Research progress of integrated photonic quantum simulation

Chen Yang; Zhang Tian-Yang; Guo Guang-Can; Ren Xi-Feng

doi:10.7498/aps.71.20221938

Abstract

Quantum simulation is to use a controllable quantum system to simulate other complicated or hard-to-control quantum system, and to deal with some complex unknown quantum systems that cannot be simulated on classical computers due to the exponential explosion of the Hilbert space. Among different kinds of physical realizations of quantum simulation, integrated optical systems have emerged as an appropriate platform in recent years due to the advantages of flexible control, weak decoherence, and no interaction in optical systems. In this review, we attempt to introduce some of the basic models used for quantum simulation in integrated photonic systems. This review article is organized as follows. In Section 2, we introduce the commonly used material platforms for integrated quantum simulation, including the silicon-based, lithium niobate-based integrated circuits, and the femtosecond laser direct writing optical waveguides. Several integrated optical platforms such as the coupled waveguide arrays, photonic crystals, coupled resonator arrays, and multiport interferometers are also introduced. In Section 3, we focus on the analog quantum simulations in the integrated photonic platform, including Anderson localization of light in disordered systems, various kinds of topological insulators, nonlinear and non-Hermitian systems. More specifically, in Subsection 3.1, we present the integrated photonic realizations of disordered and quasi-periodic systems. In Subsection 3.2, we review the integrated photonic realizations of the topological insulators with and without time-reversal symmetry, including Floquet topological insulators, quantum spin hall system, anomalous quantum hall system, valley hall system, Su-Schrieffer-Heeger (SSH) model, and photonic topological Anderson insulators. Besides, topological insulator lasers and topologically protected quantum photon sources are briefly reviewed. In Subsection 3.3, we review the nonlinear and non-Hermitian integrated optical systems. In Section 4 we present the integrated digital quantum simulations based on the multiport interferometers, including the discrete-time quantum random walk, Boson sampling, and molecular simulation. In Section 5, we summarize the content of the article and present the outlook on the future perspectives of the integrated photonic quantum simulation. We believe that the integrated photonic platforms will continue to provide an excellent platform for quantum simulation. More practical applications will be found based on this system through combining the fields of topological photonics, laser technologies, quantum information, nonlinear and non-Hermitian physics.

Keywords:

quantum simulation /
integrated photonic circuits /
simulation of condensed matter physics /
multiport interferometer

Authors and contacts

CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Ren Xi-Feng, renxf@ustc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62061160487, 12204462), the China Postdoctoral Science Foundation (Grant No. 2022M723061), and the Fundamental Research Funds for the Central Universities, China.

