Dynamics of Topological Quantum Matter: From Solid-State Materials to Quantum Computers

Summary

Topological quantum matter can host emergent particles analogous to gravitons: the elusive mediators of gravitational force in a quantum theory of gravity. For example, in solid state materials, fractional quantum Hall (FQH) phases of electrons can host graviton-like excitations which respond to the effective curvature of their host material. This project will explore the possibility of recreating a similar kind of physics in the emerging quantum technology devices, e.g., ultracold atoms in optical lattices and quantum computers. You will investigate how graviton-like particles and their dynamics could be controllably created and measured in such systems. More broadly, this project will advance the understanding of geometrical degrees of freedom in topological quantum matter, which govern their dynamics and out-of-equilibrium responses.

Fractional quantum Hall effect (FQHE) is a phenomenon where electrons form exotic types of quantum liquids by fractionalising into new kind of particles called anyons. Recent experiments have observed signatures of these exotic particles: https://www.quantamagazine.org/milestone-evidence-for-anyons-a-third-kingdom-of-particles-20200512/ However, the physics of FQHE is not fully described by anyons –these phases of matter also have additional degrees of freedom which have a geometric character. This means that their quantised excitations behave like an analog of the elusive graviton particle in theories of quantum gravity.

This PhD project will investigate dynamics of fractional quantum Hall phases, in particular focusing on their geometric degrees of freedom. While the equilibrium properties of the FQHE have been well understood due to major theoretical efforts of the past three decades, the non-equilibrium dynamics of FQHE phases remains an uncharted territory. In our recent work [Phys. Rev. Lett. 129, 056801 (2022)], we have shown that the exotic graviton dynamics in FQHE phases can be captured in a simple qubit model and directly simulated on the IBM quantum computer.

One of the goals of this project will be to understand the dynamics in the more complex non-Abelian FQHE phases, whose underlying anyon particles are fundamentally different from fermions and bosons. The second goal of the project is to investigate the dynamics of so-called higher-spin excitations in FQHE phases, which can be viewed as cousins of the “graviton” particle (which carries spin-2). The insights from such a study may prove to be of interest in various other areas of theoretical physics which have focused on higher-spin symmetry (e.g., generalisation of gauge/gravity dualities, large N gauge theory, etc.).

Desired student background: We seek talented and highly-motivated physics students to pursue this project in the general area of quantum condensed matter physics and topological phases. The project will involve numerical modelling of fractional quantum Hall systems via exact diagonalisation and tensor network techniques. The project is thus particularly suitable for those with strong interest in computational physics and numerical simulations.

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid.