Please wait a minute...
Chin. Phys. B, 2020, Vol. 29(1): 014209    DOI: 10.1088/1674-1056/ab5efe

Linear optical approach to supersymmetric dynamics

Yong-Tao Zhan(詹颙涛)1,2, Xiao-Ye Xu(许小冶)1,2, Qin-Qin Wang(王琴琴)1,2, Wei-Wei Pan(潘维韦)1,2, Munsif Jan1,2, Fu-Ming Chang(常弗鸣)1,2, Kai Sun(孙凯)1,2, Jin-Shi Xu(许金时)1,2, Yong-Jian Han(韩永建)1,2, Chuan-Feng Li(李传锋)1,2, Guang-Can Guo(郭光灿)1,2
1 CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China;
2 Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Abstract  The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose energy levels are degeneracy except one of the systems has an extra ground state possibly, and the eigenstates of the partner systems can be mapped onto each other. Recently, an interferometric scheme has been proposed to show this relationship in ultracold atoms[Phys. Rev. A 96 043624 (2017)]. Here this approach is generalized to linear optics for observing the supersymmetric dynamics with photons. The time evolution operator is simulated approximately via Suzuki-Trotter expansion with considering the realization of the kinetic and potential terms separately. The former is realized through the diffraction nature of light and the later is implemented using a phase plate. Additionally, we propose an interferometric approach which can be implemented perfectly using an amplitude alternator to realize the non-unitary operator. The numerical results show that our scheme is universal and can be realized with current technologies.
Keywords:  linear optics      supersymmetry      quantum simulation  
Received:  14 August 2019      Revised:  14 October 2019      Accepted manuscript online: 
PACS:  42.50.-p (Quantum optics)  
  03.67.-a (Quantum information)  
  11.30.Pb (Supersymmetry)  
Fund: Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0304100 and 2016YFA0302700), the National Natural Science Foundation of China (Grant Nos. 11474267, 61327901, 11774335, and 61322506), Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDY-SSW-SLH003), the Fundamental Research Funds for the Central Universities of China (Grant No. WK2470000026), the National Postdoctoral Program for Innovative Talents, China (Grant No.BX201600146), China Postdoctoral Science Foundation (Grant No. 2017M612073), and Anhui Initiative in Quantum Information Technologies, China (Grant No. AHY060300).
Corresponding Authors:  Xiao-Ye Xu, Yong-Jian Han, Chuan-Feng Li     E-mail:;;

Cite this article: 

Yong-Tao Zhan(詹颙涛), Xiao-Ye Xu(许小冶), Qin-Qin Wang(王琴琴), Wei-Wei Pan(潘维韦), Munsif Jan, Fu-Ming Chang(常弗鸣), Kai Sun(孙凯), Jin-Shi Xu(许金时), Yong-Jian Han(韩永建), Chuan-Feng Li(李传锋), Guang-Can Guo(郭光灿) Linear optical approach to supersymmetric dynamics 2020 Chin. Phys. B 29 014209

