In photonic systems, Thouless pumping enables light transport to take place in a robust way. The method is quantized — determined by the global rather than the local properties of a system. It exhibits topological features, and its ubiquitous nature leads to its occurrence in many areas of science. Though Thouless pumping is not limited to solid states, Nobel Prize-winning physicist David Thouless discovered it in a solid state, in work almost four decades ago. Building on prior work in which they discovered that optical moiré lattices can inhibit light diffraction and produce solitons at extremely low power levels, researchers at Shanghai Jiao Tong University designed a system of photonic moiré lattices to enable 2D Thouless pumping, in what the researchers characterized as a new regime. The system allows directional pumping in a fully 2D setting without relying on any confining mechanisms. The researchers demonstrated 2D topological Thouless pumping of light by bulk modes in tilted moiré lattices imprinted in a photorefractive crystal. The photonic system is based on two tilted and mutually twisted sublattices that form a dynamical moiré lattice. Most existing experiments on Thouless pumping have focused on 1D geometries. In experiments where 2D geometries were included, the geometries were carried by topological boundary states, which made it necessary for the experiments to be confined to the boundaries of the systems. Pumping light in an unconfined system occurs due to the longitudinal adiabatic and periodic modulation of the refractive index. To achieve 2D Thouless pumping, the researchers first needed to counteract the diffraction of light. They designed their moiré pattern — which consisted of the two photonic sublattices slightly tilted with respect to each other — to inhibit diffraction. Using the 3D rotations of the two sublattices, the researchers created a moiré pattern adiabatically sliding in the course of propagation along the crystal. This allowed the researchers to induce a 3D moiré lattice that periodically changed in all three dimensions. The reconfigurable pattern allowed the team to observe topological 2D Thouless pumping of a weakly diffracting signal beam being accomplished by fully 2D bulk modes. The specially prepared photonic moiré lattice led to extreme flattening of the bands which, in turn, made it possible for the researchers to suppress the 2D diffraction of the light beam and observe its topological pumping in an unconfined 2D geometry and a purely linear regime. The researchers found that the topological properties hidden in the band structure of the moiré lattice dictated the characteristics of the beam evolution, such as its displacement and the angle between the pump and the transport direction. Further, the topological nature of the pumping phenomenon manifested in the magnitude and direction of shift of the beam center-of-mass, averaged over one pumping cycle. The moiré lattice created for the experiment was periodic in all three directions. A long lattice period along the beam propagation direction emulated adiabatic periodic change of the optical potential, providing ideal conditions for the experimental implementation of topological pumping in 2D geometry. The pumping was quantified in the 3D space by two first Chern numbers. Systematic numerical simulations in the frames of the continuous Schrödinger equation governing propagation of the probe light beam in an optically induced photorefractive moiré lattice supported experimental results. As a general wave phenomenon, topological pumping is important for many branches of physics. The researchers believe that the system of photonic moiré lattices for 2D Thouless pumping of light could provide a universal platform for further investigations of 2D, and even 3D quantum transport, including lattices of different geometries and systems in commensurate and incommensurate phases. The moiré lattices system could also help further the study of topological pumping to include systems with nonlinearities. The research was published in Nature Communications (www.doi.org/10.1038/s41467-022-34394-3).
