Quantized nonlinear Thouless pumping.

@article{Jrgensen2021QuantizedNT,
  title={Quantized nonlinear Thouless pumping.},
  author={Marius J{\"u}rgensen and Sebabrata Mukherjee and Mikael C. Rechtsman},
  journal={Nature},
  year={2021},
  volume={596 7870},
  pages={
          63-67
        }
}
The topological protection of wave transport, originally observed in the context of the quantum Hall effect in two-dimensional electron gases1, has been shown to apply broadly to a range of physical platforms, including photonics2-5, ultracold atoms in optical lattices6-8 and others9-12. That said, the behaviour of such systems can be very different from the electronic case, particularly when interparticle interactions or nonlinearity play a major role13-22. A Thouless pump23 is a one… 
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Charge transport in a cyclically time-modulated periodic potential, also known as a topological Thouless pump, has been realized in an ultracold gas of fermionic atoms. An electron gas in a
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TLDR
This work experimentally observes a generalized Thouless pump that can be extensively and continuously controlled and suggests an alternative means to detect quantum or topological phase transitions.
Thouless pumping in disordered photonic systems
TLDR
Bulk Thouless pumping is experimentally demonstrated using arrays of evanescently coupled optical waveguides, and it is shown that this approach realizes near-full-unit-cell transport per pump cycle for a physically relevant class of localized initial system excitations.
Robust temporal pumping in a magneto-mechanical topological insulator
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A temporal topological pump that produces on-demand, robust transport of mechanical energy using a one-dimensional magneto-mechanical metamaterial is demonstrated and opens a path towards exploration of higher-dimensional topological physics with time as a synthetic dimension.
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TLDR
This work proposes and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges.
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The experimental realization of the Haldane model and the characterization of its topological band structure are reported, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice and a direct extension to realize spin-dependent topological Hamiltonians is proposed.
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