Floquet Chern insulators of light

He, Li; Addison, Zachariah; Jin, Jicheng; Mele, Eugene J.; Johnson, Steven G.; Zhen, Bo

doi:10.1038/s41467-019-12231-4

Title: Floquet Chern insulators of light

Journal Article · Fri Sep 13 00:00:00 EDT 2019 · Nature Communications

DOI:https://doi.org/10.1038/s41467-019-12231-4· OSTI ID:1624194

He, Li ^[1]; Addison, Zachariah ^[1]; Jin, Jicheng ^[1]; Mele, Eugene J. ^[1]; Johnson, Steven G. ^[2]; Zhen, Bo ^[1]

Pennsylvania State Univ., University Park, PA (United States). Dept. of Physics and Astronomy
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Mathematics

Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most studied topological photonic structures can be understood by solving the eigenvalue problem of Maxwell’s equations for static linear systems. Here, we extend topological phases into dynamically driven systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs. We then define topological invariant associated with Floquet bands, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven optical systems and their optoelectronic applications.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-00ER41132

OSTI ID:: 1624194

Journal Information:: Nature Communications, Vol. 10, Issue 1; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (34)

The topological theory of defects in ordered media Mermin, N. D. Reviews of Modern Physics, Vol. 51, Issue 3 https://doi.org/10.1103/RevModPhys.51.591	journal	July 1979
Weyl and Dirac semimetals in three-dimensional solids Armitage, N. P.; Mele, E. J.; Vishwanath, Ashvin Reviews of Modern Physics, Vol. 90, Issue 1 https://doi.org/10.1103/RevModPhys.90.015001	journal	January 2018
Experimental Observation of Large Chern Numbers in Photonic Crystals Skirlo, Scott A.; Lu, Ling; Igarashi, Yuichi Physical Review Letters, Vol. 115, Issue 25 https://doi.org/10.1103/PhysRevLett.115.253901	journal	December 2015
Topological photonics Ozawa, Tomoki; Price, Hannah M.; Amo, Alberto Reviews of Modern Physics, Vol. 91, Issue 1 https://doi.org/10.1103/RevModPhys.91.015006	journal	March 2019
Topological phases and nonreciprocal edge states in non-Hermitian Floquet insulators Li, Mengyao; Ni, Xiang; Weiner, Matthew Physical Review B, Vol. 100, Issue 4 https://doi.org/10.1103/PhysRevB.100.045423	journal	July 2019
Observation of bulk Fermi arc and polarization half charge from paired exceptional points Zhou, Hengyun; Peng, Chao; Yoon, Yoseob Science, Vol. 359, Issue 6379 https://doi.org/10.1126/science.aap9859	journal	January 2018
Floquet topological insulator in semiconductor quantum wells Lindner, Netanel H.; Refael, Gil; Galitski, Victor Nature Physics, Vol. 7, Issue 6 https://doi.org/10.1038/nphys1926	journal	March 2011
Bloch oscillation and unidirectional translation of frequency in a dynamically modulated ring resonator Yuan, Luqi; Fan, Shanhui Optica, Vol. 3, Issue 9 https://doi.org/10.1364/OPTICA.3.001014	journal	January 2016
Photonic Floquet topological insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan Nature, Vol. 496, Issue 7444 https://doi.org/10.1038/nature12066	journal	April 2013
Experimental observation of Weyl points Lu, L.; Wang, Z.; Ye, D. Science, Vol. 349, Issue 6248 https://doi.org/10.1126/science.aaa9273	journal	July 2015
Analogue of Rashba pseudo-spin-orbit coupling in photonic lattices by gauge field engineering Plotnik, Y.; Bandres, M. A.; Stützer, S. Physical Review B, Vol. 94, Issue 2 https://doi.org/10.1103/PhysRevB.94.020301	journal	July 2016
Topological phase transitions and chiral inelastic transport induced by the squeezing of light Peano, Vittorio; Houde, Martin; Brendel, Christian Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10779	journal	March 2016
Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem Raman, Aaswath; Fan, Shanhui Physical Review Letters, Vol. 104, Issue 8 https://doi.org/10.1103/PhysRevLett.104.087401	journal	February 2010
Handbook of Nonlinear Optics Sutherland, Richard L. CRC Press https://doi.org/10.1201/9780203912539	book	April 2003
Topological aspects of photonic time crystals Lustig, Eran; Sharabi, Yonatan; Segev, Mordechai Optica, Vol. 5, Issue 11 https://doi.org/10.1364/OPTICA.5.001390	journal	January 2018
