Experimental Observation of Aharonov-Bohm Cages in Photonic Lattices

Abstract

We report on the experimental realization of a uniform synthetic magnetic flux and the observation of Aharonov-Bohm cages in photonic lattices. Considering a rhombic array of optical waveguides, we engineer modulation-assisted tunneling processes that effectively produce nonzero magnetic flux per plaquette. This synthetic magnetic field for light can be tuned at will by varying the phase of the modulation. In the regime where half a flux quantum is realized in each plaquette, all the energy bands dramatically collapse into nondispersive (flat) bands and all eigenstates are completely localized. We demonstrate this Aharonov-Bohm caging by studying the propagation of light in the bulk of the photonic lattice. Besides, we explore the dynamics on the edge of the lattice and discuss how the corresponding edge states can be continuously connected to the topological edge states of the Creutz ladder. Our photonic lattice constitutes an appealing platform where the interplay between engineered gauge fields, frustration, localization, and topological properties can be finely studied.

Topology and Interactions in the Photonic Creutz and Creutz‐Hubbard Ladders

“…This approach is convenient for waveguide lattice setups, given that the initial state requires only pumping light into a single site. Experimental observation of AB caging has indeed been recently observed in this way for a waveguide rhombus chain using classical light …”

“…The mechanism behind this localization is the Aharonov–Bohm (AB) effect, the phase acquired by the wavefunction of a charged particle by moving through a region with a non‐zero magnetic vector potential. This effect is also seen in some bipartite lattices such as the lattice and the rhombus chain, and it has been termed “Aharonov–Bohm caging.” This localization effect has been observed experimentally in superconducting wire networks, metal wire lattices, ultracold atom lattices, and, most recently, in a photonic system …”

“…A very similar photonic rhombus chain was also realized in another recent work . The synthetic magnetic field can be obtained with auxiliary waveguides that retard the wavefunction appropriately, or with Floquet engineering, combining a periodic modulation of the refraction index with an energy gradient . In these systems, it is especially easy to observe the AB caging.…”

“…This way, an effective lattice with the geometry of the Creutz ladder is obtained. The synthetic magnetic field is inherited from the one in the rhombus chain …”

“…Another way to tackle the problem would be to simulate the Creutz ladder in a different system using the approach suggested in ref. [], which would make use of the topological similarities between the Creutz ladder and the rhombus chain. In that work, a photonic rhombus chain was constructed using a waveguide lattice.…”