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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.
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Keywords:
- quantum entanglement /
- concurrence /
- Rydberg atom /
- dipole-dipole interaction
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[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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