Dynamical preparation of Floquet Chern insulators D’Alessio, Luca; Rigol, Marcos Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9336	journal	October 2015
Nonreciprocal lasing in topological cavities of arbitrary geometries Bahari, Babak; Ndao, Abdoulaye; Vallini, Felipe Science, Vol. 358, Issue 6363 https://doi.org/10.1126/science.aao4551	journal	October 2017
Topological insulator laser: Experiments Bandres, Miguel A.; Wittek, Steffen; Harari, Gal Science, Vol. 359, Issue 6381 https://doi.org/10.1126/science.aar4005	journal	February 2018
Anomalous Quantum Hall Effect of Light in Bloch-Wave Modulated Photonic Crystals Fang, Kejie; Wang, Yunkai Physical Review Letters, Vol. 122, Issue 23 https://doi.org/10.1103/PhysRevLett.122.233904	journal	June 2019
Topological photonics Lu, Ling; Joannopoulos, John D.; Soljačić, Marin Nature Photonics, Vol. 8, Issue 11 https://doi.org/10.1038/nphoton.2014.248	journal	October 2014
Two-dimensional topological photonics Khanikaev, Alexander B.; Shvets, Gennady Nature Photonics, Vol. 11, Issue 12 https://doi.org/10.1038/s41566-017-0048-5	journal	November 2017
A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension Lin, Qian; Sun, Xiao-Qi; Xiao, Meng Science Advances, Vol. 4, Issue 10 https://doi.org/10.1126/sciadv.aat2774	journal	October 2018
Observation of photonic anomalous Floquet topological insulators Maczewsky, Lukas J.; Zeuner, Julia M.; Nolte, Stefan Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms13756	journal	January 2017
Observation of unidirectional backscattering-immune topological electromagnetic states Wang, Zheng; Chong, Yidong; Joannopoulos, J. D. Nature, Vol. 461, Issue 7265 https://doi.org/10.1038/nature08293	journal	October 2009
Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension Lin, Qian; Xiao, Meng; Yuan, Luqi Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms13731	journal	December 2016
Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry Haldane, F. D. M.; Raghu, S. Physical Review Letters, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevLett.100.013904	journal	January 2008
Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal Wang, Zheng; Chong, Y. D.; Joannopoulos, John D. Physical Review Letters, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevLett.100.013905	journal	January 2008
What is — and what is not — an optical isolator Jalas, Dirk; Petrov, Alexander; Eich, Manfred Nature Photonics, Vol. 7, Issue 8 https://doi.org/10.1038/nphoton.2013.185	journal	July 2013
Interband transitions in photonic crystals Winn, Joshua N.; Fan, Shanhui; Joannopoulos, John D. Physical Review B, Vol. 59, Issue 3 https://doi.org/10.1103/physrevb.59.1551	journal	January 1999
Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators Leykam, Daniel; Rechtsman, M. C.; Chong, Y. D. Physical Review Letters, Vol. 117, Issue 1 https://doi.org/10.1103/physrevlett.117.013902	journal	June 2016
Dynamical preparation of Floquet Chern insulators D'Alessio, Luca; Rigol, Marcos arXiv https://doi.org/10.48550/arxiv.1409.6319	text	January 2014
Experimental observation of Weyl points Lu, Ling; Wang, Zhiyu; Ye, Dexin arXiv https://doi.org/10.48550/arxiv.1502.03438	text	January 2015
Experimental Observation of Large Chern numbers in Photonic Crystals Skirlo, Scott A.; Lu, Ling; Yan, Qinghui arXiv https://doi.org/10.48550/arxiv.1504.04399	text	January 2015
Topological quantum fluctuations and travelling wave amplifiers Peano, Vittorio; Houde, Martin; Marquardt, Florian arXiv https://doi.org/10.48550/arxiv.1604.04179	text	January 2016

Cited By (4)

Fresnel drag in space–time-modulated metamaterials Huidobro, Paloma A.; Galiffi, Emanuele; Guenneau, Sébastien Proceedings of the National Academy of Sciences, Vol. 116, Issue 50 https://doi.org/10.1073/pnas.1915027116	journal	November 2019
Broadband Nonreciprocal Amplification in Luminal Metamaterials Galiffi, E.; Huidobro, P. A.; Pendry, J. B. arXiv https://doi.org/10.48550/arxiv.1907.08421	text	January 2019
Fresnel drag in space-time modulated metamaterials Huidobro, P. A.; Galiffi, E.; Guenneau, S. arXiv https://doi.org/10.48550/arxiv.1908.05883	text	January 2019
Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System Cao, Yang; Li, Yang; Yang, Xiaosen arXiv https://doi.org/10.48550/arxiv.2007.13499	text	January 2020