Multi-dimensional band structure spectroscopy in the synthetic frequency dimension

Dali Cheng; Eran Lustig; Kai Wang; Shanhui Fan

doi:10.1038/s41377-023-01196-1

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Multi-dimensional band structure spectroscopy in the synthetic frequency dimension

Original Articles

- Multi-dimensional band structure spectroscopy in the synthetic frequency dimension
- Light: Science & Applications Vol. 12, Issue 7, Pages: 1425-1433(2023)
- Affiliations：
  
  1.Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
  2.Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada
- Author bio：
  
  Shanhui Fan (shanhui@stanford.edu)
- Funds：
- DOI：10.1038/s41377-023-01196-1
  CLC：
- Published：31 July 2023，
  
  Published Online：27 June 2023，
  
  Received：21 March 2023，
  
  Revised：23 May 2023，
  
  Accepted：26 May 2023
- Accepted：
Scan QR Code
Cheng, D. L. et al. Multi-dimensional band structure spectroscopy in the synthetic frequency dimension. Light: Science & Applications, 12, 1425-1433 (2023).
DOI：

Cheng, D. L. et al. Multi-dimensional band structure spectroscopy in the synthetic frequency dimension. Light: Science & Applications, 12, 1425-1433 (2023). DOI： 10.1038/s41377-023-01196-1.

摘要

Abstract

The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional physics. Many of these physics are characterized by band structures in more than one dimensions. Existing efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either one-dimensional Brillouin zones or one-dimensional subsets of multi-dimensional Brillouin zones. Here we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency dimension. We use a single photonic resonator under dynamical modulation to create a multi-dimensional synthetic frequency lattice. We show that the band structure of such a lattice over the entire multi-dimensional Brillouin zone can be measured by introducing a gauge potential into the lattice Hamiltonian. Using this method

we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian Hamiltonian. The measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one dimensions. Our results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension.

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references

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

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. Synthetic-lattice enabled all-optical devices based on orbital angular momentum of light.Nat. Commun.8, 16097 (2017)..

Bell, B. A. et al. Spectral photonic lattices with complex long-range coupling.Optica4, 1433–1436 (2017)..

Zilberberg, O. et al. Photonic topological boundary pumping as a probe of 4D quantum Hall physics.Nature553, 59–62 (2018)..

Qin, C. Z. et al. Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials.Phys. Rev. Lett.120, 133901 (2018)..

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

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

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

Chalabi, H. et al. Synthetic gauge field for two-dimensional time-multiplexed quantum random walks.Phys. Rev. Lett.123, 150503 (2019)..

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

Chalabi, H. et al. Guiding and confining of light in a two-dimensional synthetic space using electric fields.Optica7, 506–513 (2020)..

Dutt, A. et al. Higher-order topological insulators in synthetic dimensions.Light Sci. Appl.9, 131 (2020)..

Wang, K. et al. Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion.Light Sci. Appl.9, 132 (2020)..

Hu, Y. W. et al. Realization of high-dimensional frequency crystals in electro-optic microcombs.Optica7, 1189–1194 (2020)..

Lustig, E.&Segev, M. Topological photonics in synthetic dimensions.Adv. Opt. Photon.13, 426–461 (2021)..

Cheng, D. L. et al. Arbitrary synthetic dimensions via multiboson dynamics on a one-dimensional lattice.Phys. Rev. Res.3, 033069 (2021)..

Leefmans, C. et al. Topological dissipation in a time-multiplexed photonic resonator network.Nat. Phys.18, 442–449 (2022)..

Hu, Y. W. et al. Mirror-induced reflection in the frequency domain.Nat. Commun.13, 6293 (2022)..

Cheng, D. L., Wang, K.&Fan, S. H. Artificial non-Abelian latticegauge fields for photons in the synthetic frequency dimension.Phys. Rev. Lett.130, 083601 (2023)..

Weidemann, S. et al. Topological funneling of light.Science368, 311–314 (2020)..

Wang, K. et al. Generating arbitrary topological windings of a non-Hermitian band.Science371, 1240–1245 (2021)..

Wang, K. et al. Topological complex-energy braiding of non-Hermitian bands.Nature598, 59–64 (2021)..

