Quantum topology with strong light-matter coupling (Ref: 4170)

The mathematics underpinning topological matter is of a large and growing interest, especially
since the Nobel Prize in Physics was awarded in 2016 to the British theoretical physicists
Thouless, Haldane and Kosterlitz "for theoretical discoveries of topological phase transitions
and topological phases of matter".


At its heart, topological physics allows one to explain the behavior of complicated systems
very simply, usually through some important number: a so-called topological invariant. A
famous example is in the much celebrated quantum Hall effect, where the resistance in the
material surprisingly plateaus at certain integer values. This intriguing phenomenon can be
understood elegantly through topological numbers known as Chern numbers.


We have so far only talked about conventional materials, which are primarily governed by the
behaviour of their constituent electrons. However, much less is known when it is the particle
of light (the photon) which instead plays an important role in the system. In the field of
quantum nanophotonics, we are concerned with nanoscale materials where the light-matter
interaction is decisive. In particular, in the strong light-matter coupling regime, electrons and
photons may hybridize to form a new particle, carrying desirable traits of both of its component
parts.


This sets the stage for the proposed project, which aims to make fundamental mathematical
advances in topological quantum nanophotonics. Namely, inspired by the success of topological
theories in describing electronic systems, we will develop theories to describe and exploit
topological light at the nanoscale. We will develop topological invariants capable of
describing bosonic particles such as light, and create models which explain how topological
light may be used in the next generation of quantum technology, including quantum circuitry,
communications and information.