Probe of topological invariants using quantum walks of a trapped ion in coherent state space

doi:10.1088/1674-1056/ab8893

中国物理B ›› 2020, Vol. 29 ›› Issue (7): 70501-070501.doi: 10.1088/1674-1056/ab8893

Probe of topological invariants using quantum walks of a trapped ion in coherent state space

Ya Meng(蒙雅), Feng Mei(梅锋), Gang Chen(陈刚), Suo-Tang Jia(贾锁堂)

1 State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China;
2 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China;
3 Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China

收稿日期:2020-02-25 修回日期:2020-04-06 出版日期:2020-07-05 发布日期:2020-07-05
通讯作者: Feng Mei, Gang Chen E-mail:meifeng@sxu.edu.cn;chengang971@163.com
基金资助:
Project supported by the National Key R&D Program of China (Grant No. 2017YFA0304203), the National Natural National Science Foundation of China (Grant Nos. 11604392 and 11674200), the Changjiang Scholars and Innovative Research Team in Universities of Ministry of Education of China (Grant No. IRT_17R70), the Fund for Shanxi “1331 Project” Key Subjects Construction, and the 111 Project, China (Grant No. D18001).

Probe of topological invariants using quantum walks of a trapped ion in coherent state space

Ya Meng(蒙雅)^1,2, Feng Mei(梅锋)^1,2, Gang Chen(陈刚)^1,2,3, Suo-Tang Jia(贾锁堂)^1,2

1 State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China;
2 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China;
3 Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China

Received:2020-02-25 Revised:2020-04-06 Online:2020-07-05 Published:2020-07-05
Contact: Feng Mei, Gang Chen E-mail:meifeng@sxu.edu.cn;chengang971@163.com
Supported by:
Project supported by the National Key R&D Program of China (Grant No. 2017YFA0304203), the National Natural National Science Foundation of China (Grant Nos. 11604392 and 11674200), the Changjiang Scholars and Innovative Research Team in Universities of Ministry of Education of China (Grant No. IRT_17R70), the Fund for Shanxi “1331 Project” Key Subjects Construction, and the 111 Project, China (Grant No. D18001).

摘要/Abstract

摘要： We present a protocol to realize topological discrete-time quantum walks, which comprise a sequence of spin-dependent flipping displacement operations and quantum coin tossing operations, with a single trapped ion. It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space. Interestingly, the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process. Furthermore, we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence. Our work provides a simple method to measure bulk topological features in discrete-time quantum walks, which can be experimentally realized in the system of single trapped ions.

关键词: topological quantum walk, topological invariant, trapped ion, coherent state space

Abstract: We present a protocol to realize topological discrete-time quantum walks, which comprise a sequence of spin-dependent flipping displacement operations and quantum coin tossing operations, with a single trapped ion. It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space. Interestingly, the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process. Furthermore, we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence. Our work provides a simple method to measure bulk topological features in discrete-time quantum walks, which can be experimentally realized in the system of single trapped ions.

Key words: topological quantum walk, topological invariant, trapped ion, coherent state space

中图分类号: (Random walks and Levy flights)

05.40.Fb

03.67.Ac (Quantum algorithms, protocols, and simulations) 03.65.Vf (Phases: geometric; dynamic or topological) 37.10.Vz (Mechanical effects of light on atoms, molecules, and ions)

蒙雅, 梅锋, 陈刚, 贾锁堂. Probe of topological invariants using quantum walks of a trapped ion in coherent state space[J]. 中国物理B, 2020, 29(7): 70501-070501.

Ya Meng(蒙雅), Feng Mei(梅锋), Gang Chen(陈刚), Suo-Tang Jia(贾锁堂). Probe of topological invariants using quantum walks of a trapped ion in coherent state space[J]. Chin. Phys. B, 2020, 29(7): 70501-070501.