FullText HTML : translate this paragraph

References

[1]	Feynman R P 1982 Int. J. Theor. Phys. 21 467 Google Scholar
[2]	Georgescu I M, Ashhab S, Nori F 2014 Rev. Modern Phys. 86 153 Google Scholar
[3]	Monroe C, Campbell W C, Duan L M, Gong Z X, Gorshkov A V, Hess P W, Islam R, Kim K, Linke N M, Pagano G, Richerme P, Senko C, Yao N Y 2021 Rev. Modern Phys. 93 025001 Google Scholar
[4]	Houck A A, Tureci H E, Koch J 2012 Nat. Phys. 8 292 Google Scholar
[5]	Schäfer F, Fukuhara T, Sugawa S, Takasu Y, Takahashi Y 2020 Nat. Rev. Phys. 2 411 Google Scholar
[6]	Wang J W, Sciarrino F, Laing A, Thompson M G 2020 Nat. Photonics 14 273 Google Scholar
[7]	Elshaari A W, Pernice W, Srinivasan K, Benson O, Zwiller V 2020 Nat. Photonics 14 285 Google Scholar
[8]	Politi A, Matthews J C F, Thompson M G, O'Brien J L 2009 IEEE J. Quantum Electron. 15 1673 Google Scholar
[9]	Feng L, Zhang M, Wang J, Zhou X, Qiang X, Guo G, Ren X 2022 Photonics Res. 10 A135 Google Scholar
[10]	Tang H, Lin X F, Feng Z, Chen J Y, Gao J, Sun K, Wang C Y, Lai P C, Xu X Y, Wang Y, Qiao L F, Yang A L, Jin X M 2018 Sci. Adv. 4 eaat3174 Google Scholar
[11]	Perets H B, Lahini Y, Pozzi F, Sorel M, Morandotti R, Silberberg Y 2008 Phys. Rev. Lett. 100 170506 Google Scholar
[12]	Sansoni L, Sciarrino F, Vallone G, Mataloni P, Crespi A, Ramponi R, Osellame R 2012 Phys. Rev. Lett. 108 010502 Google Scholar
[13]	Peruzzo A, Lobino M, Matthews J C, Matsuda N, Politi A, Poulios K, Zhou X Q, Lahini Y, Ismail N, Worhoff K, Bromberg Y, Silberberg Y, Thompson M G, Obrien J L 2010 Science 329 1500 Google Scholar
[14]	Crespi A, Osellame R, Ramponi R, Giovannetti V, Fazio R, Sansoni L, De Nicola F, Sciarrino F, Mataloni P 2013 Nat. Photonics 7 322 Google Scholar
[15]	Spring J B, Metcalf B J, Humphreys P C, Kolthammer W S, Jin X M, Barbieri M, Datta A, Thomas-Peter N, Langford N K, Kundys D, Gates J C, Smith B J, Smith P G, Walmsley I A 2013 Science 339 798 Google Scholar
[16]	Crespi A, Osellame R, Ramponi R, Brod D J, Galvao E F, Spagnolo N, Vitelli C, Maiorino E, Mataloni P, Sciarrino F 2013 Nat. Photonics 7 545 Google Scholar
[17]	Tillmann M, Dakic B, Heilmann R, Nolte S, Szameit A, Walther P 2013 Nat. Photonics 7 540 Google Scholar
[18]	Spagnolo N, Vitelli C, Bentivegna M, Brod D J, Crespi A, Flamini F, Giacomini S, Milani G, Ramponi R, Mataloni P, Osellame R, Galvao E F, Sciarrino F 2014 Nat. Photonics 8 615 Google Scholar
[19]	Wang H, Qin J, Ding X, Chen M C, Chen S, You X, He Y M, Jiang X, You L, Wang Z, Schneider C, Renema J J, Hofling S, Lu C Y, Pan J W 2019 Phys. Rev. Lett. 123 250503 Google Scholar
[20]	Hoch F, Piacentini S, Giordani T, Tian Z N, Iuliano M, Esposito C, Camillini A, Carvacho G, Ceccarelli F, Spagnolo N 2021 arXiv: 2106.08260
[21]	Mukherjee S, Rechtsman M C 2020 Science 368 856 Google Scholar
[22]	Xia S, Kaltsas D, Song D, Komis I, Xu J, Szameit A, Buljan H, Makris K G, Chen Z 2021 Science 372 72 Google Scholar
[23]	Ozawa T, Price H M, Amo A, Goldman N, Hafezi M, Lu L, Rechtsman M C, Schuster D, Simon J, Zilberberg O 2019 Rev. Modern Phys. 91 015006 Google Scholar
[24]	Lu L, Joannopoulos J D, Soljacic M 2016 Nat. Phys. 12 626 Google Scholar
[25]	Rechtsman M C, Zeuner J M, Plotnik Y, Lumer Y, Podolsky D, Dreisow F, Nolte S, Segev M, Szameit A 2013 Nature 496 196 Google Scholar
[26]	Maczewsky L J, Heinrich M, Kremer M, Ivanov S K, Ehrhardt M, Martinez F, Kartashov Y V, Konotop V V, Torner L, Bauer D, Szameit A 2020 Science 370 701 Google Scholar
[27]	Sparrow C, Martin-Lopez E, Maraviglia N, Neville A, Harrold C, Carolan J, Joglekar Y N, Hashimoto T, Matsuda N, O'Brien J L, Tew D P, Laing A 2018 Nature 557 660 Google Scholar
[28]	McArdle S, Endo S, Aspuru-Guzik A, Benjamin S, Yuan X 2020 Rev. Modern Phys. 92 015003 Google Scholar
[29]	Cao Y, Romero J, Olson J P, Degroote M, Johnson P D, Kieferova M, Kivlichan I D, Menke T, Peropadre B, Sawaya N P D, Sim S, Veis L, Aspuru-Guzik A 2019 Chem. Rev. 119 10856 Google Scholar
[30]	Bogdanov S, Shalaginov M Y, Boltasseva A, Shalaev V M 2017 Opt. Mater. Express 7 111 Google Scholar
[31]	Corrielli G, Crespi A, Osellame R 2021 Nanophotonics 10 3789 Google Scholar
[32]	Ramakrishnan R K, Ravichandran A B, Mishra A, Kaushalram A, Hegde G, Talabattula S, Rohde P P 2022 arXiv: 2206.15383
[33]	Feng L T, Guo G C, Ren X F 2020 Adv. Quantum Technol. 3 1900058 Google Scholar
[34]	Feng L T, Zhang M, Xiong X, Chen Y, Wu H, Li M, Guo G P, Guo G C, Dai D X, Ren X F 2019 NPJ Quantum Inf. 5 2 Google Scholar
[35]	Feng L T, Zhang M, Zhou Z Y, Chen Y, Li M, Dai D X, Ren H L, Guo G P, Guo G C, Tame M, Ren X F 2019 NPJ Quantum Inf. 5 90 Google Scholar
[36]	Wang Y, Lu Y H, Mei F, Gao J, Li Z M, Tang H, Zhu S L, Jia S, Jin X M 2019 Phys. Rev. Lett. 122 193903 Google Scholar
[37]	Xie B Y, Su G X, Wang H F, Su H, Shen X P, Zhan P, Lu M H, Wang Z L, Chen Y F 2019 Phys. Rev. Lett. 122 233903 Google Scholar
[38]	Zhang M, Feng L T, Zhou Z Y, Chen Y, Wu H, Li M, Gao S M, Guo G P, Guo G C, Dai D X, Ren X F 2019 Light Sci. Appl. 8 41 Google Scholar
[39]	Engin E, Bonneau D, Natarajan C M, Clark A S, Tanner M G, Hadfield R H, Dorenbos S N, Zwiller V, Ohira K, Suzuki N, Yoshida H, Iizuka N, Ezaki M, O'Brien J L, Thompson M G 2013 Opt. Express 21 27826 Google Scholar
[40]	Lu X Y, Li Q, Westly D A, Moille G, Singh A, Anant V, Srinivasan K 2019 Nat. Phys. 15 373 Google Scholar
[41]	Xu B Y, Chen L K, Lin J T, Feng L T, Niu R, Zhou Z Y, Gao R H, Dong C H, Guo G C, Gong Q H, Cheng Y, Xiao Y F, Ren X F 2022 Sci. China Phys. Mech. 65 294262 Google Scholar
[42]	Jin H, Liu F M, Xu P, Xia J L, Zhong M L, Yuan Y, Zhou J W, Gong Y X, Wang W, Zhu S N 2014 Phys. Rev. Lett. 113 103601 Google Scholar
[43]	Guo X, Zou C L, Schuck C, Jung H, Cheng R, Tang H X 2017 Light Sci. Appl. 6 e16249 Google Scholar
[44]	Lahini Y, Avidan A, Pozzi F, Sorel M, Morandotti R, Christodoulides D N, Silberberg Y 2008 Phys. Rev. Lett. 100 013906 Google Scholar
[45]	Hafezi M, Mittal S, Fan J, Migdall A, Taylor J M 2013 Nat. Photonics 7 1001 Google Scholar
[46]	Longhi S 2009 Laser Photonics Rev. 3 243 Google Scholar
[47]	Chen Y, Chen X M, Ren X F, Gong M, Guo G C 2021 Phys. Rev. A 104 023501 Google Scholar
[48]	Christodoulides D N, Lederer F, Silberberg Y 2003 Nature 424 817 Google Scholar
[49]	Jones A L 1965 JOSA 55 261 Google Scholar
[50]	Somekh S, Garmire E, Yariv A, Garvin H L, Hunsperger R G 1973 Appl. Phys. Lett. 22 46 Google Scholar
[51]	Jamois C, Wehrspohn R, Andreani L, Hermann C, Hess O, Gösele U 2003 Photonic. Nanostruct. Appl. 1 1 Google Scholar
[52]	Tanaka Y, Nakamura H, Sugimoto Y, Ikeda N, Asakawa K, Inoue K 2005 IEEE J. Quantum Electron. 41 76 Google Scholar
[53]	Johnson S G, Villeneuve P R, Fan S H, Joannopoulos J D 2000 Phys. Rev. B 62 8212
[54]	He L, Addison Z, Mele E J, Zhen B 2020 Nat. Commun. 11 3119 Google Scholar
[55]	Xie B, Su G, Wang H F, Liu F, Hu L, Yu S Y, Zhan P, Lu M H, Wang Z, Chen Y F 2020 Nat. Commun. 11 3768 Google Scholar
[56]	Jin M C, Gao Y F, Ma Q L, Zhang W, Song H, Sun J P 2021 Phys. Rev. Mater. 5 024204 Google Scholar
[57]	Chen Y, He X T, Cheng Y J, Qiu H Y, Feng L T, Zhang M, Dai D X, Guo G C, Dong J W, Ren X F 2021 Phys. Rev. Lett. 126 230503 Google Scholar
[58]	Yariv A, Xu Y, Lee R K, Scherer A 1999 Opt. Lett. 24 711 Google Scholar
[59]	Hafezi M, Demler E A, Lukin M D, Taylor J M 2011 Nat. Phys. 7 907 Google Scholar
[60]	Liang G Q, Chong Y D 2013 Phys. Rev. Lett. 110 203904 Google Scholar
[61]	Pasek M, Chong Y D 2014 Phys. Rev. B 89 075113 Google Scholar
[62]	Afzal S, Zimmerling T J, Ren Y, Perron D, Van V 2020 Phys. Rev. Lett. 124 253601 Google Scholar
[63]	Leykam D, Mittal S, Hafezi M, Chong Y D 2018 Phys. Rev. Lett. 121 023901 Google Scholar
[64]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 Google Scholar
[65]	Mittal S, Orre V V, Leykam D, Chong Y D, Hafezi M 2019 Phys. Rev. Lett. 123 043201 Google Scholar
[66]	Reck M, Zeilinger A, Bernstein H J, Bertani P 1994 Phys. Rev. Lett. 73 58 Google Scholar
[67]	Clements W R, Humphreys P C, Metcalf B J, Kolthammer W S, Walmsley I A 2016 Optica 3 1460 Google Scholar
[68]	Harris N C, Bunandar D, Pant M, Steinbrecher G R, Mower J, Prabhu M, Baehr-Jones T, Hochberg M, Englund D 2016 Nanophotonics 5 456 Google Scholar
[69]	Yu S, Qiu C W, Chong Y, Torquato S, Park N 2021 Nat. Rev. Mater. 6 226 Google Scholar
[70]	Lagendijk A, van Tiggelen B, Wiersma D S 2009 Phys. Today 62 24
[71]	Segev M, Silberberg Y, Christodoulides D N 2013 Nat. Photonics 7 197 Google Scholar
[72]	Rothammer M, Zollfrank C, Busch K, von Freymann G 2021 Adv. Opt. Mater. 9 2100787 Google Scholar
[73]	Anderson P W 1958 Phys. Rev. 109 1492 Google Scholar
[74]	Mott N 1967 Adv. Phys. 16 49 Google Scholar
[75]	De Raedt H, Lagendijk A, de Vries P 1989 Phys. Rev. Lett. 62 47 Google Scholar
[76]	Schwartz T, Bartal G, Fishman S, Segev M 2007 Nature 446 52 Google Scholar
[77]	Eisenberg H S, Silberberg Y, Morandotti R, Boyd A R, Aitchison J S 1998 Phys. Rev. Lett. 81 3383 Google Scholar
[78]	Martin L, Di Giuseppe G, Perez-Leija A, Keil R, Dreisow F, Heinrich M, Nolte S, Szameit A, Abouraddy A F, Christodoulides D N, Saleh B E 2011 Opt. Express 19 13636 Google Scholar
