Experimental band structure spectroscopy along a synthetic dimension
Open accessAbstract
There has been significant recent interest in synthetic dimensions, where internal degrees of freedom of a particle are coupled to form higher-dimensional lattices in lower-dimensional physical structures. For these systems, the concept of band structure along the synthetic dimension plays a central role in their theoretical description. Here we provide a direct experimental measurement of the band structure along the synthetic dimension. By dynamically modulating a resonator at frequencies commensurate with its mode spacing, we create a periodically driven lattice of coupled modes in the frequency dimension. The strength and range of couplings can be dynamically reconfigured by changing the modulation amplitude and frequency. We show theoretically and demonstrate experimentally that time-resolved transmission measurements of this system provide a direct readout of its band structure. We also realize long-range coupling, gauge potentials and nonreciprocal bands by simply incorporating additional frequency drives, enabling great flexibility in band structure engineering.
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If such a closed loop in the Brillouin zone encircles a Dirac point, the winding of the trajectory can be associated with the topological charge of the Dirac point.
“If such a closed loop in the Brillouin zone encircles a Dirac point, the winding of the trajectory can be associated with the topological charge of the Dirac point [44,45].”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [45]
The Results > Theory section describes Bloch quasimomentum and Floquet band-structure measurements, while Results > Experimental results discusses a Brillouin zone and synthetic gauge potentials; page numbers are unavailable in our copy. Searches for Dirac points, winding, closed loops, and topological charge found no passage connecting a loop around a Dirac point to its charge. (LLM, conf=0.76)
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Cheng, D., Wang, K., Roques-Carmes, C., Lustig, E., Long, O. Y., Wang, H., & Fan, S. (2025) · Nature · doi:10.1038/s41586-024-08259-2 · Cited by 58 · see citing works
“We can, therefore, assume that the laser frequency detuning δω remains the same within a single roundtrip time T R = 250 ns, but is slightly different for neighbouring roundtrips 45 .”
Self-citationBloch oscillations of coherently driven dissipative solitons in a synthetic dimension
Englebert, N., Goldman, N., Erkintalo, M. J., Mostaan, N., Gorza, S.-P., Léo, F., & Fatome, J. (2023) · Nature Physics · doi:10.1038/s41567-023-02005-7 · Cited by 67 · see citing works
Nonreciprocal Transport Based on Cavity Floquet Modes in Optomechanics
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Arbitrary linear transformations for photons in the frequency synthetic dimension
Buddhiraju, S., Dutt, A., Minkov, M., Williamson, I. A. D., & Fan, S. (2021) · RePEc: Research Papers in Economics · Cited by 55 · see citing works
Self-citationComprehensive review on developments of synthetic dimensions
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Self-citationDynamic band structure measurement in the synthetic space
Li, G., Zheng, Y., Dutt, A., Yu, D., Shan, Q., Liu, S., Yuan, L., Fan, S., & Chen, X. (2021) · Science Advances · doi:10.1126/sciadv.abe4335 · Cited by 57 · see citing works
Self-citationProgrammable large-scale simulation of bosonic transport in optical synthetic frequency lattices
Senanian, A., Wright, L. G., Wade, P. F., Doyle, H. K., & McMahon, P. L. (2023) · Nature Physics · doi:10.1038/s41567-023-02075-7 · Cited by 53 · see citing works
Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion
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Piezoelectric actuation for integrated photonics
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Real-time observation of frequency Bloch oscillations with fibre loop modulation
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Nonlinear states and dynamics in a synthetic frequency dimension
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Experimental realization of convolution processing in photonic synthetic frequency dimensions
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Self-citationArtificial Non-Abelian Lattice Gauge Fields for Photons in the Synthetic Frequency Dimension
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Self-citationA Perspective on Synthetic Dimensions in Photonics
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Multi-dimensional band structure spectroscopy in the synthetic frequency dimension
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Self-citationOrbital topological edge states and phase transitions in one-dimensional acoustic resonator chains
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Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems
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Theory of chiral edge state lasing in a two-dimensional topological system
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Mirror-induced reflection in the frequency domain
