Higher-order topological insulators in synthetic dimensions

Avik Dutt; Momchil Minkov; Ian A. D. Williamson; Shanhui Fan

doi:10.1038/s41377-020-0334-8

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Higher-order topological insulators in synthetic dimensions

Article

- Higher-order topological insulators in synthetic dimensions
- Light: Science & Applications Vol. 9, Issue 4, Pages: 1253-1261(2020)
- Affiliations：
  
  Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
- Author bio：
  
  Shanhui Fan (shanhui@stanford.edu)
- Funds：
- DOI：10.1038/s41377-020-0334-8
  CLC：
- Published：2020，
  
  Published Online：20 July 2020，
  
  Received：24 November 2019，
  
  Revised：07 April 2020，
  
  Accepted：11 May 2020
- Accepted：
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Dutt, A. et al. Higher-order topological insulators in synthetic dimensions. Light: Science & Applications, 9, 1253-1261 (2020).
DOI：

Dutt, A. et al. Higher-order topological insulators in synthetic dimensions. Light: Science & Applications, 9, 1253-1261 (2020). DOI： 10.1038/s41377-020-0334-8.

摘要

Abstract

Conventional topological insulators support boundary states with dimension one lower than that of the bulk system that hosts them

and these states are topologically protected due to quantized bulk dipole moments. Recently

higher-order topological insulators have been proposed as a way of realizing topological states with dimensions two or more lower than that of the bulk due to the quantization of bulk quadrupole or octupole moments. However

all these proposals as well as experimental realizations have been restricted to real-space dimensions. Here

we construct photonic higher-order topological insulators (PHOTIs) in synthetic dimensions. We show the emergence of a quadrupole PHOTI supporting topologically protected corner modes in an array of modulated photonic molecules with a synthetic frequency dimension

where each photonic molecule comprises two coupled rings. By changing the phase difference of the modulation between adjacent coupled photonic molecules

we predict a dynamical topological phase transition in the PHOTI. Furthermore

we show that the concept of synthetic dimensions can be exploited to realize even higher-order multipole moments such as a fourth-order hexadecapole (16-pole) insulator supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.

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references

Benalcazar, W. A., Bernevig, B. A.&Hughes, T. L. Quantized electric multipole insulators.Science357, 61–66 (2017)..

Schindler, F. et al. Higher-order topology in bismuth.Nat. Phys.14, 918–924 (2018)..

Serra-Garcia, M. et al. Observation of a phononic quadrupole topological insulator.Nature555, 342–345 (2018)..

Xue, H. R. et al. Acoustic higher-order topological insulator on a Kagome lattice.Nat. Mater.18, 108–112 (2019)..

Ni, X. et al. Observation of higher-order topological acoustic states protected by generalized chiral symmetry.Nat. Mater.18, 113–120 (2019)..

Imhof, S. et al. Topolectrical-circuit realization of topological corner modes.Nat. Phys.14, 925–925 (2018)..

Mittal, S. et al. Photonic quadrupole topological phases.Nat. Photonics13, 692–696 (2019)..

Yuan, L. et al. Synthetic dimension in photonics.Optica5, 1396–1405 (2018)..

Ozawa, T.&Price, H. M. Topological quantum matter in synthetic dimensions.Nat. Rev. Phys.1, 349–357 (2019)..

Jukić, D.&Buljan, H. Four-dimensional photonic lattices and discrete tesseract solitons.Phys. Rev. A87, 013814 (2013)..

Boada, O. et al. Quantum simulation of an extra dimension.Phys. Rev. Lett.108, 133001 (2012)..

Lustig, E. et al. Photonic topological insulator in synthetic dimensions.Nature567, 356–360 (2019)..

Yuan, L., Shi, Y.&Fan, S. Photonic gauge potential in a system with a synthetic frequency dimension.Opt. Lett.41, 741–744 (2016)..

Ozawa, T. et al. Synthetic dimensions in integrated photonics: from optical isolation to four-dimensional quantum Hall physics.Phys. Rev. A93, 043827 (2016)..

Luo, X. W. et al. Quantum simulation of 2D topological physics in a 1D array of optical cavities.Nat. Commun.6, 7704 (2015)..

Mancini, M. et al. Observation of chiral edge states with neutral fermions in synthetic Hall ribbons.Science349, 1510–1513 (2015)..

Stuhl, B. K. et al. Visualizing edge states withan atomic Bose gas in the quantum Hall regime.Science349, 1514–1518 (2015)..

