Linking topological features of the Hofstadter model to optical diffraction figures

@article{DiColandrea2021LinkingTF,
  title={Linking topological features of the Hofstadter model to optical diffraction figures},
  author={F. Di Colandrea and Alessio D’Errico and Maria Maffei and Hannah M. Price and Maciej Lewenstein and Lorenzo Marrucci and Filippo Cardano and Alexandre Dauphin and Pietro Massignan},
  journal={New Journal of Physics},
  year={2021},
  volume={24}
}
In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian. These remarkable features, solely arising from the magnetic translational symmetry, are captured by Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern… 

Universality of Hofstadter Butterflies on Hyperbolic Lattices.

Motivated by recent realizations of hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. Utilizing large

References

SHOWING 1-10 OF 79 REFERENCES

Mapping the Berry curvature from semiclassical dynamics in optical lattices

We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry

Measuring quantized circular dichroism in ultracold topological matter

The topology of two-dimensional materials traditionally manifests itself through the quantization of the Hall conductance, which is revealed in transport measurements1–3. Recently, it was predicted

Photonic topological boundary pumping as a probe of 4D quantum Hall physics

This work uses tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally, and provides a platform for the study of higher-dimensional topological physics.

Exploring 4D quantum Hall physics with a 2D topological charge pump

These findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

Measuring topology from dynamics by obtaining the Chern number from a linking number

This work defines and measures a linking number between static and dynamical vortices, which directly corresponds to the ground-state Chern number, and measures the instantaneous Chern number and shows that it remains zero under the unitary dynamics.

Observation of Hofstadter butterfly and topological edge states in reconfigurable quasi-periodic acoustic crystals

The emergence of a fractal energy spectrum is the quintessence of the interplay between two periodic parameters with incommensurate length scales. crystals can emulate such interplay and also exhibit

Four-dimensional topological lattices through connectivity

Thanks to recent advances, the 4D quantum Hall (QH) effect is becoming experimentally accessible in ultracold atoms and photonics. In this paper, we propose a new type of 4D topological system that,

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

This work proposes and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems and proves the robustness of the measure by introducing dynamical disorder in the system.

Scheme to Measure the Topological Number of a Chern Insulator from Quench Dynamics.

It is shown how the topological number of astatic Hamiltonian can be measured from a dynamical quench process, and it is shown that the linking number of the trajectories of the phase vortices determines the phase boundary of the static Hamiltonian.

Probing topology by “heating”: Quantized circular dichroism in ultracold atoms

The quantized circular dichroism revealed in this work designates depletion rate measurements as a universal probe for topological order in quantum matter.
...