CoChat
Sign Up
Cited by 65Topological Materials and PhenomenaQuantum Mechanics and Non-Hermitian PhysicsMetamaterials and Metasurfaces Applications

Creating boundaries along a synthetic frequency dimension

Open access
Dutt, Avik, Yuan, Luqi, Yang, Ki Youl, Wang, Kai, Buddhiraju, Siddharth, Vučković, Jelena, Fan, Shanhui·2022·Nature Communications
DOI 10.1038/s41467-022-31140-7PMC PMC9192711
Open this paper in CoChat — free accountOpen PDF

Abstract

Synthetic dimensions have garnered widespread interest for implementing high dimensional classical and quantum dynamics on low-dimensional geometries. Synthetic frequency dimensions, in particular, have been used to experimentally realize a plethora of bulk physics effects. However, in synthetic frequency dimension there has not been a demonstration of a boundary which is of paramount importance in topological physics due to the bulk-edge correspondence. Here we construct boundaries in the frequency dimension of dynamically modulated ring resonators by strongly coupling an auxiliary ring. We explore various effects associated with such boundaries, including confinement of the spectrum of light, discretization of the band structure, and the interaction of boundaries with one-way chiral modes in a quantum Hall ladder, which exhibits topologically robust spectral transport. Our demonstration of sharp boundaries fundamentally expands the capability of exploring topological physics, and has applications in classical and quantum information processing in synthetic frequency dimensions.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1038/s41467-022-31140-7

Cites

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Dirac points are common in two-dimensional systems.

    “Dirac points are common in two-dimensional systems [46][47][48].”

    From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [48]

    The Results section, “Demonstration of boundary effects in a quantum Hall ladder” (page unavailable), discusses chiral modes and a parent 2D quantum Hall lattice, not Dirac points. Searches for “Dirac points,” “Dirac cones,” and “Dirac” found no passage in our copy addressing whether Dirac points are common in two-dimensional systems. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

  • In many existing works Dirac points are observed only at time-reversal-breaking wavevectors, such as the K- and K'-points in a honeycomb lattice.

    “However, in many existing works Dirac points are observed only at time-reversal-breaking wavevectors, such as the Kand K'-points in a honeycomb lattice [46][47][48].”

    From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [48]

    The Results section on the quantum Hall ladder discusses time-reversal symmetry breaking and chiral modes, but not Dirac points or where they occur. Searches for “Dirac,” “honeycomb,” and K/K′ wavevectors found no passage addressing the claimed pattern across existing works. Page numbers are unavailable in our copy. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

