The research on topological insulators is advancing rapidly, promising a broad spectrum of applications ranging from metrology to quantum computation. Topological insulators are characterised by protected edge states, which are a direct manifestation of their band structure. To understand the effects of topology, physicists around the world are working simultaneously on a plethora of experimental architectures. Among these, quantum walks are powerful models in which topological phases of matter can be simulated in static and out-of-equilibrium scenarios. Most of the quantum walk architectures built so far have generated one-dimensional processes. There are currently significant efforts to investigate the broad range of topological phenomena that exist in 2D and 3D.

In their study entitled “Two-dimensional topological quantum walks in the momentum space of structured light”, recently published in 'Optica', the researcher Pietro Massignan, from the Department of Physics of the Universitat Politècnica de Catalunya · BarcelonaTech (UPC), and researchers from the Università degli Studi di Napoli Federico II and the Institute of Photonic Sciences (ICFO)—a research institute affiliated to the UPC—report the realisation of a photonic platform generating a quantum walk on a two-dimensional square lattice, which emulates a periodically-driven quantum Hall insulator. The device consists of cascaded liquid crystal slabs, patterned to give polarisation-dependent kicks to the impinging photons. Suitable combinations of these plates allow to manipulate dynamically the evolution of a light beam, realising a quantum walk between light spatial modes carrying a variable amount of transverse momentum. The authors demonstrate the non-trivial topological character of their photonic system by directly reading out the anomalous displacement of a wave packet when a constant force is introduced in the system.

The demonstration of the novel two-dimensional quantum walk platform paves the way for experimenting and studying two-dimensional quantum dynamics. The simulation of other condensed matter systems, the investigation of the evolution of quantum light and the study of dynamical phase transitions are among the possible avenues that the authors of this work intend to explore in the next future.

Reference paper

• D’Errico et al., Two-dimensional topological quantum walks in the momentum space of structured light, Optica 7, 108 (2020)