Non-Abelian braiding on photonic chips

Zhang, Xu-Lin; Yu, Feng; Chen, Ze‐Guo; Tian, Zhen‐Nan; Chen, Qi‐Dai; Sun, Hong–Bo; Ma, Guancong

doi:10.1038/s41566-022-00976-2

Cited by 78 publications

(40 citation statements)

References 37 publications

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“…Here, we show that Lindbladians involving dissipative couplings can be governed by matrix-valued modified Wilson lines 52 , leading to non-Abelian effects 56,[59][60][61] . To do so, we experimentally measure nontrivial geometric phases and demonstrate signatures of non-Abelian effects in a dissipatively-coupled network of time-multiplexed photonic resonators.…”

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confidence: 87%

“…This is mainly due to the strict requirements, such as the existence of degenerate states in the underlying Hilbert space that are necessary in a conservative system to host non-commutative evolution operators 52,53 . Quite recently, non-Abelian effects and topological charges have been observed in a variety of photonic systems [54][55][56][57] involving coupled waveguide arrays 58,59 and nonreciprocal elements 60 . Despite intense research efforts in this area, studies have exclusively focused on systems with conservative couplings.…”

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confidence: 99%

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Non-Abelian effects in dissipative photonic topological lattices

et al. 2023

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Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to a plethora of intriguing effects such as topological lasing, exceptional surfaces, as well as non-Hermitian bulk-boundary correspondence. Here, we show that Bloch eigenstates associated with lattices with dissipatively coupled elements exhibit geometric properties that cannot be described via scalar Berry phases, in sharp contrast to conservative Hamiltonians with non-degenerate energy levels. This unusual behavior can be attributed to the significant population exchanges among the corresponding dissipation bands of such lattices. Using a one-dimensional example, we show both theoretically and experimentally that such population exchanges can manifest themselves via matrix-valued operators in the corresponding Bloch dynamics. In two-dimensional lattices, such matrix-valued operators can form non-commuting pairs and lead to non-Abelian dynamics, as confirmed by our numerical simulations. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena.

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confidence: 87%

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confidence: 99%

Non-Abelian effects in dissipative photonic topological lattices

et al. 2023

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“…[630,633,634] Although topology has been well investigated in various photonic system, such as, photonic crystals, [636][637][638][639] optical waveguides, [640] metamaterials, [628,632] particles, [641] optical cavities, [642] coupled resonators, [643] silicon photonics and optomechanics, [630] 3D TPL printing enable topological photonics exotic and unique properties, which is hard to realize in 2D system. [632,633,[644][645][646][647][648][649][650][651][652][653][654][655][656][657] Extending topological phenomenon from 2D photonic crystals to 3D version, charge-1 and charge-2 Weyl points are observed experimentally in direct printed photonic crystals (Figure 13f and g) [658] or coated 3D printed photonic crystals (Figure 13h). [659] Because of the mathematical analogy between the paraxial approximation of the Helmholtz equation and the Schrodinger equation, [630,633] photonic waveguide system can be used to examine Floquet topological phenomenon, [660,661] by introducing artificial gauge fields (AGFs) and treating the waveguide axis z as time varying dimension (Figure 13i).…”

Section: Topological Opticsmentioning

confidence: 99%

Two‐Photon Polymerization Lithography for Optics and Photonics: Fundamentals, Materials, Technologies, and Applications

Wang

Zhang

Ladika

et al. 2023

Adv Funct Materials

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The rapid development of additive manufacturing has fueled a revolution in various research fields and industrial applications. Among the myriad of advanced three-dimensional printing techniques, two-photon polymerization lithography (TPL) uniquely offers a significant electron microscope (SEM) images of SMP structures before and after programming and after recovery, respectively. Reproduced under terms of the CC-BY license. [114] Copyright 2021, The Authors, published by Nature Publishing Group. b) Stiff SMPs for high-resolution reversible nanophotonics. I-II) The deformed and recovered nanopillars under optical microscope and SEM, respectively. Reproduced with permission. [115] Copyright 2022, American Chemical Society. c) Vapor-responsive photonic arrays. I-IV) Optical image of a grid array in air, in water vapors ~ 20 s, saturation with water vapors ~ 88s, and after the gas flow stopped, respectively.Reproduced under terms of the CC-BY license. [116] Copyright 2021, The Authors, published by Royal Society of Chemistry. d) SEM image of a 40-layer face-cantered-cubic photonic structure printed by SU-8. Reproduced with permission. [117] Copyright 2004, Nature Publishing Group. e) SEM image of helices with an axial pitch of 800 nm and a radius of 800 nm fabricated by the two-step absorption photoresist. Reproduced with permission. [118]

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“…Since early demonstrations of femtosecond laser as a three-dimensional (3D) processing tool, [1][2][3][4] microdevices with exciting optical, electronic, mechanical, and magnetic functions have been manufactured, [5][6][7][8][9] by which novel concepts from 3D quantum photonic integrated circuits to intelligent micro-robots are enabled. [10][11][12] Much effort in the past decade in this eld has been devoted to improving manufacture resolution, and several tens of nanometer feature sizes, far beyond the optical diffraction limit, have been reported based on multiphoton absorption, 1 stimulation emission depletion, 13,14 fareld-induced near-eld enhancement, 15 and photoexcitation-induced chemical bonding effects. 16 Nevertheless, singleelectron transistors, single-photon emitters, single-atom memory, and quantum-bit devices require higher manufacturing accuracy, i.g., the ability to address single-atom defects complex (SADC) for initiating functions such as single-photon emission, as is still missing.…”

Section: Introductionmentioning

confidence: 99%

Close-to-Atom Scale Laser Manufacturing for 30-Color Turn-key Single-Photon Emitters

Sun

Wang

Fang³

et al. 2023

Preprint

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Atomic and close-to-atom scale manufacturing is now considered an avenue toward single-photon emitters, single-electron transistors, single-atom memory, and quantum-bit devices for future communication, computation, and sensing applications. Laser manufacturing is outstanding to this end for ease of beam manipulation and batch production, and no requirement for photomasks. It is, however, suffering from optical diffraction limit and lacks atomic and close-to-atom scale precision. Herein, we circumvent this limitation by exploiting a threshold tracing-and-lock-in method, whereby the 2-order gap between atomic point defect complexes and optical diffraction limit is surpassed. As a result, bright (up to 10 Mcounts s− 1) single-photon color centers are deterministically created from few-layer hBN with feature size of less than 5 nm and a near-unity yield. Around 94% of them emit monochromatically at around 30 individual wavelengths from 500 nm to 800 nm. A turn-key monochromic single-photon emitter of demanded color is attained by integrating it with 5-V blue laser diodes.

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Non-Abelian braiding on photonic chips

Cited by 78 publications

References 37 publications

Non-Abelian effects in dissipative photonic topological lattices

Non-Abelian effects in dissipative photonic topological lattices

Two‐Photon Polymerization Lithography for Optics and Photonics: Fundamentals, Materials, Technologies, and Applications

Close-to-Atom Scale Laser Manufacturing for 30-Color Turn-key Single-Photon Emitters

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