[79]	Geraldi A, Laneve A, Bonavena L D, Sansoni L, Ferraz J, Fratalocchi A, Sciarrino F, Cuevas Á, Mataloni P 2019 Phys. Rev. Lett. 123 140501 Google Scholar
[80]	Levi L, Krivolapov Y, Fishman S, Segev M 2012 Nat. Phys. 8 912 Google Scholar
[81]	Vasco J P, Hughes S 2018 Acs Photonics 5 1262 Google Scholar
[82]	Hsieh P, Chung C, McMillan J F, Tsai M, Lu M, Panoiu N C, Wong C W 2015 Nat. Phys. 11 268 Google Scholar
[83]	Ni X, Chen K, Weiner M, Apigo D J, Prodan C, Alu A, Prodan E, Khanikaev A B 2019 Commun. Phys. 2 55 Google Scholar
[84]	Kraus Y E, Zilberberg O 2012 Phys. Rev. Lett. 109 116404 Google Scholar
[85]	Verbin M, Zilberberg O, Kraus Y E, Lahini Y, Silberberg Y 2013 Phys. Rev. Lett. 110 076403 Google Scholar
[86]	Lahini Y, Pugatch R, Pozzi F, Sorel M, Morandotti R, Davidson N, Silberberg Y 2009 Phys. Rev. Lett. 103 013901 Google Scholar
[87]	Kraus Y E, Lahini Y, Ringel Z, Verbin M, Zilberberg O 2012 Phys. Rev. Lett. 109 106402 Google Scholar
[88]	Levi L, Rechtsman M, Freedman B, Schwartz T, Manela O, Segev M 2011 Science 332 1541 Google Scholar
[89]	Mukherjee S, Di Liberto M, Ohberg P, Thomson R R, Goldman N 2018 Phys. Rev. Lett. 121 075502 Google Scholar
[90]	Bandres M A, Wittek S, Harari G, Parto M, Ren J, Segev M, Christodoulides D N, Khajavikhan M 2018 Science 359 eaar4005 Google Scholar
[91]	Dai T X, Ao Y T, Bao J M, Mao J, Chi Y L, Fu Z R, You Y L, Chen X J, Zhai C H, Tang B, Yang Y, Li Z H, Yuan L Q, Gao F, Lino X, Thompson M G, O'Brien J L, Li Y, Hu X Y, Gong Q H, Wang J W 2022 Nat. Photonics 16 248 Google Scholar
[92]	Stutzer S, Plotnik Y, Lumer Y, Titum P, Lindner N H, Segev M, Rechtsman M C, Szameit A 2018 Nature 560 461 Google Scholar
[93]	Blanco-Redondo A, Bell B, Oren D, Eggleton B J, Segev M 2018 Science 362 568 Google Scholar
[94]	Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C, Szameit A 2017 Nat. Mater. 16 433 Google Scholar
[95]	Hasan M Z, Kane C L 2010 Rev. Modern Phys. 82 3045 Google Scholar
[96]	Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[97]	Haldane F D, Raghu S 2008 Phys. Rev. Lett. 100 013904 Google Scholar
[98]	Wang Z, Chong Y, Joannopoulos J D, Soljacic M 2009 Nature 461 772 Google Scholar
[99]	Longhi S 2014 Opt. Lett. 39 5892 Google Scholar
[100]	Keil R, Poli C, Heinrich M, Arkinstall J, Weihs G, Schomerus H, Szameit A 2016 Phys. Rev. Lett. 116 213901 Google Scholar
[101]	Kremer M, Petrides I, Meyer E, Heinrich M, Zilberberg O, Szameit A 2020 Nat. Commun. 11 907 Google Scholar
[102]	Mittal S, Goldschmidt E A, Hafezi M 2018 Nature 561 502 Google Scholar
[103]	Mittal S, Orre V V, Goldschmidt E A, Hafezi M 2021 Nat. Photonics 15 542 Google Scholar
[104]	Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809 Google Scholar
[105]	Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233 Google Scholar
[106]	Noh J, Huang S, Chen K P, Rechtsman M C 2018 Phys. Rev. Lett. 120 063902 Google Scholar
[107]	He X T, Liang E T, Yuan J J, Qiu H Y, Chen X D, Zhao F L, Dong J W 2019 Nat. Commun. 10 872 Google Scholar
[108]	Shalaev M I, Walasik W, Tsukernik A, Xu Y, Litchinitser N M 2019 Nat. Nanotechnol. 14 31 Google Scholar
[109]	Barik S, Karasahin A, Flower C, Cai T, Miyake H, DeGottardi W, Hafezi M, Waks E 2018 Science 359 666 Google Scholar
[110]	Zeng Y, Chattopadhyay U, Zhu B, Qiang B, Li J, Jin Y, Li L, Davies A G, Linfield E H, Zhang B, Chong Y, Wang Q J 2020 Nature 578 246 Google Scholar
[111]	Shen S Q 2012 Topological Insulators (Vol. 174) (Berlin, Heidelberg: Springer)
[112]	Malkova N, Hromada I, Wang X, Bryant G, Chen Z 2009 Opt. Lett. 34 1633 Google Scholar
[113]	Blanco-Redondo A, Andonegui I, Collins M J, Harari G, Lumer Y, Rechtsman M C, Eggleton B J, Segev M 2016 Phys. Rev. Lett. 116 163901 Google Scholar
[114]	Wang Y, Pang X L, Lu Y H, Gao J, Chang Y J, Qiao L F, Jiao Z Q, Tang H, Jin X M 2019 Optica 6 955 Google Scholar
[115]	Chen X D, Deng W M, Shi F L, Zhao F L, Chen M, Dong J W 2019 Phys. Rev. Lett. 122 233902 Google Scholar
[116]	Wang Y, Ke Y, Chang Y J, Lu Y H, Gao J, Lee C, Jin X M 2021 Phys. Rev. B 104 224303 Google Scholar
[117]	El Hassan A, Kunst F K, Moritz A, Andler G, Bergholtz E J, Bourennane M 2019 Nat. Photonics 13 697 Google Scholar
[118]	Parto M, Wittek S, Hodaei H, Harari G, Bandres M A, Ren J, Rechtsman M C, Segev M, Christodoulides D N, Khajavikhan M 2018 Phys. Rev. Lett. 120 113901 Google Scholar
[119]	St-Jean P, Goblot V, Galopin E, Lemaitre A, Ozawa T, Le Gratiet L, Sagnes I, Bloch J, Amo A 2017 Nat. Photonics 11 651 Google Scholar
[120]	Lustig E, Weimann S, Plotnik Y, Lumer Y, Bandres M A, Szameit A, Segev M 2019 Nature 567 356 Google Scholar
[121]	Zilberberg O, Huang S, Guglielmon J, Wang M H, Chen K P, Kraus Y E, Rechtsman M C 2018 Nature 553 59 Google Scholar
[122]	Jurgensen M, Mukherjee S, Rechtsman M C 2021 Nature 596 63 Google Scholar
[123]	Cerjan A, Wang M, Huang S, Chen K P, Rechtsman M C 2020 Light Sci. Appl. 9 178 Google Scholar
[124]	Christodoulides D N, Joseph R I 1988 Opt. Lett. 13 794 Google Scholar
[125]	Fleischer J W, Segev M, Efremidis N K, Christodoulides D N 2003 Nature 422 147 Google Scholar
[126]	Lederer F L, Stegeman G I, Christodoulides D N, Assanto G, Segev M, Silberberg Y R 2008 Phys. Rep. 463 1 Google Scholar
[127]	Smirnova D, Leykam D, Chong Y D, Kivshar Y 2020 Appl. Phys. Rev. 7 021306 Google Scholar
[128]	Dobrykh D A, Yulin A V, Slobozhanyuk A P, Poddubny A N, Kivshar Y S 2018 Phys. Rev. Lett. 121 163901 Google Scholar
[129]	Bergholtz E J, Budich J C, Kunst F K 2021 Rev. Modern Phys. 93 015005 Google Scholar
[130]	Okuma N, Kawabata K, Shiozaki K, Sato M 2020 Phys. Rev. Lett. 124 086801 Google Scholar
[131]	Weidemann S, Kremer M, Helbig T, Hofmann T, Stegmaier A, Greiter M, Thomale R, Szameit A 2020 Science 368 311 Google Scholar
[132]	Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192 Google Scholar
[133]	El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S, Christodoulides D N 2018 Nat. Phys. 14 11 Google Scholar
[134]	Pitsios I, Banchi L, Rab A S, Bentivegna M, Caprara D, Crespi A, Spagnolo N, Bose S, Mataloni P, Osellame R, Sciarrino F 2017 Nat. Commun. 8 1569 Google Scholar
[135]	Wu Y L, Bao W S, Cao S R, Chen F S, Chen M C, Chen X W, Chung T H, Deng H, Du Y J, Fan D J, Gong M, Guo C, Guo C, Guo S J, Han L C, Hong L Y, Huang H L, Huo Y H, Li L P, Li N, Li S W, Li Y, Liang F T, Lin C, Lin J, Qian H R, Qiao D, Rong H, Su H, Sun L H, Wang L Y, Wang S Y, Wu D C, Xu Y, Yan K, Yang W F, Yang Y, Ye Y S, Yin J H, Ying C, Yu J L, Zha C, Zhang C, Zhang H B, Zhang K L, Zhang Y M, Zhao H, Zhao Y W, Zhou L, Zhu Q L, Lu C Y, Peng C Z, Zhu X B, Pan J W 2021 Phys. Rev. Lett. 127 180501 Google Scholar
[136]	Zhong H S, Wang H, Deng Y H, Chen M C, Peng L C, Luo Y H, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y X, Jiang X, Gan L, Yang G W, You L X, Wang Z, Li L, Liu N L, Lu C Y, Pan J W 2020 Science 370 1460 Google Scholar
[137]	Zhu Q L, Cao S R, Chen F S, Chen M C, Chen X W, Chung T H, Deng H, Du Y J, Fan D J, Gong M, Guo C, Guo C, Guo S J, Han L C, Hong L Y, Huang H L, Huo Y H, Li L P, Li N, Li S W, Li Y, Liang F T, Lin C, Lin J, Qian H R, Qiao D, Rong H, Su H, Sun L H, Wang L Y, Wang S Y, Wu D C, Wu Y L, Xu Y, Yan K, Yang W F, Yang Y, Ye Y, Yin J H, Ying C, Yu J L, Zha C, Zhang C, Zhang H B, Zhang K L, Zhang Y M, Zhao H, Zhao Y W, Zhou L, Lu C Y, Peng C Z, Zhu X B, Pan J W 2022 Sci. Bull. 67 240 Google Scholar
[138]	Paesani S, Gentile A A, Santagati R, Wang J, Wiebe N, Tew D P, O'Brien J L, Thompson M G 2017 Phys. Rev. Lett. 118 100503 Google Scholar
[139]	黎颖, 韩泽尧, 黎超健, 吕劲, 袁骁, 吴步娇 2021 70 210201 Google Scholar Li Y, Han Z Y, Li J C, Lv J, Yuan X, Wu B J 2021 Acta Phys. Sin. 70 210201 Google Scholar
[140]	Peruzzo A, McClean J, Shadbolt P, Yung M H, Zhou X Q, Love P J, Aspuru-Guzik A, O'Brien J L 2014 Nat. Commun. 5 4213 Google Scholar
[141]	Nielsen M A, Chuang I 2002 Quantum Computation and Quantum Information (American Association of Physics Teachers)
[142]	Wiebe N, Granade C 2016 Phys. Rev. Lett. 117 010503 Google Scholar
[143]	Zhao Y, Chen Y, Hou Z S, Han B, Fan H, Lin L H, Ren X F, Sun H B 2022 Opt. Lett. 47 617 Google Scholar
[144]	Xu Y L, Fegadolli W S, Gan L, Lu M H, Liu X P, Li Z Y, Scherer A, Chen Y F 2016 Nat. Commun. 7 11319 Google Scholar
[145]	Longhi S 2008 Phys. Rev. Lett. 101 193902 Google Scholar
[146]	Crespi A, Pepe F V, Facchi P, Sciarrino F, Mataloni P, Nakazato H, Pascazio S, Osellame R 2019 Phys. Rev. Lett. 122 130401 Google Scholar
[147]	Xu X Y, Wang X W, Chen D Y, Smith C M 2021 Nat. Photonics 15 703 Google Scholar
[148]	Tang H, Di Franco C, Shi Z Y, He T S, Feng Z, Gao J, Sun K, Li Z M, Jiao Z Q, Wang T Y, Kim M S, Jin X M 2018 Nat. Photonics 12 754 Google Scholar
[149]	Kim M, Jacob Z, Rho J 2020 Light Sci. Appl. 9 130 Google Scholar
[150]	Zhang X L, Yu F, Chen Z G, Tian Z N, Chen Q D, Sun H B, Ma G C 2022 Nat. Photonics 16 390 Google Scholar
[151]	Noh J, Schuster T, Iadecola T, Huang S, Wang M, Chen K P, Chamon C, Rechtsman M C 2020 Nat. Phys. 16 989 Google Scholar