参考文献 61

[1]	Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045 doi: 10.1103/RevModPhys.82.3045
[2]	Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057 doi: 10.1103/RevModPhys.83.1057
[3]	Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev. Mod. Phys. 88 035005 doi: 10.1103/RevModPhys.88.035005
[4]	Sheng D N, Weng Z Y, Sheng L and Haldane F D M 2006 Phys. Rev. Lett. 97 036808 doi: 10.1103/PhysRevLett.97.036808
[5]	Lu L, Joannopoulos J D and Soljačić M 2014 Nat. Photon. 8 821 doi: 10.1038/nphoton.2014.248
[6]	Lu L, Joannopoulos J D and Soljačić M 2016 Nat. Phys. 12 626 doi: 10.1038/nphys3796
[7]	Ozawa T, Price H M, Amo A et al. 2019 Rev. Mod. Phys. 91 015006 doi: 10.1103/RevModPhys.91.015006
[8]	Goldman N, Budich J C and Zoller P 2016 Nat. Phys. 12 639 doi: 10.1038/nphys3803
[9]	Dauphin A and Goldman N 2013 Phys. Rev. Lett. 111 135302 doi: 10.1103/PhysRevLett.111.135302
[10]	Atala M, Aidelsburger M, Barreiro J T, Abanin D, Kitagawa T, Demler E and Bloch I 2013 Nat. Phys. 9 795 doi: 10.1038/nphys2790
[11]	Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D and Esslinger T 2014 Nature 515 237 doi: 10.1038/nature13915
[12]	Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro J T, Nascimbene S, Cooper N R, Bloch I and Goldman N 2015 Nat. Phys. 11 162 doi: 10.1038/nphys3171
[13]	Fläschner N, Rem B S, Tarnowski M, Vogel D, Lühmann D S, Sengstock K and Weitenberg C 2016 Science 352 1091 doi: 10.1126/science.aad4568
[14]	Mittal S, Ganeshan S, Fan J Y, Vaezi A and Hafezi M 2016 Nat. Photon. 10 180 doi: 10.1038/nphoton.2016.10
[15]	Aharonov Y, Davidovich L and Zagury N 1993 Phys. Rev. A 48 1687 doi: 10.1103/PhysRevA.48.1687
[16]	Kitagawa T, Rudner M S, Berg E and Demler E 2010 Phys. Rev. A 82 033429 doi: 10.1103/PhysRevA.82.033429
[17]	Kitagawa T 2012 Quantum Inf. Process. 11 1107 doi: 10.1007/s11128-012-0425-4
[18]	Karski M, Forster L, Choi J M, Steffen A, Alt W, Meschede D and Widera A 2009 Science 325 174 doi: 10.1126/science.1174436
[19]	Genske M, Alt W, Steffen A, Werner A H, Werner R F, Meschede D and Alberti A 2013 Phys. Rev. Lett. 110 190601 doi: 10.1103/PhysRevLett.110.190601
[20]	Schmitz H, Matjeschk R, Schneider C, Glueckert J, Enderlein M, Huber T and Schaetz T 2009 Phys. Rev. Lett. 103 090504 doi: 10.1103/PhysRevLett.103.090504
[21]	Zähringer F, Kirchmair G, Gerritsma R, Solano E, Blatt R and Roos C F 2010 Phys. Rev. Lett. 104 100503 doi: 10.1103/PhysRevLett.104.100503
[22]	Schreiber A, Cassemiro K N, Potoček V, Gábris A, Mosley P J, Andersson E, Jex I and Silberhorn C 2010 Phys. Rev. Lett. 104 050502 doi: 10.1103/PhysRevLett.104.050502
[23]	Broome M A, Fedrizzi A, Lanyon B P, Kassal I, Aspuru-Guzik A and White A G 2010 Phys. Rev. Lett. 104 153602 doi: 10.1103/PhysRevLett.104.153602
[24]	Ryan C A, Laforest M, Boileau J C and Laflamme R 2005 Phys. Rev. A 72 062317 doi: 10.1103/PhysRevA.72.062317
[25]	Asbóth J K 2012 Phys. Rev. B 86 195414 doi: 10.1103/PhysRevB.86.195414
[26]	Asbóth J K and Obuse H 2013 Phys. Rev. B 88 121406 doi: 10.1103/PhysRevB.88.121406
[27]	Tarasinski B, Asbóth J K and Dahlhaus J P 2014 Phys. Rev. A 89 042327 doi: 10.1103/PhysRevA.89.042327
[28]	Obuse H, Asbóth J K, Nishimura Y and Kawakami N 2015 Phys. Rev. B 92 045424 doi: 10.1103/PhysRevB.92.045424
[29]	Edge J M and Asbóth J K 2015 Phys. Rev. B 91 104202 doi: 10.1103/PhysRevB.91.104202
[30]	Asbóth J K 2015 Phys. Rev. A 91 022324 doi: 10.1103/PhysRevA.91.022324
[31]	Rakovszky T and Asbóth J K 2015 Phys. Rev. A 92 052311 doi: 10.1103/PhysRevA.92.052311
[32]	Groh T, Brakhane S, Alt W, Meschede D, Asbóth J K and Alberti A 2016 Phys. Rev. A 94 013620 doi: 10.1103/PhysRevA.94.013620
