Non-Abelian Braiding of Light

Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio

doi:10.1103/physrevlett.117.073901

Cited by 63 publications

(49 citation statements)

References 38 publications

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“…from the identity. This non-commuting behaviour shares similarities with non-Abelian excitations like anyons [36][37][38]. However, in the present study non-commutativity arises from how independent wave packets respond to external forces, while for anyons it is associated with the exchange (braiding) of these quasi-particles with each other.…”

supporting

confidence: 54%

Dualities and non-Abelian mechanics

Fruchart

Zhou

Vitelli

2020

Nature

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Dualities are mathematical mappings that reveal unexpected links between apparently unrelated systems or quantities in virtually every branch of physics [1][2][3][4][5][6][7][8]. Systems that are mapped onto themselves by a duality transformation are called self-dual and they often exhibit remarkable properties, as exemplified by an Ising magnet at the critical point. In this Letter, we unveil the role of dualities in mechanics by considering a family of so-called twisted Kagome lattices [9][10][11][12][13][14]. These are reconfigurable structures that can change shape thanks to a collapse mechanism [9] easily illustrated using LEGO. Surprisingly, pairs of distinct configurations along the mechanism exhibit the same spectrum of vibrational modes. We show that this puzzling property arises from the existence of a duality transformation between pairs of configurations on either side of a mechanical critical point. This critical point corresponds to a self-dual structure whose vibrational spectrum is two-fold degenerate over the entire Brillouin zone. The two-fold degeneracy originates from a general version of Kramers theorem that applies to classical waves in addition to quantum systems with fermionic time-reversal invariance [15]. We show that the vibrational modes of the self-dual mechanical systems exhibit non-Abelian geometric phases [15] that affect the semi-classical propagation of wave packets [16]. Our results apply to linear systems beyond mechanics and illustrate how dualities can be harnessed to design metamaterials with anomalous symmetries and non-commuting responses. * fruchart@uchicago.edu

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supporting

confidence: 54%

Dualities and non-Abelian mechanics

Fruchart

Zhou

Vitelli

2020

Nature

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“…Kekulé vortices have been shown to bind zero-energy modes in graphene, [21,22] analogs of which also appear in photonic crystals. [23] Similar physics arises here, with the crucial distinction that the zero modes are now of Majorana nature, owing to the fact that the underlying tight-binding model is one of Majoranas. It is the MZMs localized near the core of each vortex that we shall call the "logical" MZMs, which constitute the final level of the hierarchy.…”

Section: Introductionsupporting

confidence: 53%

Hierarchical Majoranas in a programmable nanowire network

et al. 2019

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We propose a hierarchical architecture for building "logical" Majorana zero modes using "physical" Majorana zero modes at the Y-junctions of a hexagonal network of semiconductor nanowires. Each Y-junction contains three "physical" Majoranas, which hybridize when placed in close proximity, yielding a single effective Majorana mode near zero energy. The hybridization of effective Majorana modes on neighboring Y-junctions is controlled by applied gate voltages on the links of the honeycomb network. This gives rise to a tunable tight-binding model of effective Majorana modes. We show that selecting the gate voltages that generate a Kekulé vortex pattern in the set of hybridization amplitudes yields an emergent "logical" Majorana zero mode bound to the vortex core. The position of a logical Majorana can be tuned adiabatically, without moving any of the "physical" Majoranas or closing any energy gaps, by programming the values of the gate voltages to change as functions of time. A nanowire network supporting multiple such "logical" Majorana zero modes provides a physical platform for performing adiabatic non-Abelian braiding operations in a fully controllable manner. CONTENTS

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“…The experimentally observed edge MP states dated back to 1985 [37] are in fact topologically protected, analogous to the 1D chiral Majorana edge states. Some simulations of Majorana-like states in photonics have been reported [43][44][45][46][47], but they only appear at finite frequencies around which the particlehole symmetry does not rigorously hold, unless using high nonlinearity [48]. Additionally, we are able to derive nonzero Chern numbers adhering to the band topology of 2D MP.…”

mentioning

confidence: 84%

Topological magnetoplasmon

et al. 2016

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Classical wave fields are real-valued, ensuring the wave states at opposite frequencies and momenta to be inherently identical. Such a particle–hole symmetry can open up new possibilities for topological phenomena in classical systems. Here we show that the historically studied two-dimensional (2D) magnetoplasmon, which bears gapped bulk states and gapless one-way edge states near-zero frequency, is topologically analogous to the 2D topological p+ip superconductor with chiral Majorana edge states and zero modes. We further predict a new type of one-way edge magnetoplasmon at the interface of opposite magnetic domains, and demonstrate the existence of zero-frequency modes bounded at the peripheries of a hollow disk. These findings can be readily verified in experiment, and can greatly enrich the topological phases in bosonic and classical systems.

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Non-Abelian Braiding of Light

Cited by 63 publications

References 38 publications

Dualities and non-Abelian mechanics

Dualities and non-Abelian mechanics

Hierarchical Majoranas in a programmable nanowire network

Topological magnetoplasmon

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