Cited By

图 1 几种常见的用于量子模拟的集成光学系统　(a) 耦合光波导阵列^[44]; (b) 光子晶体; (c) 耦合环腔阵列^[45]; (d) 多端口干涉仪^[17]

Figure 1. Several integrated optical platforms for quantum simulation: (a) Coupled optical waveguide array^[44]; (b) photonic crystal; (c) array of coupled ring resonators^[45]; (d) multiport interferometer^[17].

DownLoad: Full-Size Img PowerPoint

图 2 用于模拟拓扑绝缘体结构的耦合环腔阵列　(a) 量子自旋霍尔效应系统^[59]; (b) 周期驱动Floquet拓扑绝缘体结构^[60]; (c) 反常量子霍尔效应系统^[63]. (a)—(c)上列为周期阵列结构, 下列为周期结构中基本单元的物理图像

Figure 2. Arrays of coupled ring resonators for simulations of topological insulators: (a) Quantum spin Hall effect^[59]; (b) Floquet topological insulators^[60]; (c) anomalous quantum Hall effect^[63]. The upper panel in (a)–(c): periodic coupled resonator arrays; lower panel: basic units in the periodic structures.

DownLoad: Full-Size Img PowerPoint

图 3 多端口干涉仪用于量子模拟　(a) 三角形结构(左)^[66]和矩形结构(右)^[67]的多端口干涉仪用于实现任意的幺正变换; (b)双光子在离散型量子随机行走芯片中的安德森局域化现象^[14]; (c) 硅基多端口干涉仪^[68], 由可调马赫-曾德尔干涉仪组成

Figure 3. Multiport interferometer for quantum simulation: (a) Realizing arbitrary unitary operator using triangular (left)^[66] and rectangular (right)^[67] mesh of beam splitters; (b) two-photon Anderson localization in discrete-time quantum random walk circuits^[14]; (c) multiport interferometer in a silicon-on-insulator platform^[68], which is consist of tunable Mach-Zehnder interferometers.

DownLoad: Full-Size Img PowerPoint

图 4 (a) 二维无序光子晶格中的安德森局域化现象^[76]; (b) 一维准周期飞秒激光直写光波导阵列^[85]; (c) 飞秒激光直写螺旋式波导阵列结构实现Floquet拓扑绝缘体^[25]; (d) 弯曲波导阵列实现等效磁场, 模拟Aharonov-Bohm效应^[89]; 在耦合环腔阵列结构中产生(e) 拓扑绝缘体激光^[90]、(f) 拓扑保护多光子量子光源^[91]; (g) 基于谷光子晶体结构设计等比分束器并实现双光子量子干涉^[57]; (h) 无序拓扑安德森绝缘体结构^[92]; (i) 基于一维SSH模型在硅基结构中产生关联光子对^[93]; (j) “含时”哈密顿量系统用于研究拓扑泵浦^[87]; (k) 奇偶-时间对称与对称破缺交界面处局域的拓扑边界态^[94]; (l) 非厄米SSH模型中非线性对奇偶-时间对称相变过程的影响^[22]

Figure 4. (a) Anderson localization in a two-dimensional photonic lattice^[76]; (b) simulation of one-dimensional quasicrystals in femtosecond-laser-written (FLW) optical waveguides^[85]; (c) realization of photonic Floquet topological insulators in a FLW helical waveguide array^[25]; (d) realization of an effective magnetic field and simulation of Aharonov-Bohm effect using curved waveguide arrays^[89]; generation of (e) topological insulator laser^[90] and (f) multiphoton quantum source^[91] in coupled resonator arrays; (g) design of a 1∶1 topological beam splitter in valley photonic crystals and realize the two-photon quantum interference^[57]; (h) photonic topological Anderson insulator^[92]; (i) generation of biphoton state in a SSH photonic lattice^[93]; (j) topological pumping in a system described by a time-varying Hamiltonian^[87]; (k) topological edge state in a photonic lattice at the interface between the structures with and without parity-time symmetry^[94]; (l) nonlinear tuning of PT symmetry and non-Hermitian topological states^[22].