The citation lists haven’t been fetched yet

References 61 · Cited by 65

Research works printed but not linked: 52

  1. [1]Boada O Celi A Latorre JI Lewenstein M Quantum simulation of an extra dimension Phys. Rev. Lett. 2012 108 133001 10.1103/PhysRevLett.108.133001 22540696 · DOI
  2. [2]Yuan L Lin Q Xiao M Fan S Synthetic dimension in photonics Optica 2018 5 1396 1405 10.1364/OPTICA.5.001396 · DOI · Paper page
  3. [4]Mancini M Observation of chiral edge states with neutral fermions in synthetic Hall ribbons Science 2015 349 1510 1513 10.1126/science.aaa8736 26404829 · DOI
  4. [5]Yuan L Shi Y Fan S Photonic gauge potential in a system with a synthetic frequency dimension Opt. Lett. 2016 41 741 744 10.1364/OL.41.000741 26872177 · DOI
  5. [6]Ozawa T Price HM Goldman N Zilberberg O Carusotto I Synthetic dimensions in integrated photonics: from optical isolation to four-dimensional quantum Hall physics Phys. Rev. A 2016 93 043827 10.1103/PhysRevA.93.043827 · DOI · Paper page
  6. [7]Luo X-W Quantum simulation of 2D topological physics in a 1D array of optical cavities Nat. Commun. 2015 6 7704 10.1038/ncomms8704 26145177 PMC4506549 · DOI · Paper page
  7. [8]Regensburger A Parity-time synthetic photonic lattices Nature 2012 488 167 171 10.1038/nature11298 22874962 · DOI · Paper page
  8. [9]Chalabi H Synthetic gauge field for two-dimensional time-multiplexed quantum random walks Phys. Rev. Lett. 2019 123 150503 10.1103/PhysRevLett.123.150503 31702283 · DOI
  9. [11]Lustig E Photonic topological insulator in synthetic dimensions Nature 2019 567 356 360 10.1038/s41586-019-0943-7 30778196 · DOI
  10. [12]Thouless DJ Kohmoto M Nightingale MP den Nijs M Quantized Hall conductance in a two-dimensional periodic potential Phys. Rev. Lett. 1982 49 405 408 10.1103/PhysRevLett.49.405 · DOI · Paper page
  11. [13]Su WP Schrieffer JR Heeger AJ Solitons in polyacetylene Phys. Rev. Lett. 1979 42 1698 1701 10.1103/PhysRevLett.42.1698 · DOI · Paper page
  12. [14]Benalcazar WA Bernevig BA Hughes TL Quantized electric multipole insulators Science 2017 357 61 66 10.1126/science.aah6442 28684520 · DOI · Paper page
  13. [15]Dutt A Minkov M Williamson IAD Fan S Higher-order topological insulators in synthetic dimensions Light.: Sci. Appl. 2020 9 131 10.1038/s41377-020-0334-8 32704364 PMC7371732 · DOI
  14. [16]Mittal S Photonic quadrupole topological phases Nat. Photonics 2019 13 692 696 10.1038/s41566-019-0452-0 · DOI
  15. [17]Okuma N Kawabata K Shiozaki K Sato M Topological origin of non-Hermitian skin effects Phys. Rev. Lett. 2020 124 086801 10.1103/PhysRevLett.124.086801 32167324 · DOI
  16. [18]Weidemann S Topological funneling of light Science 2020 368 311 314 10.1126/science.aaz8727 32217752 · DOI
  17. [19]Bergholtz EJ Budich JC Kunst FK Exceptional topology of non-Hermitian systems Rev. Mod. Phys. 2021 93 015005 10.1103/RevModPhys.93.015005 · DOI
  18. [20]Ghatak A Brandenbourger M van Wezel J Coulais C Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial Proc. Natl Acad. Sci. USA 2020 117 29561 29568 10.1073/pnas.2010580117 33168722 PMC7703544 · DOI
  19. [21]Buddhiraju S Dutt A Minkov M Williamson IAD Fan S Arbitrary linear transformations for photons in the frequency synthetic dimension Nat. Commun. 2021 12 2401 10.1038/s41467-021-22670-7 33893284 PMC8065043 · DOI
  20. [22]Chen H Real-time observation of frequency Bloch oscillations with fibre loop modulation Light.: Sci. Appl. 2021 10 48 10.1038/s41377-021-00494-w 33674556 PMC7935930 · DOI
  21. [23]Lee NRA Propagation of microwave photons along a synthetic dimension Phys. Rev. A 2020 101 053807 10.1103/PhysRevA.101.053807 · DOI
  22. [24]Bersch C Onishchukov G Peschel U Experimental observation of spectral Bloch oscillations Opt. Lett. 2009 34 2372 2374 10.1364/OL.34.002372 19649101 · DOI
  23. [25]Hu Y Reimer C Shams-Ansari A Zhang M Loncar M Realization of high-dimensional frequency crystals in electro-optic microcombs Optica 2020 7 1189 1194 10.1364/OPTICA.395114 · DOI
  24. [26]Li G Dynamic band structure measurement in the synthetic space Sci. Adv. 2021 7 eabe4335 10.1126/sciadv.abe4335 33524000 PMC7793575 · DOI
  25. [27]Dutt A A single photonic cavity with two independent physical synthetic dimensions Science 2020 367 59 64 10.1126/science.aaz3071 31780626 · DOI
  26. [28]Wang K Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion Light.: Sci. Appl. 2020 9 132 10.1038/s41377-020-0299-7 32704365 PMC7371864 · DOI · Paper page
  27. [29]Balčytis A Synthetic dimension band structures on a Si CMOS photonic platform Sci. Adv. 2022 8 eabk0468 10.1126/sciadv.abk0468 35089790 PMC8797776 · DOI
  28. [30]Qin C Spectrum control through discrete frequency diffraction in the presence of photonic Gauge potentials Phys. Rev. Lett. 2018 120 133901 10.1103/PhysRevLett.120.133901 29694196 · DOI
  29. [31]Bell BA Spectral photonic lattices with complex long-range coupling Optica 2017 4 1433 1436 10.1364/OPTICA.4.001433 · DOI
  30. [33]Wang K Generating arbitrary topological windings of a non-Hermitian band Science 2021 371 1240 1245 10.1126/science.abf6568 33737483 · DOI
  31. [34]Wang K Dutt A Wojcik CC Fan S Topological complex-energy braiding of non-Hermitian bands Nature 2021 598 59 64 10.1038/s41586-021-03848-x 34616054 · DOI