[33]	Mugel S, Celi A, Massignan P, Asbóth J K, Lewenstein M and Lobo C 2016 Phys. Rev. A 94 023631 doi: 10.1103/PhysRevA.94.023631
[34]	Rakovszky T, Asbóth J K and Alberti A 2017 Phys. Rev. B 95 201407 doi: 10.1103/PhysRevB.95.201407
[35]	Ramasesh V V, Flurin E, Rudner M, Siddiqi I and Yao N Y 2017 Phys. Rev. Lett. 118 13050
[36]	Sajid M, Asbóth J K, Meschede D, Werner R F and Alberti A 2019 Phys. Rev. B 99 214303 doi: 10.1103/PhysRevB.99.214303
[37]	Kitagawa T, Broome M A, Fedrizzi A, Rudner M S, Berg E, Kassal I, Aspuru-Guzik A, Demler E and White A G 2012 Nat. Commun. 3 882 doi: 10.1038/ncomms1872
[38]	Cardano F, Maffei M, Massa F, Piccirillo B, Lisio C D, Filippis G D, Cataudella V, Santamato E and Marrucci L 2016 Nat. Commun. 7 11439 doi: 10.1038/ncomms11439
[39]	Cardano F, D'Errico A, Dauphin A et al. 2017 Nat. Commun. 8 15516 doi: 10.1038/ncomms15516
[40]	Barkhofen S, Nitsche T, Elster F, Lorz L, Gábris A, Jex I and Silberhorn C 2017 Phys. Rev. A 96 033846 doi: 10.1103/PhysRevA.96.033846
[41]	Flurin E, Ramasesh V V, Hacohen-Gourgy S, Martin L S, Yao N Y and Siddiqi I 2017 Phys. Rev. X 7 031023
[42]	Xu Y X, Wang Q Q, Pan W W et al. 2018 Phys. Rev. Lett. 120 260501 doi: 10.1103/PhysRevLett.120.260501
[43]	Xiao L, Zhan X, Bian Z H et al. 2017 Nat. Phys. 13 1117 doi: 10.1038/nphys4204
[44]	Zhan X, Xiao L, Bian Z H, Wang K K, Qiu X Z, Sanders B C, Yi W and Xue P 2017 Phys. Rev. Lett. 119 130501 doi: 10.1103/PhysRevLett.119.130501
[45]	Xiao L, Qiu X Z, Wang K K, Bian Z H, Zhan X, Obuse H, Sanders B C, Yi W and Xue P 2018 Phys. Rev. A 98 063847 doi: 10.1103/PhysRevA.98.063847
[46]	Wang K K, Qiu X Z, Xiao L, Zhan X, Bian Z H, Sanders B C, Yi W and Xue P 2019 Nat. Commun. 10 2293 doi: 10.1038/s41467-019-10252-7
[47]	Wang K K, Qiu X Z, Xiao L, Zhan X, Bian Z H, Yi W and Xue P 2019 Phys. Rev. Lett. 122 020501 doi: 10.1103/PhysRevLett.122.020501
[48]	Xiao L, Wang K K, Zhan X, Bian Z H, Kawabata K, Ueda M, Yi W and Xue P 2019 Phys. Rev. Lett. 123 230401 doi: 10.1103/PhysRevLett.123.230401
[49]	Wang B, Chen T and Zhang X 2018 Phys. Rev. Lett. 121 100501 doi: 10.1103/PhysRevLett.121.100501
[50]	Chen C, Ding X, Qin J et al. 2018 Phys. Rev. Lett. 121 100502 doi: 10.1103/PhysRevLett.121.100502
[51]	Chalabi H, Barik S, Mittal S, Murphy T E, Hafezi M and Waks E 2019 Phys. Rev. Lett. 123 150503 doi: 10.1103/PhysRevLett.123.150503
[52]	Ge Z Y and Fan H 2018 arXiv:1804.06994v2[hep-ph] [quant-ph]
[53]	Xue P, Sanders B C and Leibfried D 2009 Phys. Rev. Lett. 103 183602 doi: 10.1103/PhysRevLett.103.183602
[54]	Leibfried D, Blatt R, Monroe C and Wineland D 2003 Rev. Mod. Phys. 75 281 doi: 10.1103/RevModPhys.75.281
[55]	Brownnutt M, Kumph M, Rabl P and Blatt R 2015 Rev. Mod. Phys. 87 1419 doi: 10.1103/RevModPhys.87.1419
[56]	Harlander M, Lechner R, Brownnutt M, Blatt R and Hänsel W 2011 Nature 471 200 doi: 10.1038/nature09800
[57]	Brown K R, Ospelkaus C, Colombe Y, Wilson A C, Leibfried D and Wineland D J 2011 Nature 471 196 doi: 10.1038/nature09721
[58]	Maslennikov G, Ding S, Hablützel R, Gan J, Roulet A, Nimmrichter S, Dai J, Scarani V and Matsukevich D 2019 Nat. Commun. 10 202 doi: 10.1038/s41467-018-08090-0
[59]	Xu Y Y, Zhou F, Chen L, Xie Y, Xue P and Feng M 2012 Chin. Phys. B 21 040304 doi: 10.1088/1674-1056/21/4/040304
[60]	Kim K, Chang M S, Korenblit S, Islam R, Edwards E E, Freericks J K, Lin G D, Duan L M and Monroe C 2010 Nature 465 590 doi: 10.1038/nature09071
[61]	Alberti A, Alt W, Werner R and Meschede D 2014 New J. Phys. 16 123052 doi: 10.1088/1367-2630/16/12/123052