DownLoad: Full-Size Img PowerPoint

map

[1]	Feynman R P 1982 Int. J. Theor. Phys. 21 467 Google Scholar
[2]	Georgescu I M, Ashhab S, Nori F 2014 Rev. Modern Phys. 86 153 Google Scholar
[3]	Monroe C, Campbell W C, Duan L M, Gong Z X, Gorshkov A V, Hess P W, Islam R, Kim K, Linke N M, Pagano G, Richerme P, Senko C, Yao N Y 2021 Rev. Modern Phys. 93 025001 Google Scholar
[4]	Houck A A, Tureci H E, Koch J 2012 Nat. Phys. 8 292 Google Scholar
[5]	Schäfer F, Fukuhara T, Sugawa S, Takasu Y, Takahashi Y 2020 Nat. Rev. Phys. 2 411 Google Scholar
[6]	Wang J W, Sciarrino F, Laing A, Thompson M G 2020 Nat. Photonics 14 273 Google Scholar
[7]	Elshaari A W, Pernice W, Srinivasan K, Benson O, Zwiller V 2020 Nat. Photonics 14 285 Google Scholar
[8]	Politi A, Matthews J C F, Thompson M G, O'Brien J L 2009 IEEE J. Quantum Electron. 15 1673 Google Scholar
[9]	Feng L, Zhang M, Wang J, Zhou X, Qiang X, Guo G, Ren X 2022 Photonics Res. 10 A135 Google Scholar
[10]	Tang H, Lin X F, Feng Z, Chen J Y, Gao J, Sun K, Wang C Y, Lai P C, Xu X Y, Wang Y, Qiao L F, Yang A L, Jin X M 2018 Sci. Adv. 4 eaat3174 Google Scholar
[11]	Perets H B, Lahini Y, Pozzi F, Sorel M, Morandotti R, Silberberg Y 2008 Phys. Rev. Lett. 100 170506 Google Scholar
[12]	Sansoni L, Sciarrino F, Vallone G, Mataloni P, Crespi A, Ramponi R, Osellame R 2012 Phys. Rev. Lett. 108 010502 Google Scholar
[13]	Peruzzo A, Lobino M, Matthews J C, Matsuda N, Politi A, Poulios K, Zhou X Q, Lahini Y, Ismail N, Worhoff K, Bromberg Y, Silberberg Y, Thompson M G, Obrien J L 2010 Science 329 1500 Google Scholar
[14]	Crespi A, Osellame R, Ramponi R, Giovannetti V, Fazio R, Sansoni L, De Nicola F, Sciarrino F, Mataloni P 2013 Nat. Photonics 7 322 Google Scholar
[15]	Spring J B, Metcalf B J, Humphreys P C, Kolthammer W S, Jin X M, Barbieri M, Datta A, Thomas-Peter N, Langford N K, Kundys D, Gates J C, Smith B J, Smith P G, Walmsley I A 2013 Science 339 798 Google Scholar
[16]	Crespi A, Osellame R, Ramponi R, Brod D J, Galvao E F, Spagnolo N, Vitelli C, Maiorino E, Mataloni P, Sciarrino F 2013 Nat. Photonics 7 545 Google Scholar
[17]	Tillmann M, Dakic B, Heilmann R, Nolte S, Szameit A, Walther P 2013 Nat. Photonics 7 540 Google Scholar
[18]	Spagnolo N, Vitelli C, Bentivegna M, Brod D J, Crespi A, Flamini F, Giacomini S, Milani G, Ramponi R, Mataloni P, Osellame R, Galvao E F, Sciarrino F 2014 Nat. Photonics 8 615 Google Scholar
[19]	Wang H, Qin J, Ding X, Chen M C, Chen S, You X, He Y M, Jiang X, You L, Wang Z, Schneider C, Renema J J, Hofling S, Lu C Y, Pan J W 2019 Phys. Rev. Lett. 123 250503 Google Scholar
[20]	Hoch F, Piacentini S, Giordani T, Tian Z N, Iuliano M, Esposito C, Camillini A, Carvacho G, Ceccarelli F, Spagnolo N 2021 arXiv: 2106.08260
[21]	Mukherjee S, Rechtsman M C 2020 Science 368 856 Google Scholar
[22]	Xia S, Kaltsas D, Song D, Komis I, Xu J, Szameit A, Buljan H, Makris K G, Chen Z 2021 Science 372 72 Google Scholar
[23]	Ozawa T, Price H M, Amo A, Goldman N, Hafezi M, Lu L, Rechtsman M C, Schuster D, Simon J, Zilberberg O 2019 Rev. Modern Phys. 91 015006 Google Scholar
[24]	Lu L, Joannopoulos J D, Soljacic M 2016 Nat. Phys. 12 626 Google Scholar
[25]	Rechtsman M C, Zeuner J M, Plotnik Y, Lumer Y, Podolsky D, Dreisow F, Nolte S, Segev M, Szameit A 2013 Nature 496 196 Google Scholar
[26]	Maczewsky L J, Heinrich M, Kremer M, Ivanov S K, Ehrhardt M, Martinez F, Kartashov Y V, Konotop V V, Torner L, Bauer D, Szameit A 2020 Science 370 701 Google Scholar
[27]	Sparrow C, Martin-Lopez E, Maraviglia N, Neville A, Harrold C, Carolan J, Joglekar Y N, Hashimoto T, Matsuda N, O'Brien J L, Tew D P, Laing A 2018 Nature 557 660 Google Scholar
[28]	McArdle S, Endo S, Aspuru-Guzik A, Benjamin S, Yuan X 2020 Rev. Modern Phys. 92 015003 Google Scholar
[29]	Cao Y, Romero J, Olson J P, Degroote M, Johnson P D, Kieferova M, Kivlichan I D, Menke T, Peropadre B, Sawaya N P D, Sim S, Veis L, Aspuru-Guzik A 2019 Chem. Rev. 119 10856 Google Scholar
[30]	Bogdanov S, Shalaginov M Y, Boltasseva A, Shalaev V M 2017 Opt. Mater. Express 7 111 Google Scholar
[31]	Corrielli G, Crespi A, Osellame R 2021 Nanophotonics 10 3789 Google Scholar
[32]	Ramakrishnan R K, Ravichandran A B, Mishra A, Kaushalram A, Hegde G, Talabattula S, Rohde P P 2022 arXiv: 2206.15383
[33]	Feng L T, Guo G C, Ren X F 2020 Adv. Quantum Technol. 3 1900058 Google Scholar
[34]	Feng L T, Zhang M, Xiong X, Chen Y, Wu H, Li M, Guo G P, Guo G C, Dai D X, Ren X F 2019 NPJ Quantum Inf. 5 2 Google Scholar
[35]	Feng L T, Zhang M, Zhou Z Y, Chen Y, Li M, Dai D X, Ren H L, Guo G P, Guo G C, Tame M, Ren X F 2019 NPJ Quantum Inf. 5 90 Google Scholar
[36]	Wang Y, Lu Y H, Mei F, Gao J, Li Z M, Tang H, Zhu S L, Jia S, Jin X M 2019 Phys. Rev. Lett. 122 193903 Google Scholar
[37]	Xie B Y, Su G X, Wang H F, Su H, Shen X P, Zhan P, Lu M H, Wang Z L, Chen Y F 2019 Phys. Rev. Lett. 122 233903 Google Scholar
[38]	Zhang M, Feng L T, Zhou Z Y, Chen Y, Wu H, Li M, Gao S M, Guo G P, Guo G C, Dai D X, Ren X F 2019 Light Sci. Appl. 8 41 Google Scholar
[39]	Engin E, Bonneau D, Natarajan C M, Clark A S, Tanner M G, Hadfield R H, Dorenbos S N, Zwiller V, Ohira K, Suzuki N, Yoshida H, Iizuka N, Ezaki M, O'Brien J L, Thompson M G 2013 Opt. Express 21 27826 Google Scholar
[40]	Lu X Y, Li Q, Westly D A, Moille G, Singh A, Anant V, Srinivasan K 2019 Nat. Phys. 15 373 Google Scholar
[41]	Xu B Y, Chen L K, Lin J T, Feng L T, Niu R, Zhou Z Y, Gao R H, Dong C H, Guo G C, Gong Q H, Cheng Y, Xiao Y F, Ren X F 2022 Sci. China Phys. Mech. 65 294262 Google Scholar
[42]	Jin H, Liu F M, Xu P, Xia J L, Zhong M L, Yuan Y, Zhou J W, Gong Y X, Wang W, Zhu S N 2014 Phys. Rev. Lett. 113 103601 Google Scholar
[43]	Guo X, Zou C L, Schuck C, Jung H, Cheng R, Tang H X 2017 Light Sci. Appl. 6 e16249 Google Scholar
[44]	Lahini Y, Avidan A, Pozzi F, Sorel M, Morandotti R, Christodoulides D N, Silberberg Y 2008 Phys. Rev. Lett. 100 013906 Google Scholar
[45]	Hafezi M, Mittal S, Fan J, Migdall A, Taylor J M 2013 Nat. Photonics 7 1001 Google Scholar
[46]	Longhi S 2009 Laser Photonics Rev. 3 243 Google Scholar