Lin, Q. et al. Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension.Nat. Commun.7, 13731 (2016)..

Lin, Q. et al. A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension.Sci. Adv.4, eaat2774 (2018)..

Yuan, L. et al. Synthetic space with arbitrary dimensions in a few rings undergoing dynamic modulation.Phys. Rev. B97, 104105 (2018)..

Martin, I., Refael, G.&Halperin, B. Topological frequency conversion in strongly driven quantum systems.Phys. Rev. X7, 041008 (2017)..

Dutt, A. et al. A single photonic cavity with two independent physical synthetic dimensions.Science367, 59–64 (2020)..

Yuan, L. et al. Photonic gauge potential in one cavity with synthetic frequency and orbital angular momentum dimensions.Phys. Rev. Lett.122, 083903 (2019)..

Reimer, C. et al. High-dimensional frequency crystals and quantum walks in electro-optic microcombs. Preprint at 1909.01303 (2019).

Spreeuw, R. J. C. et al. Classical realization of a strongly driven two-level system.Phys. Rev. Lett.65, 2642–2645 (1990)..

Zhang, M. et al. Electronically programmable photonic molecule.Nat. Photonics13, 36–40 (2019)..

Su, W. P., Schrieffer, J. R.&Heeger, A. J. Solitons in polyacetylene.Phys. Rev. Lett.42, 1698–1701 (1979)..

Majumdar, A. et al. Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule.Phys. Rev. B86, 045315 (2012)..

Galbiati, M. et al. Polariton condensation in photonic molecules.Phys. Rev. Lett.108, 126403 (2012)..

Dutt, A. et al. Tunable squeezing using coupled ring resonators on a silicon nitride chip.Opt. Lett.41, 223–226 (2016)..

Nakagawa, A., Ishii, S.&Baba, T. Photonic molecule laser composed of GaInAsP microdisks.Appl. Phys. Lett.86, 041112 (2005)..

Dutt, A. et al. Experimental band structure spectroscopy along a synthetic dimension.Nat. Commun.10, 3122 (2019)..

Yuan, L.&Fan, S. Topologically nontrivial Floquet band structure in a system undergoing photonic transitions in the ultrastrong-coupling regime.Phys. Rev. A92, 053822 (2015)..

Minkov, M.&Savona, V. Haldane quantum Hall effect for light in a dynamically modulated array of resonators.Optica3, 200–206 (2016)..

Fang, K., Yu, Z.&Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation.Nat. Photonics6, 782–787 (2012)..

Dutt, A. et al. Experimental demonstration of dynamical input isolation in nonadiabatically modulated photonic cavities.ACS Photonics6, 162–169 (2019)..

Benalcazar, W. A., Bernevig, B. A.&Hughes, T. L. Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators.Phys. Rev. B96, 245115 (2017)..

Xie, B. Y. et al. Second-order photonic topological insulator with corner states.Phys. Rev. B98, 205147 (2018)..

Benalcazar, W. A.&Cerjan, A. Bound states in the continuum of higher-order topological insulators.Phys. Rev. B101, 161116(R) (2020)..

Ota, Y. et al. Photonic crystal nanocavity based on a topological corner state.Optica6, 786–789 (2019)..

Hafezi, M. et al. Imaging topological edge states in silicon photonics.Nat. Photonics7, 1001–1005 (2013)..

Chu, S. T. et al. An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid.IEEE Photonics Technol. Lett.11, 691–693 (1999)..

Sherwood-Droz, N.&Lipson, M. Scalable 3D dense integration of photonics on bulk silicon.Opt. Express19, 17758–17765 (2011)..

Grover, R. et al. Vertically coupled GaInAsP–InP microring resonators.Opt. Lett.26, 506–508 (2001)..

Yanagase, Y. et al. Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter.J. Lightwave Technol.20, 1525–1529 (2002)..

Tzuang, L. D. et al. High RF carrier frequency modulation in silicon resonators by coupling adjacent free-spectral-range modes.Opt. Lett.39, 1799–1802 (2014)..

Zhang, M. et al. Broadband electro-optic frequency comb generation in a lithium niobate microring resonator.Nature568, 373–377 (2019)..

Rueda, A. et al. Resonant electro-optic frequency comb.Nature568, 378–381 (2019)..

Zhang, W.&Zhang, X. Photonic quadrupole topological phases in zero-dimensional cavity with synthetic dimensions. Preprint at 1906.02967 (2019).

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