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

Lead Research Organisation:
UNIVERSITY OF EXETER

Department Name: Mathematics

### Abstract

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.

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.

### Organisations

### Studentship Projects

Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|

EP/W523859/1 | 30/09/2021 | 29/09/2025 | |||

2581422 | Studentship | EP/W523859/1 | 30/09/2021 | 29/09/2025 | Oliver Fox |