[47]	Chen Y, Chen X M, Ren X F, Gong M, Guo G C 2021 Phys. Rev. A 104 023501 Google Scholar
[48]	Christodoulides D N, Lederer F, Silberberg Y 2003 Nature 424 817 Google Scholar
[49]	Jones A L 1965 JOSA 55 261 Google Scholar
[50]	Somekh S, Garmire E, Yariv A, Garvin H L, Hunsperger R G 1973 Appl. Phys. Lett. 22 46 Google Scholar
[51]	Jamois C, Wehrspohn R, Andreani L, Hermann C, Hess O, Gösele U 2003 Photonic. Nanostruct. Appl. 1 1 Google Scholar
[52]	Tanaka Y, Nakamura H, Sugimoto Y, Ikeda N, Asakawa K, Inoue K 2005 IEEE J. Quantum Electron. 41 76 Google Scholar
[53]	Johnson S G, Villeneuve P R, Fan S H, Joannopoulos J D 2000 Phys. Rev. B 62 8212
[54]	He L, Addison Z, Mele E J, Zhen B 2020 Nat. Commun. 11 3119 Google Scholar
[55]	Xie B, Su G, Wang H F, Liu F, Hu L, Yu S Y, Zhan P, Lu M H, Wang Z, Chen Y F 2020 Nat. Commun. 11 3768 Google Scholar
[56]	Jin M C, Gao Y F, Ma Q L, Zhang W, Song H, Sun J P 2021 Phys. Rev. Mater. 5 024204 Google Scholar
[57]	Chen Y, He X T, Cheng Y J, Qiu H Y, Feng L T, Zhang M, Dai D X, Guo G C, Dong J W, Ren X F 2021 Phys. Rev. Lett. 126 230503 Google Scholar
[58]	Yariv A, Xu Y, Lee R K, Scherer A 1999 Opt. Lett. 24 711 Google Scholar
[59]	Hafezi M, Demler E A, Lukin M D, Taylor J M 2011 Nat. Phys. 7 907 Google Scholar
[60]	Liang G Q, Chong Y D 2013 Phys. Rev. Lett. 110 203904 Google Scholar
[61]	Pasek M, Chong Y D 2014 Phys. Rev. B 89 075113 Google Scholar
[62]	Afzal S, Zimmerling T J, Ren Y, Perron D, Van V 2020 Phys. Rev. Lett. 124 253601 Google Scholar
[63]	Leykam D, Mittal S, Hafezi M, Chong Y D 2018 Phys. Rev. Lett. 121 023901 Google Scholar
[64]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 Google Scholar
[65]	Mittal S, Orre V V, Leykam D, Chong Y D, Hafezi M 2019 Phys. Rev. Lett. 123 043201 Google Scholar
[66]	Reck M, Zeilinger A, Bernstein H J, Bertani P 1994 Phys. Rev. Lett. 73 58 Google Scholar
[67]	Clements W R, Humphreys P C, Metcalf B J, Kolthammer W S, Walmsley I A 2016 Optica 3 1460 Google Scholar
[68]	Harris N C, Bunandar D, Pant M, Steinbrecher G R, Mower J, Prabhu M, Baehr-Jones T, Hochberg M, Englund D 2016 Nanophotonics 5 456 Google Scholar
[69]	Yu S, Qiu C W, Chong Y, Torquato S, Park N 2021 Nat. Rev. Mater. 6 226 Google Scholar
[70]	Lagendijk A, van Tiggelen B, Wiersma D S 2009 Phys. Today 62 24
[71]	Segev M, Silberberg Y, Christodoulides D N 2013 Nat. Photonics 7 197 Google Scholar
[72]	Rothammer M, Zollfrank C, Busch K, von Freymann G 2021 Adv. Opt. Mater. 9 2100787 Google Scholar
[73]	Anderson P W 1958 Phys. Rev. 109 1492 Google Scholar
[74]	Mott N 1967 Adv. Phys. 16 49 Google Scholar
[75]	De Raedt H, Lagendijk A, de Vries P 1989 Phys. Rev. Lett. 62 47 Google Scholar
[76]	Schwartz T, Bartal G, Fishman S, Segev M 2007 Nature 446 52 Google Scholar
[77]	Eisenberg H S, Silberberg Y, Morandotti R, Boyd A R, Aitchison J S 1998 Phys. Rev. Lett. 81 3383 Google Scholar
[78]	Martin L, Di Giuseppe G, Perez-Leija A, Keil R, Dreisow F, Heinrich M, Nolte S, Szameit A, Abouraddy A F, Christodoulides D N, Saleh B E 2011 Opt. Express 19 13636 Google Scholar
[79]	Geraldi A, Laneve A, Bonavena L D, Sansoni L, Ferraz J, Fratalocchi A, Sciarrino F, Cuevas Á, Mataloni P 2019 Phys. Rev. Lett. 123 140501 Google Scholar
[80]	Levi L, Krivolapov Y, Fishman S, Segev M 2012 Nat. Phys. 8 912 Google Scholar
[81]	Vasco J P, Hughes S 2018 Acs Photonics 5 1262 Google Scholar
[82]	Hsieh P, Chung C, McMillan J F, Tsai M, Lu M, Panoiu N C, Wong C W 2015 Nat. Phys. 11 268 Google Scholar
[83]	Ni X, Chen K, Weiner M, Apigo D J, Prodan C, Alu A, Prodan E, Khanikaev A B 2019 Commun. Phys. 2 55 Google Scholar
[84]	Kraus Y E, Zilberberg O 2012 Phys. Rev. Lett. 109 116404 Google Scholar
[85]	Verbin M, Zilberberg O, Kraus Y E, Lahini Y, Silberberg Y 2013 Phys. Rev. Lett. 110 076403 Google Scholar
[86]	Lahini Y, Pugatch R, Pozzi F, Sorel M, Morandotti R, Davidson N, Silberberg Y 2009 Phys. Rev. Lett. 103 013901 Google Scholar
[87]	Kraus Y E, Lahini Y, Ringel Z, Verbin M, Zilberberg O 2012 Phys. Rev. Lett. 109 106402 Google Scholar
[88]	Levi L, Rechtsman M, Freedman B, Schwartz T, Manela O, Segev M 2011 Science 332 1541 Google Scholar
[89]	Mukherjee S, Di Liberto M, Ohberg P, Thomson R R, Goldman N 2018 Phys. Rev. Lett. 121 075502 Google Scholar
[90]	Bandres M A, Wittek S, Harari G, Parto M, Ren J, Segev M, Christodoulides D N, Khajavikhan M 2018 Science 359 eaar4005 Google Scholar
[91]	Dai T X, Ao Y T, Bao J M, Mao J, Chi Y L, Fu Z R, You Y L, Chen X J, Zhai C H, Tang B, Yang Y, Li Z H, Yuan L Q, Gao F, Lino X, Thompson M G, O'Brien J L, Li Y, Hu X Y, Gong Q H, Wang J W 2022 Nat. Photonics 16 248 Google Scholar
[92]	Stutzer S, Plotnik Y, Lumer Y, Titum P, Lindner N H, Segev M, Rechtsman M C, Szameit A 2018 Nature 560 461 Google Scholar
[93]	Blanco-Redondo A, Bell B, Oren D, Eggleton B J, Segev M 2018 Science 362 568 Google Scholar
[94]	Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C, Szameit A 2017 Nat. Mater. 16 433 Google Scholar
[95]	Hasan M Z, Kane C L 2010 Rev. Modern Phys. 82 3045 Google Scholar
[96]	Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[97]	Haldane F D, Raghu S 2008 Phys. Rev. Lett. 100 013904 Google Scholar
[98]	Wang Z, Chong Y, Joannopoulos J D, Soljacic M 2009 Nature 461 772 Google Scholar
[99]	Longhi S 2014 Opt. Lett. 39 5892 Google Scholar
[100]	Keil R, Poli C, Heinrich M, Arkinstall J, Weihs G, Schomerus H, Szameit A 2016 Phys. Rev. Lett. 116 213901 Google Scholar
[101]	Kremer M, Petrides I, Meyer E, Heinrich M, Zilberberg O, Szameit A 2020 Nat. Commun. 11 907 Google Scholar
[102]	Mittal S, Goldschmidt E A, Hafezi M 2018 Nature 561 502 Google Scholar
[103]	Mittal S, Orre V V, Goldschmidt E A, Hafezi M 2021 Nat. Photonics 15 542 Google Scholar
[104]	Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809 Google Scholar
[105]	Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233 Google Scholar
[106]	Noh J, Huang S, Chen K P, Rechtsman M C 2018 Phys. Rev. Lett. 120 063902 Google Scholar
