project supported by the National Nature Science Foundation of China (Grant No. 11204019), the Science Foundation of Education Department of Jilin Province, China (Grant No. 2016287), and the General Financial Grant from the China Postdoctoral Science Foundation (Grant No. 2015M570260).

参考文献

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[5]	Lukin M D, Fleischhauer M, Ct R, Duan L M, Jaksch D, Cirac J I, Zoller P 2001 Phys. Rev. Lett. 87 037901
[6]	Tong D, Farooqi S M, Stanojevic J, Krishnan S, Zhang Y P, Ct R, Eyler E E, Gould P L 2004 Phys. Rev. Lett. 93 063001
[7]	Porras D, Cirac J I 2008 Phys. Rev. A 78 053816
[8]	Pedersen L H, Mlmer K 2009 Phys. Rev. A 79 012320
[9]	Gorniaczyk H, Tresp C, Schmidt J, Fedder H, Hofferberth S 2014 Phys. Rev. Lett. 113 053601
[10]	Tiarks D, Baur S, Schneider K, Drr S, Rempe G 2014 Phys. Rev. Lett. 113 053602
[11]	Pritchard J D, Maxwell D, Gauguet A, Weatherill K J, Jones M P A, Adams C S 2010 Phys. Rev. Lett. 105 193603
[12]	Vogt T, Viteau M, Zhao J, Chotia A, Comparat D, Pillet P 2006 Phys. Rev. Lett. 97 083003
[13]	Ye S, Zhang X, Dunning F B, Yoshida S, Hiller M, Burgdrfer J 2014 Phys. Rev. A 90 013401
[14]	Labuhn H, Barredo D, Ravets S, de Lsleuc S, Macr T, Lahaye T, Browaeys A 2016 Nature 534 667
[15]	Gillet J, Agarwal G S, Bastin T 2010 Phys. Rev. A 81 013837
[16]	Fan C H, Yan D, Liu Y M, Wu J H 2017 J. Phys. B: At. Mol. Opt. Phys. 50 115501
[17]	Lee T E, Hffner H, Cross M C 2011 Phys. Rev. A 84 031402
[18]	Lee T E, Hffner H, Cross M C 2012 Phys. Rev. Lett. 108 023602
[19]	ibali N, Wade C G, Adams C S, Weatherill K J, Pohl T 2016 Phys. Rev. A 94 011401
[20]	Dauphin A, Mller M, Martin-Delgado M A 2016 Phys. Rev. A 93 043611
[21]	Petrosyan D, Otterbach J, Fleischhauer M 2011 Phys. Rev. Lett. 107 213601
[22]	Yan D, Liu Y M, Bao Q Q, Fu C B, Wu J H 2012 Phys. Rev. A 86 023828
[23]	Grttner M, Whitlock S, Schnleber D W, Evers J 2014 Phys. Rev. Lett. 113 233002
[24]	Carmele A, Vogell B, Stannigel K, Zoller P 2014 New J. Phys. 16 063042
[25]	Weber T M, Hning M, Niederprm T, Manthey T, Thomas O, Guarrera V, Fleischhauer M, Barontini G, Ott H 2015 Nat. Phys. 11 157
[26]	Zeiher J, Schau P, Hild S, Macr T, Bloch I, Gross C 2015 Phys. Rev. X 5 031015
[27]	Liu Y M, Tian X D, Wang X, Yan D, Wu J H 2016 Opt. Lett. 41 408
[28]	Ates C, Pohl T, Pattard T, Rost J M 2007 Phys. Rev. A 76 013413
[29]	Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[30]	Wootters W K 1998 Phys. Rev. Lett. 80 2245
[31]	Yan D, Song L J 2010 Acta Phys. Sin. 59 6832 (in Chinese) [严冬, 宋立军 2010 59 6832]
[32]	Ates C, Pohl T, Pattard T, Rost J M 2007 Phys. Rev. Lett. 98 023002
[33]	Amthor T, Giese C, Hofmann C S, Weidemller M 2010 Phys. Rev. Lett. 104 013001
[34]	Honer J, Lw R, Weimer H, Pfau T, Bchler H P 2011 Phys. Rev. Lett. 107 093601