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Geometric characterization of anomalous Landau levels of isolated flat bands
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Multidimensional Convolution Operation with Synthetic Frequency Dimensions in Photonics
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Self-citationRealization of exceptional points along a synthetic orbital angular momentum dimension
Yang, M., Zhang, H., Liao, Y., Liu, Z., Zhou, Z.-W., Zhou, X., Xu, J., Han, Y., Li, C., & Guo, G. (2023) · Science Advances · doi:10.1126/sciadv.abp8943 · Cited by 38 · see citing works
Wave-Function Tomography of Topological Dimer Chains with Long-Range Couplings
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Time reflection and refraction in synthetic frequency dimension
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Self-citationTopological band structure via twisted photons in a degenerate cavity
Yang, M., Zhang, H., Liao, Y., Liu, Z., Zhou, Z.-W., Zhou, X., Xu, J., Han, Y., Li, C., & Guo, G. (2022) · Nature Communications · doi:10.1038/s41467-022-29779-3 · Cited by 34 · see citing works
Time-variant metasurfaces enable tunable spectral bands of negative extinction
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Creating locally interacting Hamiltonians in the synthetic frequency dimension for photons
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Self-citationObserving non-Hermiticity induced chirality breaking in a synthetic Hall ladder
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Self-citationTopological holographic quench dynamics in a synthetic frequency dimension
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Self-citationReconfigurable synthetic dimension frequency lattices in an integrated lithium niobate ring cavity
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Ultrafast All-Optical Metasurfaces: Challenges and New Frontiers
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General construction scheme for geometrically nontrivial flat band models
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Self-citationObservation of flat-band and band transition in the synthetic space
Li, G., Wang, L., Ye, R., Liu, S., Zheng, Y., Yuan, L., & Chen, X. (2022) · Advanced Photonics · doi:10.1117/1.ap.4.3.036002 · Cited by 23 · see citing works
Self-citationPropagation of microwave photons along a synthetic dimension
Lee, N., Pechal, M., Wollack, E. A., Arrangoiz-Arriola, P., Wang, Z., & Safavi‐Naeini, A. H. (2020) · Physical Review A · doi:10.1103/physreva.101.053807 · Cited by 21 · see citing works
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Self-citationCounterdiabatic Driving for Periodically Driven Systems
Schindler, P. M., & Bukov, M. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.123402 · Cited by 21 · see citing works
Tunable super- and subradiant boundary states in one-dimensional atomic arrays
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Self-citationGuiding and confining of light in a two-dimensional synthetic space using electric fields
Chalabi, H., Barik, S., Mittal, S., Murphy, T. E., Hafezi, M., & Edo Waks, A. (2020) · Optica · doi:10.1364/optica.386347 · Cited by 21 · see citing works
Photonic Topological Spin Pump in Synthetic Frequency Dimensions
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Self-citationKapitza light guiding in photonic mesh lattice
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Self-citationOn-Chip Photonic Simulating Band Structures toward Arbitrary-Range Coupled Frequency Lattices
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Colloquium : Synthetic quantum matter in nonstandard geometries
Graß, T., Bercioux, D., Bhattacharya, U., Lewenstein, M., Nguyen, H. S., & Weitenberg, C. (2025) · Reviews of Modern Physics · doi:10.1103/revmodphys.97.011001 · Cited by 19 · see citing works
Arbitrary synthetic dimensions via multiboson dynamics on a one-dimensional lattice
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Self-citationPhonon-induced anomalous gauge potential for photonic isolation in frequency space
Yang, J., Yuan, L., Qin, T., Zhang, F., Chen, Y., Jiang, X., Chen, X., Fan, S., & Wan, W. (2021) · Optica · doi:10.1364/optica.429945 · Cited by 19 · see citing works
Self-citationSimulating topological materials with photonic synthetic dimensions in cavities
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Collective quench dynamics of active photonic lattices in synthetic dimensions
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Synthetic $${{\mathbb{Z}}}_{2}$$ gauge theories based on parametric excitations of trapped ions
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Flow equations for disordered Floquet systems
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Self-citationDeep-learning-empowered synthetic dimension dynamics: morphing of light into topological modes
Xia, S., Lei, S., Song, D., Lauro, L. D., Alamgir, I., Tang, L., Xu, J., Morandotti, R., Buljan, H., & Chen, Z. (2024) · Advanced Photonics · doi:10.1117/1.ap.6.2.026005 · Cited by 15 · see citing works
