Topological state engineering via supersymmetric transformations

Queraltó, G.; Kremer, Mark; Maczewsky, Lukas J.; Heinrich, Matthias; Mompart, J.; Ahufinger, V.; Szameit, Alexander

doi:10.1038/s42005-020-0316-4

Cited by 27 publications

(14 citation statements)

References 48 publications

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“…In quantum topological physics, the famous Su-Schrieffer-Heeger (SSH) soliton manifests a variety of important concepts including Thouless topological charge pumping, fractional charge, particle-antiparticle (PA) symmetry and spin-charge separation 2 – 7 . Such exotic properties and potential applications have stimulated many studies: conducting polymers 7 , diatomic chain model 8 , fractionalized domain wall excitations in 1D chain and wire 9 , 10 , acoustic experimental system 11 , realization of Zak phase and topological charge pumping in the cold atom system 12 – 14 , topological photonic crystal nanocavity lasers using SSH edge mode 15 – 17 , artificially engineered SSH lattices 18 , 19 , and topological quaternary operation using chiral soliton 20 , 21 . Among such exotic properties, PA symmetry and fractionalization are essential to understand not only the pair creation but also topological properties of topological solitons.…”

Section: Introductionmentioning

confidence: 99%

Particle-antiparticle duality and fractionalization of topological chiral solitons

Han

Jeong

et al. 2021

Sci Rep

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Although a prototypical Su–Schrieffer–Heeger (SSH) soliton exhibits various important topological concepts including particle-antiparticle (PA) symmetry and fractional fermion charges, there have been only few advances in exploring such properties of topological solitons beyond the SSH model. Here, by considering a chirally extended double-Peierls-chain model, we demonstrate novel PA duality and fractional charge e/2 of topological chiral solitons even under the chiral symmetry breaking. This provides a counterexample to the belief that chiral symmetry is necessary for such PA relation and fractionalization of topological solitons in a time-reversal invariant topological system. Furthermore, we discover that topological chiral solitons are re-fractionalized into two subsolitons which also satisfy the PA duality. As a result, such dualities and fractionalizations support the topological $$\mathbb {Z}_4$$ Z 4 algebraic structures. Our findings will inspire researches seeking feasible and promising topological systems, which may lead to new practical applications such as solitronics.

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Section: Introductionmentioning

confidence: 99%

Particle-antiparticle duality and fractionalization of topological chiral solitons

Han

Jeong

et al. 2021

Sci Rep

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“…In addition to the basic and classical configurations used in 1D topological photonics, topological waveguides can be regarded as “one‐plus‐1D” topological structures. [ 55 ] In all 1D topological photonic structures, the light field is known to be localized at the ends of the boundaries, which limits the application of these structures. To move the light in these structures, an extended dimension is then added to the 1D topological photonic structures.…”

Section: Basic Concepts and Realization Of Quantum Optics And Topological Photonicsmentioning

confidence: 99%

Quantum Topological Photonics

Yan

et al. 2021

Advanced Optical Materials

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Quantum topological photonics is a new research field with great potential that is based on developments in both quantum optics and topological photonics. Topological photonics offers unique properties, including topological robustness and an anti‐backscattering property, and these advantages are strongly required in quantum optics. Quantum technology, which includes quantum optics, represents an important direction for future technological development. However, existing quantum light sources are unstable and quantum information may easily be lost during transmission. These disadvantages have troubled researchers for a long time and no perfect solution is available thus far. Fortunately, application of topological photonics to quantum optics can help to generate robust quantum light sources and protect photons from decoherence during photon propagation. This allows the correlation and entanglement to be maintained even when photons travel over long distances. To date, quantum topological photonics has provided major breakthroughs in certain quantum devices. This Review presents the basic concepts of quantum topological photonics and summarizes how the topological protection property works in quantum light sources, quantum information transmission, and other quantum devices. Finally, an outlook is provided on the remaining challenges and potential future directions of quantum topological photonics, which can aid in exploration of additional new phenomena.

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“…A potential application of discrete SUSY would be to probe topological properties of a system. Since a single iteration of supersymmetry removes or adds a zero mode, the topological (Witten) index of a system can itself be altered -it would be interesting to pursue an analysis in this direction [68].…”

Section: Jhep07(2021)055mentioning

confidence: 99%

Solitons in lattice field theories via tight-binding supersymmetry

Balasubramanian

Patoary

Galitski

2021

J. High Energ. Phys.

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Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems (such as the Korteweg-de Vries equation), non-perturbative solutions of various large-N field theories (such as the Gross-Neveu model), and closely related solitonic solutions to the Bogoliubov-de Gennes equations in the theory of superconductivity. These solutions rely on the inverse scattering method, which reduces these seemingly unrelated problems to identifying reflectionless potentials of an auxiliary one-dimensional quantum scattering problem. There are several ways of constructing these potentials, one of which is quantum mechanical supersymmetry (SUSY). In this paper, motivated by recent experimental platforms, we generalize this framework to develop a theory of lattice solitons. We first briefly review the classical inverse scattering method in the continuum limit, focusing on the Korteweg-de Vries (KdV) equation and SU(N) Gross-Neveu model in the large N limit. We then generalize this methodology to lattice versions of interacting field theories. Our analysis hinges on the use of trace identities, which are relations connecting the potential of an equation of motion to the scattering data. For a discrete Schrödinger operator, such trace identities had been known as far back as Toda; however, we derive a new set of identities for the discrete Dirac operator. We then use these identities in a lattice Gross-Neveu and chiral Gross-Neveu (Nambu-Jona-Lasinio) model to show that lattice solitons correspond to reflectionless potentials associated with the discrete scattering problem. These models are of significance as they are equivalent to a mean-field theory of a lattice superconductor. To explicitly construct these solitons, we generalize supersymmetric quantum mechanics to tight-binding models. We show that a matrix transformation exists that maps a tight-binding model to an isospectral one which shares the same structure and scattering properties. The corresponding soliton solutions have both modulated hopping and onsite potential, the former of which has no analogue in the continuum limit. We explicitly compute both topological and non-topological soliton solutions as well as bound state spectra in the aforementioned models.

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Topological state engineering via supersymmetric transformations

Cited by 27 publications

References 48 publications

Particle-antiparticle duality and fractionalization of topological chiral solitons

Particle-antiparticle duality and fractionalization of topological chiral solitons

Quantum Topological Photonics

Solitons in lattice field theories via tight-binding supersymmetry

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