施引文献

[1]	Gallagher T F 1994 Rydberg Atoms (Cambridge: Cambridge University Press)
[2]	Saffman M, Walker T G, Mlmer K 2010 Rev. Mod. Phys. 82 2313
[3]	Comparat D, Pillet P 2010 J. Opt. Soc. Am. B 27 A208
[4]	Jaksch D, Cirac J I, Zoller P, Rolston S L, Ct R, Lukin M D 2000 Phys. Rev. Lett. 85 2208
[5]	Lukin M D, Fleischhauer M, Ct R, Duan L M, Jaksch D, Cirac J I, Zoller P 2001 Phys. Rev. Lett. 87 037901
[6]	Tong D, Farooqi S M, Stanojevic J, Krishnan S, Zhang Y P, Ct R, Eyler E E, Gould P L 2004 Phys. Rev. Lett. 93 063001
[7]	Porras D, Cirac J I 2008 Phys. Rev. A 78 053816
[8]	Pedersen L H, Mlmer K 2009 Phys. Rev. A 79 012320
[9]	Gorniaczyk H, Tresp C, Schmidt J, Fedder H, Hofferberth S 2014 Phys. Rev. Lett. 113 053601
[10]	Tiarks D, Baur S, Schneider K, Drr S, Rempe G 2014 Phys. Rev. Lett. 113 053602
[11]	Pritchard J D, Maxwell D, Gauguet A, Weatherill K J, Jones M P A, Adams C S 2010 Phys. Rev. Lett. 105 193603
[12]	Vogt T, Viteau M, Zhao J, Chotia A, Comparat D, Pillet P 2006 Phys. Rev. Lett. 97 083003
[13]	Ye S, Zhang X, Dunning F B, Yoshida S, Hiller M, Burgdrfer J 2014 Phys. Rev. A 90 013401
[14]	Labuhn H, Barredo D, Ravets S, de Lsleuc S, Macr T, Lahaye T, Browaeys A 2016 Nature 534 667
[15]	Gillet J, Agarwal G S, Bastin T 2010 Phys. Rev. A 81 013837
[16]	Fan C H, Yan D, Liu Y M, Wu J H 2017 J. Phys. B: At. Mol. Opt. Phys. 50 115501
[17]	Lee T E, Hffner H, Cross M C 2011 Phys. Rev. A 84 031402
[18]	Lee T E, Hffner H, Cross M C 2012 Phys. Rev. Lett. 108 023602
[19]	ibali N, Wade C G, Adams C S, Weatherill K J, Pohl T 2016 Phys. Rev. A 94 011401
[20]	Dauphin A, Mller M, Martin-Delgado M A 2016 Phys. Rev. A 93 043611
[21]	Petrosyan D, Otterbach J, Fleischhauer M 2011 Phys. Rev. Lett. 107 213601
[22]	Yan D, Liu Y M, Bao Q Q, Fu C B, Wu J H 2012 Phys. Rev. A 86 023828
[23]	Grttner M, Whitlock S, Schnleber D W, Evers J 2014 Phys. Rev. Lett. 113 233002
[24]	Carmele A, Vogell B, Stannigel K, Zoller P 2014 New J. Phys. 16 063042
[25]	Weber T M, Hning M, Niederprm T, Manthey T, Thomas O, Guarrera V, Fleischhauer M, Barontini G, Ott H 2015 Nat. Phys. 11 157
[26]	Zeiher J, Schau P, Hild S, Macr T, Bloch I, Gross C 2015 Phys. Rev. X 5 031015
[27]	Liu Y M, Tian X D, Wang X, Yan D, Wu J H 2016 Opt. Lett. 41 408
[28]	Ates C, Pohl T, Pattard T, Rost J M 2007 Phys. Rev. A 76 013413
[29]	Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[30]	Wootters W K 1998 Phys. Rev. Lett. 80 2245
[31]	Yan D, Song L J 2010 Acta Phys. Sin. 59 6832 (in Chinese) [严冬, 宋立军 2010 59 6832]
[32]	Ates C, Pohl T, Pattard T, Rost J M 2007 Phys. Rev. Lett. 98 023002
[33]	Amthor T, Giese C, Hofmann C S, Weidemller M 2010 Phys. Rev. Lett. 104 013001
[34]	Honer J, Lw R, Weimer H, Pfau T, Bchler H P 2011 Phys. Rev. Lett. 107 093601

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