[1] Dine M 2016 Supersymmetry and string theory: Beyond the standard model (Cambridge: Cambridge University Press)
[2] Kane G L and Shifman M A 2001 The supersymmetric world: the beginnings of the theory (Singapore: World Scientific)
[3] Weinberg S 2005 The Quantum Theory of Fields: Volume 3, Supersymmetry (Cambridge: Cambridge University Press)
[4] Grodon K 2010 Perspectives On Supersymmetry II (Singapore: World Scientific)
[5] Nath P 2016 Supersymmetry, Supergravity, and Unification (Cambridge: Cambridge University Press)
[6] Binétruy P 2012 Supersymmetry: Theory, Experiment, and Cosmology (Oxford: OUP Oxford)
[7] Witten E 1981 Nucl. Phys. B 188 513
[8] Sukumar C V 1985 J. Phys. A: Math. Gen. 18 2917
[9] Cooper F, Khare A and Sukhatme U 1995 Phys. Rep. 251 267
[10] Gangopadhyaya A, Mallow J V and Rasinariu C 2011 Supersymmetric Quantum Mechanics: An Introduction (Singapore: World Scientific)
[11] Haber H E and Haskins L S 2018 Anticipating the Next Discoveries in Particle Physics (Singapore: World Scientific) pp. 355–499
[12] Ovchinnikov I V and Enßlin T A 2016 Phys. Rev. D 93 085023
[13] Efetov K 1999 Supersymmetry in disorder and chaos (Cambridge: Cambridge University Press)
[14] Miri M, Heinrich M, El-Ganainy R and Christodoulides D N 2013 Phys. Rev. Lett. 110 233902
[15] Miri M, Heinrich M and Christodoulides D N 2014 Optica 1 89
[16] Heinrich M, Miri M, Stützer S, El-Ganainy R, Nolte S, Szameit A and Christodoulides D N 2014 Nat. Commun. 5 3698
[17] Lahrz M, Weitenberg C and Mathey L 2017 Phys. Rev. A 96 043624
[18] Aspuru-Guzik A and Walther P 2012 Nat. Phys. 8 285
[19] Georgescu I M, Ashhab S and Nori F 2014 Rev. Mod. Phys. 86 153
[20] Makri N and Miller W H 1989 J. Chem. Phys. 90 904
[21] Zagury N, Aragão A, Casanova J and Solano E 2010 Phys. Rev. A 82 042110
[22] Argeri M, Di Vita S, Mastrolia P, Mirabella E, Schlenk J, Schubert U and Tancredi L 2010 J. High Energy Phys. 2014 82
[23] Suzuki M 1976 Comm. Math. Phys. 51 183
[24] Dhand I and Sanders B C 2014 J. Phys. A: Math. Gen. 47 265206
[25] Sakurai J J and Napolitano J 2011 Modern quantum mechanics (2nd Edn.) (Boston: Addison-Wesley)
[26] Goodman J W 2017 Introduction to Fourier optics (4nd Edn.) (New York: W. H. Freeman, Macmillan Learning)
[27] Tyson R K 2015 Principles of Adaptive Optics (4nd Edn.) (New York: CRC Press)
[28] Lundeen J S, Sutherland B, Patel A, Stewart C and Bamber C 2011 Nature 474 188
[1] Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture
Lei Chen(陈磊), Pan Li(李磐), He-Shan Liu(刘河山), Jin Yu(余锦), Chang-Jun Ke(柯常军), and Zi-Ren Luo(罗子人). Chin. Phys. B, 2023, 32(2): 024213.
[2] Variational quantum simulation of thermal statistical states on a superconducting quantum processer
Xue-Yi Guo(郭学仪), Shang-Shu Li(李尚书), Xiao Xiao(效骁), Zhong-Cheng Xiang(相忠诚), Zi-Yong Ge(葛自勇), He-Kang Li(李贺康), Peng-Tao Song(宋鹏涛), Yi Peng(彭益), Zhan Wang(王战), Kai Xu(许凯), Pan Zhang(张潘), Lei Wang(王磊), Dong-Ning Zheng(郑东宁), and Heng Fan(范桁). Chin. Phys. B, 2023, 32(1): 010307.