Topological insulator in two synthetic dimensions based on an optomechanical resonator
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Classifying topology in photonic crystal slabs with radiative environments
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Synthetic Non-Abelian Electric Fields and Spin-Orbit Coupling in Photonic Synthetic Dimensions
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Synthetic dimensions and topological chiral currents in mesoscopic rings
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Single-Photon Transport in a Topological Waveguide from a Dynamically Modulated Photonic System
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Self-citationPT -symmetric non-Hermitian zigzag-edged ribbon of bilayer photonic graphene
Zhang, L.-L., Li, J., Zhang, D., Xu, T., Cui, W., & Gong, W. (2022) · Results in Physics · doi:10.1016/j.rinp.2022.105274 · Cited by 13 · see citing works
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Construction of Various Time-Varying Hamiltonians on Thin-Film Lithium Niobate Chip
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Self-citationAll-Optical Control of the Photonic Hall Lattice in a Pumped Waveguide Array
Lin, S., Wang, L., Yuan, L., & Chen, X. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.17.064029 · Cited by 11 · see citing works
Self-citationSimulating graphene dynamics in synthetic space with photonic rings
Yu, D., Li, G., Xiao, M., Wang, D., Wan, Y., Yuan, L., & Chen, X. (2021) · Communications Physics · doi:10.1038/s42005-021-00719-9 · Cited by 11 · see citing works
Self-citationUltra high-Q tunable microring resonators enabled by slow light
Barya, P., Prabhu, A. V., Heller, L., Chow, E. K. C., & Goldschmidt, E. A. (2025) · Nature Communications · doi:10.1038/s41467-025-65533-1 · Cited by 11 · see citing works
Villa, G., Carusotto, I., & Ozawa, T. (2024) · Communications Physics · doi:10.1038/s42005-024-01727-1 · Cited by 10 · see citing works
Frequency modulation on magnons in synthetic dimensions
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Quadrature-dependent lattice dynamics of dissipative microcombs
Lustig, E., Guidry, M. A., Lukin, D. M., Fan, S., & Vučković, J. (2025) · Nature Photonics · doi:10.1038/s41566-025-01777-z · Cited by 11 · see citing works
Self-citationQuadrupole topological phases in the zero-dimensional optical cavity
Zhang, W., & Zhang, X. (2020) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/131/24004 · Cited by 10 · see citing works
Single-shot measurement of the photonic band structure in a fiber-based Floquet-Bloch lattice
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Dynamical signatures of point-gap Weyl semimetal
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Weakly Dispersive Band in Synthetic Moiré Superlattice Inducing Optimal Compact Comb Generation
Li, G., He, Y., Wang, L., Yang, Y., Yu, D., Zheng, Y., Yuan, L., & Chen, X. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.083803 · Cited by 9 · see citing works
Self-citationStrong-coupling and high-bandwidth cavity electro-optic modulation for advanced pulse-comb synthesis
Lei, T., Song, Y., Xue, Y., Gong, Q., Lončar, M., & Hu, Y. (2025) · Light Science & Applications · doi:10.1038/s41377-025-02046-y · Cited by 9 · see citing works
Mode-locking in anti-PT symmetric frequency lattices
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Realization of edge states along a synthetic orbital angular momentum dimension
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Quantized Hall Drift in a Frequency-Encoded Photonic Chern Insulator
Chénier, A., d'Aligny, B., Pellerin, F., Blanchard, P.-É., Ozawa, T., Carusotto, I., & St-Jean, P. (2026) · Physical Review X · doi:10.1103/2dyh-yhrb · Cited by 11 · see citing works
- Authors
- Dutt, A., Minkov, M., Lin, Q., Yuan, L., Miller, D. A. B., & Fan, S.
- Affiliations
- Stanford University (US)
- Shanghai Jiao Tong University (CN)
- Corresponding author
- Yuan, Luqi
- Fan, Shanhui
- Venue
- Nature Communications
- Published
- 2019-07-16
- Volume
- 10
- Issue
- 1
- Pages
- 3122-3122
- ISSN
- 2041-1723 (ISSN-L)
- PMC
- PMC6635488
- OpenAlex
- W2951236500
- Cited by
- 178
- References
- 75
- Citations by year
- 2026: 22 · 2025: 37 · 2024: 23 · 2023: 21 · 2022: 17 · 2021: 30 · 2020: 22 · 2019: 5 · 2018: 1
- FWCI
- 8.13
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Nature Communications (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion, cc-by-nc-sa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Figshare (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- United States Department of Defense | United States Navy | Office of Naval Research (N00014-17-1-3030)
- United States Department of Defense | United States Air Force | AFMC | Air Force Office of Scientific Research (FA9550-17-1-0002)
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (P300P2_177721)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Engineering › Biomedical Engineering › Acoustic Wave Phenomena Research
- Keywords
- synthetic dimensions, electronic band structure, long-range coupling, gauge potential, band structure engineering
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