Four-dimensional quantum Hall physics with light
Abstract: he quantum Hall effect is one of the most beautiful discoveries of our time in the study of the physics of solids (and has been appropriately responsible for three Nobel prizes in physics - 1985, 1998, and 2016). As first demonstrated by von Klitzing in 1980, when electrons in a two dimensional plane are cooled down to near absolute zero temperature and are immersed in a magnetic field, their conductivity is ‘quantized’ – i.e., fixed to a fundamental constant. This makes the system incredibly robust, because even significant disorder in the system cannot change this value. In 2001, the theorists Zhang and Hu predicted that a new type of quantum Hall effect could be achieved in four spatial dimensions – but of course the universe is only composed of three, so it seemed that it would never be realized experimentally. In this proposal, I plan to experimentally realize the four-dimensional quantum Hall effect using ‘synthetic dimensions’ – a recent concept that has been proposed by Lewenstein and Buljan. Furthermore, I will probe the effect using the flow of photons (particles of light) in a synthetic material called a ‘photonic crystal’, as opposed to electrons flowing through a solid. The synthetic dimensions correspond to changes in the structure of the photonic crystal that are mathematically equivalent to having extra spatial dimensions in the system. Successful completion of this project will mean the 4D quantum Hall effect – previously considered a mathematical curiosity – will be brought into the realm of physical reality. I expect that this will spur a new cohort of theorists and experimentalists to revive interest into this strange and interesting phenomenon.