Topology is an important unifying concept in quantum mechanics. Topological invariants characterise excitations such as vortices and skyrmions, while the topology of energy bands underlies the quantum Hall effect and topological insulators.
My research focuses on the novel features of such phenomena in photonic systems and ultracold gases, where experiments have key advantages over those in solid state materials. These experiments are controllable, tuneable and clean, and can measure many properties that were previously inaccessible, allowing scientists to study various important aspects of topology for the first time.
I am particularly interested in the physical consequences of non-zero Berry curvature on a single quantum particle. The Berry curvature is a geometrical property of an energy band, which acts as an artificial momentum-space magnetic field in the effective Hamiltonian of a wide-range of systems. Bands with nonzero Berry curvature arise in key areas of current research, such as lattices with more than one band; strong artificial magnetic fields and 2D spin-orbit coupling.
More recently, I have also focused on higher-dimensional topological systems, proposing how the four-dimensional quantum Hall effect could be observed experimentally for the first time using ultracold atoms and with integrated photonics. For more details about my research, check out my publications list in the link at the top of the page.