[107]	He X T, Liang E T, Yuan J J, Qiu H Y, Chen X D, Zhao F L, Dong J W 2019 Nat. Commun. 10 872 Google Scholar
[108]	Shalaev M I, Walasik W, Tsukernik A, Xu Y, Litchinitser N M 2019 Nat. Nanotechnol. 14 31 Google Scholar
[109]	Barik S, Karasahin A, Flower C, Cai T, Miyake H, DeGottardi W, Hafezi M, Waks E 2018 Science 359 666 Google Scholar
[110]	Zeng Y, Chattopadhyay U, Zhu B, Qiang B, Li J, Jin Y, Li L, Davies A G, Linfield E H, Zhang B, Chong Y, Wang Q J 2020 Nature 578 246 Google Scholar
[111]	Shen S Q 2012 Topological Insulators (Vol. 174) (Berlin, Heidelberg: Springer)
[112]	Malkova N, Hromada I, Wang X, Bryant G, Chen Z 2009 Opt. Lett. 34 1633 Google Scholar
[113]	Blanco-Redondo A, Andonegui I, Collins M J, Harari G, Lumer Y, Rechtsman M C, Eggleton B J, Segev M 2016 Phys. Rev. Lett. 116 163901 Google Scholar
[114]	Wang Y, Pang X L, Lu Y H, Gao J, Chang Y J, Qiao L F, Jiao Z Q, Tang H, Jin X M 2019 Optica 6 955 Google Scholar
[115]	Chen X D, Deng W M, Shi F L, Zhao F L, Chen M, Dong J W 2019 Phys. Rev. Lett. 122 233902 Google Scholar
[116]	Wang Y, Ke Y, Chang Y J, Lu Y H, Gao J, Lee C, Jin X M 2021 Phys. Rev. B 104 224303 Google Scholar
[117]	El Hassan A, Kunst F K, Moritz A, Andler G, Bergholtz E J, Bourennane M 2019 Nat. Photonics 13 697 Google Scholar
[118]	Parto M, Wittek S, Hodaei H, Harari G, Bandres M A, Ren J, Rechtsman M C, Segev M, Christodoulides D N, Khajavikhan M 2018 Phys. Rev. Lett. 120 113901 Google Scholar
[119]	St-Jean P, Goblot V, Galopin E, Lemaitre A, Ozawa T, Le Gratiet L, Sagnes I, Bloch J, Amo A 2017 Nat. Photonics 11 651 Google Scholar
[120]	Lustig E, Weimann S, Plotnik Y, Lumer Y, Bandres M A, Szameit A, Segev M 2019 Nature 567 356 Google Scholar
[121]	Zilberberg O, Huang S, Guglielmon J, Wang M H, Chen K P, Kraus Y E, Rechtsman M C 2018 Nature 553 59 Google Scholar
[122]	Jurgensen M, Mukherjee S, Rechtsman M C 2021 Nature 596 63 Google Scholar
[123]	Cerjan A, Wang M, Huang S, Chen K P, Rechtsman M C 2020 Light Sci. Appl. 9 178 Google Scholar
[124]	Christodoulides D N, Joseph R I 1988 Opt. Lett. 13 794 Google Scholar
[125]	Fleischer J W, Segev M, Efremidis N K, Christodoulides D N 2003 Nature 422 147 Google Scholar
[126]	Lederer F L, Stegeman G I, Christodoulides D N, Assanto G, Segev M, Silberberg Y R 2008 Phys. Rep. 463 1 Google Scholar
[127]	Smirnova D, Leykam D, Chong Y D, Kivshar Y 2020 Appl. Phys. Rev. 7 021306 Google Scholar
[128]	Dobrykh D A, Yulin A V, Slobozhanyuk A P, Poddubny A N, Kivshar Y S 2018 Phys. Rev. Lett. 121 163901 Google Scholar
[129]	Bergholtz E J, Budich J C, Kunst F K 2021 Rev. Modern Phys. 93 015005 Google Scholar
[130]	Okuma N, Kawabata K, Shiozaki K, Sato M 2020 Phys. Rev. Lett. 124 086801 Google Scholar
[131]	Weidemann S, Kremer M, Helbig T, Hofmann T, Stegmaier A, Greiter M, Thomale R, Szameit A 2020 Science 368 311 Google Scholar
[132]	Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192 Google Scholar
[133]	El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S, Christodoulides D N 2018 Nat. Phys. 14 11 Google Scholar
[134]	Pitsios I, Banchi L, Rab A S, Bentivegna M, Caprara D, Crespi A, Spagnolo N, Bose S, Mataloni P, Osellame R, Sciarrino F 2017 Nat. Commun. 8 1569 Google Scholar
[135]	Wu Y L, Bao W S, Cao S R, Chen F S, Chen M C, Chen X W, Chung T H, Deng H, Du Y J, Fan D J, Gong M, Guo C, Guo C, Guo S J, Han L C, Hong L Y, Huang H L, Huo Y H, Li L P, Li N, Li S W, Li Y, Liang F T, Lin C, Lin J, Qian H R, Qiao D, Rong H, Su H, Sun L H, Wang L Y, Wang S Y, Wu D C, Xu Y, Yan K, Yang W F, Yang Y, Ye Y S, Yin J H, Ying C, Yu J L, Zha C, Zhang C, Zhang H B, Zhang K L, Zhang Y M, Zhao H, Zhao Y W, Zhou L, Zhu Q L, Lu C Y, Peng C Z, Zhu X B, Pan J W 2021 Phys. Rev. Lett. 127 180501 Google Scholar
[136]	Zhong H S, Wang H, Deng Y H, Chen M C, Peng L C, Luo Y H, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y X, Jiang X, Gan L, Yang G W, You L X, Wang Z, Li L, Liu N L, Lu C Y, Pan J W 2020 Science 370 1460 Google Scholar
[137]	Zhu Q L, Cao S R, Chen F S, Chen M C, Chen X W, Chung T H, Deng H, Du Y J, Fan D J, Gong M, Guo C, Guo C, Guo S J, Han L C, Hong L Y, Huang H L, Huo Y H, Li L P, Li N, Li S W, Li Y, Liang F T, Lin C, Lin J, Qian H R, Qiao D, Rong H, Su H, Sun L H, Wang L Y, Wang S Y, Wu D C, Wu Y L, Xu Y, Yan K, Yang W F, Yang Y, Ye Y, Yin J H, Ying C, Yu J L, Zha C, Zhang C, Zhang H B, Zhang K L, Zhang Y M, Zhao H, Zhao Y W, Zhou L, Lu C Y, Peng C Z, Zhu X B, Pan J W 2022 Sci. Bull. 67 240 Google Scholar
[138]	Paesani S, Gentile A A, Santagati R, Wang J, Wiebe N, Tew D P, O'Brien J L, Thompson M G 2017 Phys. Rev. Lett. 118 100503 Google Scholar
[139]	黎颖, 韩泽尧, 黎超健, 吕劲, 袁骁, 吴步娇 2021 70 210201 Google Scholar Li Y, Han Z Y, Li J C, Lv J, Yuan X, Wu B J 2021 Acta Phys. Sin. 70 210201 Google Scholar
[140]	Peruzzo A, McClean J, Shadbolt P, Yung M H, Zhou X Q, Love P J, Aspuru-Guzik A, O'Brien J L 2014 Nat. Commun. 5 4213 Google Scholar
[141]	Nielsen M A, Chuang I 2002 Quantum Computation and Quantum Information (American Association of Physics Teachers)
[142]	Wiebe N, Granade C 2016 Phys. Rev. Lett. 117 010503 Google Scholar
[143]	Zhao Y, Chen Y, Hou Z S, Han B, Fan H, Lin L H, Ren X F, Sun H B 2022 Opt. Lett. 47 617 Google Scholar
[144]	Xu Y L, Fegadolli W S, Gan L, Lu M H, Liu X P, Li Z Y, Scherer A, Chen Y F 2016 Nat. Commun. 7 11319 Google Scholar
[145]	Longhi S 2008 Phys. Rev. Lett. 101 193902 Google Scholar
[146]	Crespi A, Pepe F V, Facchi P, Sciarrino F, Mataloni P, Nakazato H, Pascazio S, Osellame R 2019 Phys. Rev. Lett. 122 130401 Google Scholar
[147]	Xu X Y, Wang X W, Chen D Y, Smith C M 2021 Nat. Photonics 15 703 Google Scholar
[148]	Tang H, Di Franco C, Shi Z Y, He T S, Feng Z, Gao J, Sun K, Li Z M, Jiao Z Q, Wang T Y, Kim M S, Jin X M 2018 Nat. Photonics 12 754 Google Scholar
[149]	Kim M, Jacob Z, Rho J 2020 Light Sci. Appl. 9 130 Google Scholar
[150]	Zhang X L, Yu F, Chen Z G, Tian Z N, Chen Q D, Sun H B, Ma G C 2022 Nat. Photonics 16 390 Google Scholar
[151]	Noh J, Schuster T, Iadecola T, Huang S, Wang M, Chen K P, Chamon C, Rechtsman M C 2020 Nat. Phys. 16 989 Google Scholar