Probe of topological invariants using quantum walks of a trapped ion in coherent state space

Probe of topological invariants using quantum walks of a trapped ion in coherent state space

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 61

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Tian Guo(郭天), Peiliang Liu(刘培亮), and Chaohong Lee(李朝红). New designed helical resonator to improve measurement accuracy of magic radio frequency[J]. 中国物理B, 2022, 31(9): 93201-093201.
[2]	Wentao Chen(陈文涛), Jaren Gan, Jing-Ning Zhang(张静宁), Dzmitry Matuskevich, and Kihwan Kim(金奇奂). Quantum computation and simulation with vibrational modes of trapped ions[J]. 中国物理B, 2021, 30(6): 60311-060311.
[3]	刘建森, 韩炎桢, 刘承师. A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect[J]. 中国物理B, 2020, 29(1): 10302-010302.
[4]	贺雨晴, 蒋毅, 张田田, 黄荷, 方辰, 金钟. SymTopo:An automatic tool for calculating topological properties of nonmagnetic crystalline materials[J]. 中国物理B, 2019, 28(8): 87102-087102.
[5]	张满超, 吴伟, 何林泽, 谢艺, 吴春旺, 黎全, 陈平形. Demonstration of quantum anti-Zeno effect with a single trapped ion[J]. 中国物理B, 2018, 27(9): 90305-090305.
[6]	王夏烘, 李平, 冉召, 罗卫东. Quantum spin Hall insulators in chemically functionalized As (110) and Sb (110) films[J]. 中国物理B, 2018, 27(8): 87305-087305.
[7]	郭西华, 徐天赋, 刘承师. Topologically protected edge gap solitons of interacting Bosons in one-dimensional superlattices[J]. 中国物理B, 2018, 27(6): 60307-060307.
[8]	张硕, 吴伟, 吴春旺, 李风光, 李坦, 汪翔, 鲍皖苏. Quantum feedback cooling of two trapped ions[J]. 中国物理B, 2017, 26(7): 74205-074205.
[9]	万吴兵, 吕红红, 候格, 吴晨旭. Static and dynamic properties of polymer brush with topological ring structures: Molecular dynamic simulation[J]. 中国物理B, 2016, 25(10): 106101-106101.
[10]	胡艳敏, 杨万里, 肖兴, 冯芒, 李朝红. Multi-ion Mach–Zehnder interferometer with artificial nonlinear interactions[J]. 中国物理B, 2014, 23(3): 34205-034205.
[11]	谢艺, 万威, 周飞, 陈亮, 李朝红, 冯芒. Linear ion trap imperfection and the compensation of excess micromotion[J]. 中国物理B, 2012, 21(6): 63201-063201.
[12]	郑小娟, 徐慧, 方卯发, 朱开成. Preparation of the four-qubit cluster states in cavity QED and the trapped-ion system[J]. 中国物理B, 2010, 19(3): 34207-034207.
[13]	黄彬, 林霞, 林慧, 蔡振华, 杨榕灿. Two-qutrit maximally entangled states prepared via adiabatic passage in ion-trapped system[J]. 中国物理B, 2010, 19(12): 124206-124206.
[14]	周飞, 谢艺, 徐酉阳, 黄学人, 冯芒. Measurement of the secular motion frequency and the space charge density in the linear ion trap[J]. 中国物理B, 2010, 19(11): 113206-113208.
[15]	郑小娟, 罗益民, 蔡建武. Quantum logic gates with two-level trapped ions beyond Lamb--Dicke limit[J]. 中国物理B, 2009, 18(4): 1352-1356.