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

Li, G. Z. et al. Dynamic band structure measurement in the synthetic space.Sci. Adv.7, eabe4335 (2021)..

Yang, M. et al. Topological band structure via twisted photons in a degenerate cavity.Nat. Commun.13, 2040 (2022)..

Li, G. Z. et al. Direct extraction of topological Zak phase with the synthetic dimension.Light Sci. Appl.12, 81 (2023)..

Balčytis, A. et al. Synthetic dimension band structures on a Si CMOS photonic platform.Sci. Adv.8, eabk0468 (2022)..

Dutt, A. et al. Creating boundaries along a synthetic frequency dimension.Nat. Commun.13, 3377 (2022)..

Senanian, A. et al. Programmable large-scale simulation of bosonic transport in optical synthetic frequency lattices.Nat. Phys.(2023).

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

Fang, K. J., Yu, Z. F.&Fan, S. H. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation.Nat. Photon.6, 782–787 (2012)..

Bender, C. M. et al. Faster than Hermitian quantum mechanics.Phys. Rev. Lett.98, 040403 (2007)..

Barreiro, J. T. et al. An open-system quantum simulator with trapped ions.Nature470, 486–491 (2011)..

Zheng, C., Hao, L.&Long, G. L. Observation of a fast evolution in a parity-time-symmetric system.Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.371, 20120053 (2013)..

Sergi, A.&Zloshchastiev, K. G. Quantum entropy of systems described by non-Hermitian Hamiltonians.J. Stat. Mech. TheoryExp.2016, 033102 (2016)..

Wen, J. W. et al. Observation of information flow in the anti-PT-symmetric system with nuclear spins.npj Quant. Inf.6, 28 (2020)..

Del Re, L. et al. Driven-dissipative quantum mechanics on a lattice: simulating a fermionic reservoir on a quantum computer.Phys. Rev. B102, 125112 (2020)..

Zheng, C. Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm.Sci. Rep.11, 3960 (2021)..

Li, D. L.&Zheng, C. Non-Hermitian generalization of Rényi entropy.Entropy24, 1563 (2022)..

Wu, C., Fan, A. N.&Liang, S. D. Complex Berry curvature and complex energy band structures in non-Hermitian graphene model.AAPPS Bull.32, 39 (2022)..

Shen, H. T., Zhen, B.&Fu, L. Topological band theory for non-Hermitian Hamiltonians.Phys. Rev. Lett.120, 146402 (2018)..

Gong, Z. P. et al. Topological phases of non-Hermitian systems.Phys. Rev. X8, 031079 (2018)..

Okuma, N. et al. Topological origin of non-Hermitian skin effects.Phys. Rev. Lett.124, 086801 (2020)..

Bergholtz, E. J., Budich, J. C.&Kunst, F. K. Exceptional topology of non-Hermitian systems.Rev. Mod. Phys.93, 015005 (2021)..

Lee, T. E. Anomalous edge state in a non-Hermitian lattice.Phys. Rev. Lett.116, 133903 (2016)..

Yao, S. Y.&Wang, Z. Edge states and topological invariants of non-Hermitian systems.Phys. Rev. Lett.121, 086803 (2018)..

Zhang, K., Yang, Z. S.&Fang, C. Correspondence between winding numbers and skin modes in non-Hermitian systems.Phys. Rev. Lett.125, 126402 (2020)..

Liu, T. et al. Second-order topological phases in non-Hermitian systems.Phys. Rev. Lett.122, 076801 (2019)..

Kawabata, K., Sato, M.&Shiozaki, K. Higher-order non-Hermitian skin effect.Phys. Rev. B102, 205118 (2020)..

Zhong, J. et al. Nontrivial point-gap topology and non-Hermitian skin effect in photonic crystals.Phys. Rev. B104, 125416 (2021)..

Zhang, K., Yang, Z. S.&Fang, C. Universal non-Hermitian skin effect in two and higher dimensions.Nat. Commun.13, 2496 (2022)..

Wojcik, C. C. et al. Eigenvalue topology of non-Hermitian band structures in two and three dimensions.Phys. Rev. B106, L161401 (2022)..

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