Generating arbitrary topological windings of a non-Hermitian band

Wang, Kai; Dutt, Avik; Yang, Ki Youl; Wojcik, Charles C.; Vučković, Jelena; Fan, Shanhui

doi:10.1126/science.abf6568

Cited by 245 publications

(157 citation statements)

References 46 publications

(46 reference statements)

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“…In the absence of group velocity dispersion (GVD) in waveguides that compose rings, the frequency of the mth resonant mode in ring A (ring B) is ω m,A = ω 0 + mΩ (ω m,B = ω 0 − Ω/2 + mΩ), where Ω = 2πv g /L is the free spectral ranges (FSR) with v g being the group velocity inside both rings. The approximation that GVD of waveguides is zero makes the synthetic frequency dimension being uniform, which is valid for considering finite resonant modes near the zero GVD point and is confirmed by previous experiments [41][42][43][44] . We place electro-optic modulators (EOM) inside two rings, with modulation frequency Ω/2 and modulation phase ϕ.…”

Section: Resultssupporting

confidence: 75%

“…The highly tunable parameters of modulated ring resonators are of apparent significance in our theoretical design for achieving the synthetic honeycomb lattice, which can be realized in potential experiments based on established platforms with fiber loops [41][42][43][44] , and lithium niobate technologies 45,61 . For the fiber-based ring resonator, the modulation frequency is ~10 MHz for a fiber length of ~10 m. 2 × 2 fiber couplers with a high-contract splitting ratio can be used to couple two rings.…”

Section: Discussionmentioning

confidence: 99%

“…Different physics associated with the photonic graphene can be simulated in this unique platform, such as Klein tunneling 14 , valley-dependent edge states 13 , topological edge states with the effective magnetic field 40 , and valleydependent Lorentz force 8 . The modulated ring systems can be realized in either fiber-based system [41][42][43][44] or on-chip lithium niobate resonator 45 , which brings our proposal to a flexible experimental setup with state-of-art technologies in bulk optics or integrated photonics. Our work not only broadens the current research on synthetic dimensions in photonics 26,27 , but also enriches quantum simulations with topological photonics 46,47 , which shows potential applications in optical signal processing 48,49 and quantum computations 50,51 .…”

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confidence: 99%

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Simulating graphene dynamics in synthetic space with photonic rings

Xiao

et al. 2021

Commun Phys

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Photonic honeycomb lattices have attracted broad interests for their fruitful ways in manipulating light, which yet hold difficulties in achieving arbitrary reconfigurability and hence flexible functionality due to fixed geometry configurations. Here we theoretically propose to construct the honeycomb lattice in a one-dimensional ring array under dynamic modulations, with an additional synthetic dimension created by connecting the frequency degree of freedom of light. Such a system is highly re-configurable with parameters flexibly controlled by external modulations. Therefore, various physical phenomena associated with graphene including Klein tunneling, valley-dependent edge states, effective magnetic field, as well as valley-dependent Lorentz force can be simulated in this lattice, which exhibits important potentials for manipulating photons in different ways. Our work unveils an alternative platform for constructing the honeycomb lattice in a synthetic space, which holds complex functionalities and could be important for optical signal processing as well as quantum simulation.

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Section: Resultssupporting

confidence: 75%

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

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Simulating graphene dynamics in synthetic space with photonic rings

Xiao

et al. 2021

Commun Phys

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“…For a long time, the complex spectral winding number has been exploited in predicting the non-Hermitian pumping under the open boundary conditions (OBCs) [known as the non-Hermitian skin effect (NHSE)] 9 – 12 , leading to the breaking of bulk-boundary correspondence and various anomalous topological phenomena 9 – 37 . In a recent experiment, arbitrary spectral winding is observed by visualizing the frequency band structure of optical frequency modes 38 . However, no directly measurable quantity has been associated with the spectral winding.…”

Section: Introductionmentioning

confidence: 99%

Quantized classical response from spectral winding topology

Lee

et al. 2021

Nat Commun

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Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge states as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green’s function, and shows up in steady-state response, without invoking a conventional linear response theory. Specifically, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

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“…A noticeable exception is provided by the Hatano-Nelson model in the limiting case of unidirectional hopping [1], which is amenable for some analytical treatment. The realization of synthetic lattices with asymmetric hopping and controlled disorder, demonstrated in recent experiments [14,87,88], have stimulated a renewed interest in the understanding of the interplay among non-Hermiticity, topology and disorder [89][90][91][92] with potential impact to applications, such as in the design of non-Hermitian topological classical or quantum sensors [93].…”

Section: Introductionmentioning

confidence: 99%

Spectral deformations in non-Hermitian lattices with disorder and skin effect: A solvable model

Longhi

2021

Phys. Rev. B

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We derive analytical results on energy spectral phase transitions and deformations in the simplest model of one-dimensional lattice displaying the non-Hermitian skin effect, namely the Hatano-Nelson model with unidirectional hopping, under on-site potential uncorrelated disorder in complex energy plane. While the energy spectrum under open boundary conditions (OBC) exactly reproduces the distribution of on-site potential disorder, the energy spectrum under periodic boundary conditions (PBC) undergoes spectral deformations, from one or more closed loops in the fully delocalized phase, with no overlap with the OBC spectrum, to a mixed spectrum (closed loops and some OBC energies) in the mobility edge phase, to a complete collapse toward the OBC spectrum in the bulk localized phase. Such transitions are observed as the strength of disorder is increased. Depending on the kind of disorder, different interesting behaviors are found. In particular, for continuous disorder with a radial distribution in complex energy plane it is shown that in the delocalized phase the energy spectrum under PBC is locked and fully insensitive to disorder, while transition to the bulk localized phase is signaled by the change of a topological winding number. When the disorder is described by a discrete distribution, the bulk localization transition never occurs, while topological phase transitions associated to PBC energy spectral splittings can be observed.

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Generating arbitrary topological windings of a non-Hermitian band

Cited by 245 publications

References 46 publications

Simulating graphene dynamics in synthetic space with photonic rings

Simulating graphene dynamics in synthetic space with photonic rings

Quantized classical response from spectral winding topology

Spectral deformations in non-Hermitian lattices with disorder and skin effect: A solvable model

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