Four-dimensional photonic lattices and discrete tesseract solitons

Jukić, Dario; Buljan, Hrvoje

doi:10.1103/physreva.87.013814

Cited by 67 publications

(60 citation statements)

References 25 publications

(44 reference statements)

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“…The excellent agreement between our results for light propagation in realistic (continuous) systems and the evolution in the corresponding discrete models, clearly confirms that the 2D dielectric photonic lattice with grating assisted tunneling constitutes the realization of the Harper-Hofstadter Hamiltonian. We envision that this approach can open the way for other studies of light propagation in tailored dielectric structures (including nonlinear propagation, solitons, instabilities and the creation of synthetic dimensions [47]) being mapped on intriguing discrete models with complex tunneling matrix elements and synthetic magnetic fields.…”

Section: Resultsmentioning

confidence: 99%

The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

et al. 2015

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We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one-and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. We compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.

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Section: Resultsmentioning

confidence: 99%

The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

et al. 2015

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“…A similar dictionary can be obtained for other platforms. For instance, in the spirit of [67], a synthetic dimension can be achieved also in photonic crystals as in [88,89], by changing the connectivity of the lattice.…”

Section: Cold Atom Implementationmentioning

confidence: 99%

Quantum simulation of non-trivial topology

et al. 2015

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We propose several designs to simulate quantum many-body systems in manifolds with a nontrivial topology. The key idea is to create a synthetic lattice combining real-space and internal degrees of freedom via a suitable use of induced hoppings. The simplest example is the conversion of an open spin-ladder into a closed spin-chain with arbitrary boundary conditions. Further exploitation of the idea leads to the conversion of open chains with internal degrees of freedom into artificial tori and Möbius strips of different kinds. We show that in synthetic lattices the Hubbard model on sharp and scalable manifolds with non-Euclidean topologies may be realized. We provide a few examples of the effect that a change of topology can have on quantum systems amenable to simulation, both at the single-particle and at the many-body level.

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“…Traditionally, the underlying model of these systems is a spatial lattice in two or three dimensions. However, it recently became clear that many lattice systems can exist also in synthetic dimensions which are not spatial but extend over a different degree of freedom 15,16 . Thus far, topological insulators in synthetic dimensions were demonstrated only in cold atoms [17][18][19] , where synthetic dimensions have now become a useful tool for demonstrating a variety of lattice models that are not available in spatial lattices [20][21][22][23][24] .…”

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confidence: 99%

Photonic topological insulator in synthetic dimensions

Lustig

Weimann

Plotnik

et al. 2019

Nature

310

206

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Topological phases enable protected transport along the edges of materials, offering immunity against scattering from disorder and imperfections 1 . These phases were suggested and demonstrated not only for electronic systems, but also for electromagnetic waves 2-9 , cold atoms 10-12 , acoustics 13 , and even mechanics 14 . Their potential applications range from spintronics and quantum computing to highly efficient lasers. Traditionally, the underlying model of these systems is a spatial lattice in two or three dimensions. However, it recently became clear that many lattice systems can exist also in synthetic dimensions which are not spatial but extend over a different degree of freedom 15,16 . Thus far, topological insulators in synthetic dimensions were demonstrated only in cold atoms [17][18][19] , where synthetic dimensions have now become a useful tool for demonstrating a variety of lattice models that are not available in spatial lattices [20][21][22][23][24] . Subsequently, efforts have been directed towards realizing topological lattices with synthetic dimensions in photonics, where they are connected to physical phenomena in high-dimensions, interacting photons, and more [25][26][27][28][29] . Here we demonstrate experimentally the first photonic topological insulator in synthetic dimensions. The ability to study experimentally photonic systems in synthetic dimensions opens the door for a plethora of unexplored physical phenomena ranging from PT-symmetry 30,31 , exceptional points [31][32][33] and unidirectional invisibility 34 to Anderson localization in high dimensions and high-2 dimensional lattice solitons 16 , topological insulator lasers in synthetic dimensions 35,36 and more. Our study here paves the way to these exciting phenomena, which are extremely hard (if not impossible) to observe in other physical systems.In the field of topological insulators, one of the most striking phenomena is the appearance of topological edge-states 1 . Topological edge-states are eigenstates of the system that reside in a topological band gap, are robust to disorder, immune to backscattering from defects and are localized at the edge of the lattice. In light of these properties, transport via topological edge-states is important both for its fundamental aspects and for potential technological applications. The concepts underlying topological edge-states extend much beyond condensed matter. In fact, topological edge-states were demonstrated in a variety of physical systems, ranging from electromagnetic waves both in the microwave regime 3,37 and at optical frequencies 8,9 , to cold atoms 11,12 , acoustics 13 and even mechanical systems 14 . Despite of their different manifestations, all of these topological insulators systems rely on spatial lattices, and the wavepackets occupying the lattice, whether they are electrons, photons or phonons, are subjected to gauge fields that give rise to the topological phenomena.However, lattices may take other forms than a spatial arrangement of sites: they can be assigned to a l...

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Four-dimensional photonic lattices and discrete tesseract solitons

Cited by 67 publications

References 25 publications

The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

Quantum simulation of non-trivial topology

Photonic topological insulator in synthetic dimensions

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