Non-Abelian Gauge Fields and Topological Insulators in Shaken Optical Lattices

Hauke, Philipp; Tieleman, O.; Celi, Alessio; Ölschläger, C.; Simonet, Juliette; Struck, Julian; Weinberg, Malte; Windpassinger, Patrick; Sengstock, K.; Lewenstein, Maciej; Eckardt, André

doi:10.1103/physrevlett.109.145301

Cited by 340 publications

(387 citation statements)

References 57 publications

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“…When the static (non-irradiated) system is already topological, photons are also useful to probe the properties and the robustness of the chiral/helical edge modes. Finally, cold atomic vapors trapped in optical lattices provide very interesting routes to design synthetic gauge fields and induce topological phases [51], either by using Raman resonances or by using periodic driving (shaking) of the lattice [52].…”

Section: Discussionmentioning

confidence: 99%

Floquet topological insulators

Cayssol

Dóra

Simón

et al. 2013

Physica Rapid Research Ltrs

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354

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Topological insulators represent unique phases of matter with insulating bulk and conducting edge or surface states, immune to small perturbations such as backscattering due to disorder. This stems from their peculiar band structure, which provides topological protections. While conventional tools (pressure, doping etc.) to modify the band structure are available, time periodic perturbations can provide tunability by adding time as an extra dimension enhanced to the problem. In this short review, we outline the recent research on topological insulators in non equilibrium situations. Firstly, we introduce briefly the Floquet formalism that allows to describe steady states of the electronic system with an effective time-independent Hamiltonian. Secondly, we summarize recent theoretical work on how light irradiation drives semi-metallic graphene or a trivial semiconducting system into a topological phase. Finally, we show how photons can be used to probe topological edge or surface states.Comment: 7 pages, 4 figures, comments are welcom

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Section: Discussionmentioning

confidence: 99%

Floquet topological insulators

Cayssol

Dóra

Simón

et al. 2013

Physica Rapid Research Ltrs

450

354

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“…Cold atoms in optical lattices, moreover, can be forced into regimes of parameters or subject to external fields, which are difficult to achieve in or unaccessible to natural graphene. Examples include the regime of ultrastrong spin-orbit coupling [62] and nonAbelian gauge fields [63,64] akin to those that appear in the Langrangian of quantum chromodynamics. Note that with the advent of molecular graphene and Abelian gauge fields [19], proposals now also exist for realizing non-Abelian gauge fields in solid-state incarnations [65].…”

Section: Confining Atoms and Ionsmentioning

confidence: 99%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.

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“…Theoretical models based on Floquet's theorem are being developed to simulate systems in regimes otherwise inaccessible in conventional condensed matter materials [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . Experimentally, cold atoms' unique controllability was employed to observe dynamical localisation and phase-coherence in strongly shaken bosonic systems [19][20][21][22][23][24] .…”

Section: Introductionmentioning

confidence: 99%

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

Bukov

Polkovnikov

2014

Phys. Rev. A

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We study the stroboscopic and non-stroboscopic dynamics in the Floquet realization of the HarperHofstadter Hamiltonian. We show that the former produces the evolution expected in the highfrequency limit only for observables which commute with the operator to which the driving protocol couples. On the contrary, non-stroboscopic dynamics is capable of capturing the evolution governed by the Floquet Hamiltonian of any observable associated with the effective high-frequency model. We provide exact numerical simulations for the dynamics of the number operator following a quantum cyclotron orbit on a 2 × 2 plaquette, as well as the chiral current operator flowing along the legs of a 2 × 20 ladder. The exact evolution is compared with its stroboscopic and non-stroboscopic counterparts, including finite-frequency corrections.

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Non-Abelian Gauge Fields and Topological Insulators in Shaken Optical Lattices

Cited by 340 publications

References 57 publications

Floquet topological insulators

Floquet topological insulators

Artificial honeycomb lattices for electrons, atoms and photons

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

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