[3] Scanning the optical characteristics of lead-free cesium titanium bromide double perovskite nanocrystals
Chenxi Yu(于晨曦), Long Gao(高龙), Wentong Li(李文彤), Qian Wang(王倩), Meng Wang(王萌), and Jiaqi Zhang(张佳旗). Chin. Phys. B, 2022, 31(5): 054218.
[4] Noncollinear phase-matching geometries in ultra-broadband quasi-parametric amplification
Ji Wang(王佶), Yanqing Zheng(郑燕青), and Yunlin Chen(陈云琳). Chin. Phys. B, 2022, 31(5): 054213.
[5] Measuring Loschmidt echo via Floquet engineering in superconducting circuits
Shou-Kuan Zhao(赵寿宽), Zi-Yong Ge(葛自勇), Zhong-Cheng Xiang(相忠诚), Guang-Ming Xue(薛光明), Hai-Sheng Yan(严海生), Zi-Ting Wang(王子婷), Zhan Wang(王战), Hui-Kai Xu(徐晖凯), Fei-Fan Su(宿非凡), Zhao-Hua Yang(杨钊华), He Zhang(张贺), Yu-Ran Zhang(张煜然), Xue-Yi Guo(郭学仪), Kai Xu(许凯), Ye Tian(田野), Hai-Feng Yu(于海峰), Dong-Ning Zheng(郑东宁), Heng Fan(范桁), and Shi-Ping Zhao(赵士平). Chin. Phys. B, 2022, 31(3): 030307.
[6] Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics
Zi-Yong Ge(葛自勇), Rui-Zhen Huang(黄瑞珍), Zi-Yang Meng(孟子杨), and Heng Fan(范桁). Chin. Phys. B, 2022, 31(2): 020304.
[7] High-order harmonic generations in tilted Weyl semimetals
Zi-Yuan Li(李子元), Qi Li(李骐), and Zhou Li(李舟). Chin. Phys. B, 2022, 31(12): 124204.
[8] Quantum simulation and quantum computation of noisy-intermediate scale
Kai Xu(许凯), and Heng Fan(范桁). Chin. Phys. B, 2022, 31(10): 100304.
[9] Up-conversion detection of mid-infrared light carrying orbital angular momentum
Zheng Ge(葛正), Chen Yang(杨琛), Yin-Hai Li(李银海), Yan Li(李岩), Shi-Kai Liu(刘世凯), Su-Jian Niu(牛素俭), Zhi-Yuan Zhou(周志远), and Bao-Sen Shi(史保森). Chin. Phys. B, 2022, 31(10): 104210.
[10] Quantum simulation of τ-anti-pseudo-Hermitian two-level systems
Chao Zheng(郑超). Chin. Phys. B, 2022, 31(10): 100301.
[11] Bandwidth-tunable silicon nitride microring resonators
Jiacheng Liu(刘嘉成), Chao Wu(吴超), Gongyu Xia(夏功榆), Qilin Zheng(郑骑林), Zhihong Zhu(朱志宏), and Ping Xu(徐平). Chin. Phys. B, 2022, 31(1): 014201.
[12] A low-threshold multiwavelength Brillouin fiber laser with double-frequency spacing based on a small-core fiber
Lu-Lu Xu(徐路路), Ying-Ying Wang(王莹莹), Li Jiang(江丽), Pei-Long Yang(杨佩龙), Lei Zhang(张磊), and Shi-Xun Dai(戴世勋). Chin. Phys. B, 2021, 30(8): 084210.
[13] Quantum computation and simulation with superconducting qubits
Kaiyong He(何楷泳), Xiao Geng(耿霄), Rutian Huang(黄汝田), Jianshe Liu(刘建设), and Wei Chen(陈炜). Chin. Phys. B, 2021, 30(8): 080304.
[14] Third-order nonlinear optical properties of graphene composites: A review
Meng Shang(尚萌), Pei-Ling Li(李培玲), Yu-Hua Wang(王玉华), and Jing-Wei Luo(罗经纬). Chin. Phys. B, 2021, 30(8): 080703.
[15] Low-threshold bistable reflection assisted by oscillating wave interaction with Kerr nonlinear medium
Yingcong Zhang(张颖聪), Wenjuan Cai(蔡文娟), Xianping Wang(王贤平), Wen Yuan(袁文), Cheng Yin(殷澄), Jun Li(李俊), Haimei Luo(罗海梅), and Minghuang Sang(桑明煌). Chin. Phys. B, 2021, 30(8): 084203.
No Suggested Reading articles found!