Non-abelian Thouless pumping in a photonic lattice

Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate non-dispersive modes and we show that, when the lattice parameters are slowly modulated, the propagation of the photons bear the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control on photon propagation. Our work paves the way to the generation and detection of non-abelian gauge fields in photonic and optical lattices.

Non-abelian gauge fields lie at the very heart of many modern physical theories. We need new experimental routes and observables to disclose the importance of the Wilczek and Zee holonomy. We have shown that properly
designed photonic lattices enable the control of the beam evolution by non-commutative fields. These lattices may lead to the direct observation of the quantization of the displacement due to a non-abelian Chern number. This work can be extended in several directions, including nonlinear effects or considering the propagation of non-classical light in non-abelian lattices. Both these possibilities are unexplored so far and open several new questions concerning – for example – the effect of the non-abelian holonomy on entanglement or the impact of nonlinearity in breaking the hidden symmetries. Non-abelian topological photonics may stimulate further developments and applications for classical and quantum information and tests of fundamental physics.

Brosco, Pilozzi, Fazio, and Conti, in https://arxiv.org/abs/2010.15159

Direct Observation of Topological Protected Edge States in Slow-Light

We use split-ring resonators to demonstrate topologically protected edge states in the Su-Schieffer-Heeger model experimentally, but in a slow-light wave with the group velocity down to ∼0.1 of light speed in free space. A meta-material formed by an array of complementary split-ring resonators with controllable hopping strength enables the direct observation in transmission and reflection of non-trivial topology eigenstates, including a negative phase velocity regime. By rotating the texture orientation of the diatomic resonators, we can explore all the band structures and unveil the onset of the trivial and non-trivial protected eigenmodes at GHz frequencies, even in the presence of non-negligible loss. Our system realizes a fully tunable and controllable artificial optical system to study the interplay between topology and slow-light towards applications in quantum technologies

arXiv:2004.09282

Topological photonic crystal fibers and ring resonators

With an exact recursive approach, we study photonic crystal fibers and resonators with topological features induced by Aubry–Andre–Harper cladding modulation. We find nontrivial gaps and edge states at the interface between regions with different topological invariants. These structures show topological protection against symmetry-preserving local perturbations that do not close the gap and sustain strong field localization and energy concentration at a given radial distance. As topological light guiding and trapping devices, they may bring about many opportunities for both fundamentals and applications unachievable with conventional devices.

Laura Pilozzi et al. Optics Letters 45, 1415 (2020)