Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices

Jiao, Zhi-Qiang; Longhi, Stefano; Wang, Xiaowei; Gao, Jun; Zhou, Wen‐Hao; Wang, Yao; Fu, Yu-Xuan; Wang, Li; Ren, Ruo-Jing; Qiao, Lu-Feng; Jin, Xian-Min

doi:10.1103/physrevlett.127.147401

Cited by 58 publications

(22 citation statements)

References 53 publications

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“…2(a,b), can be explained in terms of the asymptotic quantization of the mean displacement that the signal and SFG photons undergo in the tandem quantum walk in the synthetic frequency space. In fact, as shown in previous works [53][54][55][56][57][58] for a gapped 1D topological insulator such a mean displacement is asymptotically quantized and equals the winding number ν ∞ of the topological lattice. According to the bulk-boundary correspondence [41,52,59], |ν ∞ | measures the number of topologically-protected zero-energy edge states, and the quantum walk provides a bulk probing method to measure |ν| [53].…”

Section: Frequency Conversion and Winding Numbersupporting

confidence: 63%

Topological aspects in nonlinear optical frequency conversion

Longhi

2022

Phys. Rev. A

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Nonlinear optical frequency conversion, observed more than half a century ago, is a corner stone in modern applications of nonlinear and quantum optics. It is well known that frequency conversion processes are constrained by conservation laws, such as momentum conservation that requires phase matching conditions for efficient conversion. However, conservation laws alone could not fully capture the features of nonlinear frequency conversion. Here it is shown that topology can provide additional constraints in nonlinear multi-frequency conversion processes. Unlike conservation laws, a topological constraint concerns with the conserved properties under continuous deformation, and can be regarded as a new indispensable degree of freedom to describe multi-frequency processes. We illustrate such a paradigm by considering sum frequency generation under a multi-frequency pump wave, showing that, akin topological phases in topological insulators, topological phase transitions can be observed in the frequency conversion process both at classical and quantum level.

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Section: Frequency Conversion and Winding Numbersupporting

confidence: 63%

Topological aspects in nonlinear optical frequency conversion

Longhi

2022

Phys. Rev. A

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“…Despite the simplicity of the 1D SSH model, the system platforms and physics that could be explored with it are very rich. For example, the 1D SSH model has been studied in diverse photonic platforms, such as, photonic superlattice in a photorefractive material [24], photonic crystal of alternating dielectric slabs [25] or nanobeam cavities [26], quantum emitters interacting with a waveguide [27], split-ring-resonators [28], dielectric nanoparticles [29,30], array of coupled waveguides [31][32][33][34][35][36][37], plasmonic systems [38][39][40][41][42][43][44], and exciton-polaritons [45][46][47][48][49]. The topological edge states of 1D photonic SSH systems have also been observed through imaging, such as, spectral imaging [50], near-field imaging [51](Fig.…”

Section: Topological Photonics In 1dmentioning

confidence: 99%

A brief review of topological photonics in one, two, and three dimensions

Lan,

Chen,

Gao

et al. 2022

Preprint

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FIG. 2. 1D photonic SSH systems and their applications. (a) Near-field imaging of topological edge states in plasmonic nanochains. Reproduced with permission from [51], Copyright (2021), under CC BY-NC-ND. (b) Lasing at the topological edge states in a photonic crystal nanocavity dimer array. Reproduced with permission from [57], Copyright (2019), under CC BY 4.0. (c) Selective enhancement of interface states in a dielectric resonator chain. Reproduced with permission from [60], Copyright (2015), under CC BY 4.0. (d) Periodically bended ultrathin metallic waveguides for the observation of anomalous π modes via photonic floquet engineering. Reproduced with permission from [66], Copyright (2019) by the American Physical Society. (e) Protection of biphoton entanglement in an array of silicon nanowires. Reproduced with permission from [68], Copyright (2018) by the American Association for the Advancement of Science. (f) Photonic topological baths for quantum simulation. Reproduced with permission from [70], Copyright (2022) by the American Chemical Society. (g) Two coupled topological interfaces in waveguide arrays. Reproduced with permission from [72], Copyright (2020) by the American Chemical Society. (h) Selective excitation of topological edge states controlled by the handedness of incident light. Reproduced with permission from [76], Copyright (2016) by John Wiley and Sons.

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“…These edge states are spatially localized on the boundaries of the system, decaying exponentially into the bulk [27,28]. Several recent works have shown (both theoretical and experimentally) that deviations from the tenfold way classification and weakening of the bulk-boundary correspondence may arise when one considers long-ranged interacting systems, e.g., with hopping constants that go beyond nearest neighbors [29][30][31][32][33][34][35][36][37][38][39]. Many of these works consider interactions that decay as a power law of the distance between sites.…”

Section: Introductionmentioning

confidence: 99%

Subradiant edge states in an atom chain with waveguide-mediated hopping

McDonnell¹,

Olmos²

2022

Preprint

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We analyze the topological and dynamical properties of a system formed by two chains of identical emitters coupled to a waveguide, whose guided modes induce all-to-all excitation hopping. We find that, in the single excitation limit, the bulk topological properties of the Hamiltonian that describes the coherent dynamics of the system are identical to the ones of a one-dimensional Su-Schrieffer-Heeger (SSH) model. However, due to the long-range character of the exchange interactions, we find weakening of the bulk-boundary correspondence. This is illustrated by the variation of the localization length and mass gap of the edge states encountered as we vary the lattice constant and offset between the chains. Most interestingly, we analytically identify parameter regimes where edge states arise which are fully localized to the boundaries of the chain, independently of the system size. These edge states are shown to be not only robust against positional disorder of the atoms in the chain, but also subradiant, i.e., dynamically stable even in the presence of inevitable dissipation processes, establishing the capacity of waveguide QED systems for the realization of symmetry protected topological phases.

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Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices

Cited by 58 publications

References 53 publications

Topological aspects in nonlinear optical frequency conversion

Topological aspects in nonlinear optical frequency conversion

A brief review of topological photonics in one, two, and three dimensions

Subradiant edge states in an atom chain with waveguide-mediated hopping

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