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量子关联是量子信息、量子计算与量子计量领域的重要资源, 在量子纠缠和贝尔非局域性中, 两子系统起着同等关键的作用, Einstein-Podolsky-Rosen (EPR)量子引导关联的强度介于量子纠缠和贝尔非局域性之间, 对单向EPR量子引导关联而言两子系统的作用不对等. 本文研究了双模Bose-Hubbard模型中模间量子关联的动态特性, 揭示了EPR量子引导关联的取向对系统初态模间交换对称性的依赖关系. 根据Hillery-Zubairy纠缠判据以及基于最大平均量子Fisher信息的纠缠判据考察了系统初态对模间量子纠缠演化规律的影响. 如果模间耦合强度远大于同一势阱内粒子间的相互作用, 初始处于SU(2)相干态的系统在具有确定的两子系统交换对称性的条件下, 其量子关联呈现简单的周期性演化规律; 当这种对称性破缺时, 模间量子关联的演化呈现较复杂的崩塌与回复现象.Quantum correlation is an important resource in quantum information, quantum computation, and quantum metrology. Quantum entanglement, Einstein-Podolsky-Rosen (EPR) quantum steering and Bell nonlocality are the major quantum correlations. For quantum entanglement and Bell nonlocality, two subsystems play the same significant roles. EPR quantum steering is stronger than entanglement and weaker than Bell nonlocality. It represents the ability of one subsystem to nonlocally affect another subsystem's states through local measurements. In this paper, the dynamic quantum correlation between the modes in the two-site Bose-Hubbard model is investigated. According to Hillery-Zubairy entanglement criterion and based on maximum mean quantum Fisher information, the influences of initial states on the quantum entanglement evolutions are explored. If the coupling between the modes is much greater than that of the particles at the same site, and the initial states are symmetric or anti-symmetric SU(2) coherent states, the quantum correlations show simple periodic evolutions. The oscillation amplitudes of the evolutions increase with the interaction between the particles at the same site. The oscillation period decreases with the coupling strength between the modes. The dependence of the period on the interaction of the particles at the same site is related to the initial states. In other words, the time evolutions of quantum correlation are closely related to the symmetry of the initial states. In the case of symmetric (anti-symmetric) SU(2) coherent state and repulsive (attractive) interaction of the particles at the same site, the system presents two-way quantum steering. When the subsystem exchange symmetry of the initial states is broken, the collapse and revival of quantum correlation appear, moreover one-way quantum steering emerges in the infancy. One-way quantum steering is asymmetric for two subsystems. So exchange asymmetry of the initial state is necessary condition of one-way quantum steering when the Hamiltonian of the system is symmetric for two subsystems.
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Keywords:
- Bose-Hubbard model /
- quantum entanglement /
- Einstein-Podolsky-Rosen quantum steering /
- quantum Fisher information
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[1] Haas F, Volz J, Gehr R, Reichel J, Estve J 2014 Science 344 180
[2] Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photon. 5 222
[3] Sahota J, Quesada N 2015 Phys. Rev. A 91 013808
[4] Marino A M, Pooser R C, Boyer V, Lett P D 2009 Nature 457 859
[5] Piani M, Watrous J 2015 Phys. Rev. Lett. 114 060404
[6] Bowles J, Vrtesi T, Quintino M T, Brunner N 2014 Phys. Rev. Lett. 112 200402
[7] Hndchen V, Eberle T, Steinlechner S, Samblowski A, Franz T, Werner R F, Schnabel R 2012 Nat. Photon. 6 596
[8] Hillery M, Zubairy M S 2006 Phys. Rev. Lett. 96 050503
[9] Hillery M, Zubairy M S 2006 Phys. Rev. A 74 032333
[10] Smerzi A 2009 Phys. Rev. Lett. 102 100401
[11] Ma J, Wang X G 2009 Phys. Rev. A 80 012318
[12] Li N, Luo S 2013 Phys. Rev. A 88 014301
[13] Blch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885
[14] Blch I, Dalibard J, Nascimbne S 2012 Nat. Phys. 8 267
[15] Blch I 2008 Nature 453 1015
[16] Zhang Z H, Lu P, Feng S P, Yang S J 2012 Phys. Rev. A 85 033617
[17] Giri S K, Sen B, Ooi C H R, Pathak A 2014 Phys. Rev. A 89 033628
[18] McConnell R, Zhang H, Hu J Z, Ćuk S, Vuleti V 2015 Nature 519 439
[19] Gersch H A Knollman G C 1963 Phys. Rev. 129 959
[20] Jaksch D, Bruder C, Cirac J I, Gardiner C W, Zoller P 1998 Phys. Rev. Lett. 81 3018
[21] Eichler C, Salathe Y, Mlynek J, Schmidt S, Wallraff A 2014 Phys. Rev. Lett. 113 110502
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[24] He Q Y, Drummond P D, Olsen M K, Reid M D 2012 Phys. Rev. A 86 023626
[25] Marzolino U, Buchleitner A 2015 Phys. Rev. A 91 032316
[26] Milburn G J, Corney J, Wright E M, Walls D F 1997 Phys. Rev. A 55 4318
[27] Meng X J, Feng H R, Zheng Y J 2014 Chin. Phys. B 23 040305
[28] OpancĆuk B, He Q Y, Reid M D, Drummond P D 2012 Phys. Rev. A 86 023625
[29] Yang S J. Nie S M 2010 Phys. Rev. A 82 061607
[30] Arecchi F T, Courtens E, Gilmore R, Thomas H 1972 Phys. Rev. A 6 2211
[31] Sanders B C, Gerry C C 2014 Phys. Rev. A 90 045804
[32] Bohmann M, Sperling J, Vogel W 2015 Phys. Rev. A 91 042332
[33] Ma J, Huang Y X, Wang X G, Sun C P 2011 Phys. Rev. A 84 022302
[34] Hyllus P, Laskowski W, Krischek R, Schwemmer C, Wieczorek W, Weinfurter H, Pezz L, Smerzi A 2012 Phys. Rev. A 85 022321
[35] Strobel H, Muessel W, Linnemann D, Zibold T, Hume D B, Pezz L, Smerzi A, Oberthaler M K 2014 Science 345 424
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