[1]	Zou Yun-Peng, Chan Vincent, Chen Wei. Improvement of critical gradient model and establishment of an energetic particle module for integrated simulation. Acta Physica Sinica, 2023, 72(21): 215206. doi: 10.7498/aps.72.20230681
[2]	Tan Hui, Cao Rui, Li Yong-Qiang. Quantum simulation of ultracold atoms in optical lattice based on dynamical mean-field theory. Acta Physica Sinica, 2023, 72(18): 183701. doi: 10.7498/aps.72.20230701
[3]	Xu Da, Wang Yi-Pu, Li Tie-Fu, You Jian-Qiang. Coherent coupling in a driven qubit-magnon hybrid quantum system. Acta Physica Sinica, 2022, 71(15): 150302. doi: 10.7498/aps.71.20220260
[4]	Cheng En-Hong, Lang Li-Jun. Electrical circuit simulation of nonreciprocal Aubry-André models. Acta Physica Sinica, 2022, 71(16): 160301. doi: 10.7498/aps.71.20220219
[5]	Gao Xue-Er, Li Dai-Li, Liu Zhi-Hang, Zheng Chao. Recent progress of quantum simulation of non-Hermitian systems. Acta Physica Sinica, 2022, 71(24): 240303. doi: 10.7498/aps.71.20221825
[6]	Wang Chen-Xu, He Ran, Li Rui-Rui, Chen Yan, Fang Ding, Cui Jin-Ming, Huang Yun-Feng, Li Chuan-Feng, Guo Guang-Can. Advances in the study of ion trap structures in quantum computation and simulation. Acta Physica Sinica, 2022, 71(13): 133701. doi: 10.7498/aps.71.20220224
[7]	Luo Yu-Chen, Li Xiao-Peng. Quantum simulation of interacting fermions. Acta Physica Sinica, 2022, 71(22): 226701. doi: 10.7498/aps.71.20221756
[8]	Ji Yi-Ru, Chu Yan-Bang, Xian Le-De, Yang Wei, Zhang Guang-Yu. From magic angle twisted bilayer graphene to moiré superlattice quantum simulator. Acta Physica Sinica, 2021, 70(11): 118101. doi: 10.7498/aps.70.20210476
[9]	Lin Jian, Ye Meng, Zhu Jia-Wei, Li Xiao-Peng. Machine learning assisted quantum adiabatic algorithm design. Acta Physica Sinica, 2021, 70(14): 140306. doi: 10.7498/aps.70.20210831
[10]	Lu Bo, Wang Da-Jun. Ultracold dipolar molecules. Acta Physica Sinica, 2019, 68(4): 043301. doi: 10.7498/aps.68.20182274
[11]	Zhao Xing-Dong, Zhang Ying-Ying, Liu Wu-Ming. Magnetic excitation of ultra-cold atoms trapped in optical lattice. Acta Physica Sinica, 2019, 68(4): 043703. doi: 10.7498/aps.68.20190153
[12]	Zhu Yan-Qing, Zhang Dan-Wei, Zhu Shi-Liang. Simulating Dirac, Weyl and Maxwell equations with cold atoms in optical lattices. Acta Physica Sinica, 2019, 68(4): 046701. doi: 10.7498/aps.68.20181929
[13]	Kong Xiang-Yu, Zhu Yuan-Ye, Wen Jing-Wei, Xin Tao, Li Ke-Ren, Long Gui-Lu. New research progress of nuclear magnetic resonance quantum information processing. Acta Physica Sinica, 2018, 67(22): 220301. doi: 10.7498/aps.67.20180754
[14]	Zhao Shi-Ping, Liu Yu-Xi, Zheng Dong-Ning. Novel superconducting qubits and quantum physics. Acta Physica Sinica, 2018, 67(22): 228501. doi: 10.7498/aps.67.20180845
[15]	Yu Xiang-Min, Tan Xin-Sheng, Yu Hai-Feng, Yu Yang. Topological quantum material simulated with superconducting quantum circuits. Acta Physica Sinica, 2018, 67(22): 220302. doi: 10.7498/aps.67.20181857
[16]	Fan Heng. Quantum computation and quantum simulation. Acta Physica Sinica, 2018, 67(12): 120301. doi: 10.7498/aps.67.20180710
[17]	Shu Hua, Fu Si-Zu, Huang Xiu-Guang, Ye Jun-Jian, Zhou Hua-Zhen, Xie Zhi-Yong, Long Tao. Line-imaging optical recording velocity interferometer at Shenguang-II laser facility and its applications. Acta Physica Sinica, 2012, 61(11): 114102. doi: 10.7498/aps.61.114102
[18]	Lu Dan-Feng, Qi Zhi-Mei. Characterization and chemical/biosensing application of a high-sensitivity integrated optical polarimetric interferometer. Acta Physica Sinica, 2012, 61(11): 114212. doi: 10.7498/aps.61.114212
[19]	Shang Ya-Na, Wang Dong, Yan Zhi-Hui, Wang Wen-Zhe, Jia Xiao-Jun, Peng Kun-Chi. Measurement of entangled state of light with non-degenerate frequency utilizing non-balanced fiber Mach-Zehnder interferometer. Acta Physica Sinica, 2008, 57(6): 3514-3518. doi: 10.7498/aps.57.3514
[20]	LI ZHU-QI, KUAN JING-HUI, WU SHAN-LING, YANG TONG-HUA, HE MIN, LU TING, CHENG ZHI-XU, CHEN GUI-YING, YE CHUN-TANG. A ROTATING CRYSTAL NEUTRON TIME-OF-FLIGHT SPECTRO-METER FOR CONDENSED MATTER INVESTIGATION. Acta Physica Sinica, 1980, 29(11): 1462-1470. doi: 10.7498/aps.29.1462

Catalog

Vol. 71, Issue 24 - 2022-12-20

Metrics

Abstract views: 5969
PDF Downloads: 268
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板