  32. [35]Schwennicke K Yuen-Zhou J Enantioselective topological frequency conversion J. Phys. Chem. Lett. 2022 13 2434 2441 10.1021/acs.jpclett.1c04161 35259295 · DOI
  33. [36]Shan Q Yu D Li G Yuan L Chen aX One-way topological states along vague boundaries in synthetic frequency dimensions including group velocity dispersion (invited) Prog. Electromagn. Res. 2020 169 33 43 10.2528/PIER20083101 · DOI
  34. [37]Baum Y Refael G Setting boundaries with memory: generation of topological boundary states in floquet-induced synthetic crystals Phys. Rev. Lett. 2018 120 106402 10.1103/PhysRevLett.120.106402 29570341 · DOI
  35. [38]Yuan L Dutt A Fan S Synthetic frequency dimensions in dynamically modulated ring resonators APL Photonics 2021 6 071102 10.1063/5.0056359 · DOI
  36. [39]Haldar R Das S Varshney SK Theory and design of off-axis microring resonators for high-density on-chip photonic applications J. Lightwave Technol. 2013 31 3976 3986 10.1109/JLT.2013.2278552 · DOI
  37. [40]Souza MCMM Embedded coupled microrings with high-finesse and close-spaced resonances for optical signal processing Opt. Express 2014 22 10430 10.1364/OE.22.010430 24921744 · DOI
  38. [41]Li, G. et al. Observation of flat-band and band transition in the synthetic space. arXiv:2108.11581 (2021). · arXiv
  39. [42]Wang J Simultaneous observation of superluminal and slow light propagation in a nested fiber ring resonator Opt. Express 2010 18 13180 13186 10.1364/OE.18.013180 20588446 · DOI
  40. [43]Haldar R Banik AD Varshney SK Design of CMOS compatible and compact, thermally-compensated electro-optic modulator based on off-axis microring resonator for dense wavelength division multiplexing applications Opt. Express 2014 22 22411 10.1364/OE.22.022411 25321712 · DOI
  41. [44]Hu Y On-chip electro-optic frequency shifters and beam splitters Nature 2021 599 587 593 10.1038/s41586-021-03999-x 34819680 · DOI
  42. [45]Smith DD Chang H Fuller KA Rosenberger AT Boyd RW Coupled-resonator-induced transparency Phys. Rev. A 2004 69 063804 10.1103/PhysRevA.69.063804 · DOI
  43. [46]Dutt A Experimental demonstration of dynamical input isolation in nonadiabatically modulated photonic cavities ACS Photonics 2019 6 162 169 10.1021/acsphotonics.8b01310 · DOI
  44. [47]Hügel D Paredes B Chiral ladders and the edges of quantum Hall insulators Phys. Rev. A 2014 89 023619 10.1103/PhysRevA.89.023619 · DOI
  45. [50]Tzuang LD Soltani M Lee YHD Lipson M High RF carrier frequency modulation in silicon resonators by coupling adjacent free-spectral-range modes Opt. Lett. 2014 39 1799 1802 10.1364/OL.39.001799 24686608 · DOI
  46. [51]Yuan L Photonic gauge potential in one cavity with synthetic frequency and orbital angular momentum dimensions Phys. Rev. Lett. 2019 122 083903 10.1103/PhysRevLett.122.083903 30932579 · DOI
  47. [52]Yuan L Xiao M Lin Q Fan S Synthetic-space with arbitrary dimensions in a few rings undergoing dynamic modulation Phys. Rev. B 2018 97 104105 10.1103/PhysRevB.97.104105 · DOI · Paper page
  48. [53]Lu X Rao A Moille G Westly DA Srinivasan K Universal frequency engineering tool for microcavity nonlinear optics: multiple selective mode splitting of whispering-gallery resonances Photon. Res. 2020 8 1676 1686 10.1364/PRJ.401755 PMC8607357 34815982 · DOI
  49. [54]Lu X McClung A Srinivasan K High-Q slow light and its localization in a photonic crystal microring Nat. Photon. 2022 16 66 71 10.1038/s41566-021-00912-w · DOI
  50. [56]Numata K Camp J Krainak MA Stolpner L Performance of planar-waveguide external cavity laser for precision measurements Opt. Express 2010 18 22781 22788 10.1364/OE.18.022781 21164616 · DOI
  51. [57]Martin I Floquet dynamics of classical and quantum cavity fields Ann. Phys. 2019 405 101 129 10.1016/j.aop.2019.03.017 · DOI
  52. [58]Yuan L Lin Q Xiao M Dutt A Fan S Pulse shortening in an actively mode-locked laser with parity-time symmetry APL Photonics 2018 3 086103 10.1063/1.5039375 · DOI

Authors
Dutt, A., Yuan, L., Yang, K. Y., Wang, K., Buddhiraju, S., Vučković, J., & Fan, S.
Affiliations
  • University of Maryland, College Park (US)
  • Shanghai Jiao Tong University (CN)
  • Stanford University (US)
Corresponding author
Fan, Shanhui
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2022-06-13
Volume
13
Issue
1
Pages
3377-3377
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-022-31140-7
PMC
PMC9192711
OpenAlex
W4226115176
Cited by
65
References
61
Citations by year
2026: 15 · 2025: 18 · 2024: 15 · 2023: 11 · 2022: 6
FWCI
5.13
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • United States Department of Defense | United States Air Force | AFMC | Air Force Office of Scientific Research (FA9550-18-1-0379)
  • National Natural Science Foundation of China (11974245, 12122407)
  • U.S. Department of Defense (N00014-17-1-3030)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
  • Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
Keywords
synthetic frequency dimension, synthetic dimensions, boundaries, bulk-boundary correspondence, ring resonator, chiral modes, topological photonics, spectral confinement

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review