PhD Opportunities

If you are considering to apply for one of the PhD projects below, please feel free to first contact your potential supervisor for more information. Applying is relatively straightforward and can be done electronically. Some of the projects below have funding; for others, you will need to apply for funding from external sources. More information about available scholarships (for UK, EU and international students) can be found here.

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PhD Project: Quantum Many-Body Scars and Weak Ergodicity Breaking in Rydberg-Atom Quantum Simulators

Supervisor:  Dr. Zlatko Papic

A perennial mystery of nature is how order can exist amidst chaos. Familiar systems such as the clock pendulum exhibit regular periodic motion. This ordered behaviour, however, is fragile. For example, interactions between particles rapidly lead to chaos, forcing the system to thermalise and forget its initial state. This can be visualised as an ice cream that melts away and never finds its way back to the frozen state, see

https://www.quantamagazine.org/quantum-scarring-appears-to-defy-universes-push-for-disorder-20190320/
Quantum scars refer to the surprising behaviour that defies such common intuition: for special initial states, the ice cream periodically melts away and then freezes up again. Recent experiments on ultracold Rydberg atoms have found evidence of similar behaviour where the atoms were able to return to their initial state many times during the measurement. At this point, the origins of quantum many-body scars largely remain a mystery. Your project will develop computer simulations of quantum many-body scars in systems of ultra cold atoms in optical lattices, with the goal of predicting future experiments on these systems that may unlock a range of applications in the emerging quantum technologies. For an introduction to quantum many-body scars, see our recent review article: https://arxiv.org/abs/2011.09486

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PhD Project: Simulating black holes and quantum gravity with optical lattices

Supervisors: Prof. Jiannis Pachos

Unlike the fundamental forces of the Standard Model, such as electromagnetic, weak and strong forces, the quantum effects of gravity are still experimentally inaccessible. The weak coupling of gravity with matter makes it significant only for large masses where quantum effects are too subtle to be measured with current technology. Nevertheless, insight into quantum aspects of gravity is key to understanding unification theories, cosmology or the physics of black holes. The project aims to simulate quantum gravity with optical lattices which allows us to arbitrarily control coupling strengths. Possible realisations will be considered of (1+1) or (2+1)-dimensional Dirac fermions, with ultra-cold fermionic atoms arranged in a honeycomb lattice, coupled to massive quantum gravity, simulated by bosonic atoms positioned at the links of the lattice. Configurations of black holes will be considered and studied within the quantum information framework.

Apply via https://phd.leeds.ac.uk/project/1088-simulating-black-holes-and-quantum-gravity-with-optical-lattices

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PhD Project: Chiral Gravitons in Topological Quantum Matter: From Solid-State Materials to Quantum Computers

Supervisor:  Dr. Zlatko Papic

A major open problem in modern physics is the table-top generation and detection of emergent particles analogous to gravitons – the elusive mediators of gravitational force in a quantum theory of gravity. In solid state materials, recent work by Haldane has pointed out that fractional quantum Hall (FQH) phases of matter host graviton-like excitations as they respond to the curvature of space they live in. Unfortunately, direct experimental observation of gravitons in FQH phases remains a challenge. This project will explore the possibility of recreating a similar kind of physics in the emerging quantum technology machines, e.g., ultracold atoms in optical lattices and quantum computers made of trapped ions. You will investigate how graviton-like particles and their dynamics could be controllably created and measured in such systems. To accomplish this task, your project will advance the understanding of geometrical degrees of freedom of fractional quantum Hall states, and then apply this knowledge to design quantum algorithms that can efficiently simulate graviton dynamics using the existing quantum hardware. For more information, see: https://arxiv.org/abs/2107.10267

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PhD Project: Topological quantum systems: synthesis and applications

Supervisor: Prof. Jiannis Pachos

Topological phases of matter (Nobel Prize in Physics, 2016) is one of the most exciting topics of modern physics. This area of research investigates the novel properties of materials that are robust against deformations of their parameters. This robustness makes topological material of interest to quantum technologies that request fault-tolerance in order to be useful.

The PhD project will aim to employ a variety of techniques and approaches from mathematics and theoretical physics (e.g. topology, quantum field theory, quantum gravity) in order to diagnose the exotic properties quantum matter can have. A final goal is the application of these investigations to proposing topological quantum computation schemes that are robust against errors.

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PhD Project: Computer Simulations of Biological Macromolecules

Supervisor: Dr. Sarah Harris

Computational models are invaluable for visualisation in molecular biology, as they employ our best quantitative physical understanding of biomolecules and their interactions to predict their dynamics, which is often missing from biophysical experiments. Now that biophysical techniques are revealing highly organised supermacromolecular architectures at the length-scale directly above that of single molecules, which was invisible until very recently, there is a need for new computational tools to intepret these experiments. We are developing two lines of research in supermacromoleular biology – one for DNA, and one for proteins.

While it is well known that DNA is the molecule of heredity and that the sequence of bases in DNA encodes the genetic information that defines an organism, the way in which genomes are regulated is not understood. Recent experimental data shows that the physical arrangement of DNA within the nucleus is critical to genetic control. We have developed a model system involving small DNA circles that we can analyse both by experimental methods and atomistic computer modelling using well established computer programs to understand how the packaging of DNA helps in the control and regulation of the cell, and how it influences recognition by other molecules, such as proteins and drug molecules.

We are also writing our own modelling software that provides a continuum mechanics description of proteins, and which uses experimental electron microscopy data as input to the calculations. The model uses the Finite Element algorithm that we have generalised to include thermal fluctuations, known as Fluctuating Finite Element Analysis (FFEA), we are using this program to model the action of molecular motors such as myosin and dynein, and are improving our physical description of biomolecules and their interactions by adding more accurate representations of the hydrodynamic environment

Our approach is highly multidisciplinary, and we can adapt projects to suit researchers with backgrounds as diverse as physics, maths, chemistry, biology and computer science. Collaborative projects including experimental work are also available.

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PhD Project: Local relativistic quantisation for novel photonic devices

Supervisor: Dr. Almut Beige and Prof. Gin Jose

Background.

For many years, quantum opticians have recognised the importance of local photon theories in the study of locally-interacting quantum systems. Recently, the need for such theories has become even more urgent. For example, highly-localised wave packets which constitute ultra-broadband photons are now frequently used in linear optics experiments [1].

Recent related work.

These and other experiments [2,3] clearly demonstrate the need for a better understanding of the quantum physics of tightly confined light fields. In two recent papers [4,5], we have already shown that a local description of light, which must overcome several no-go theorems, is indeed possible. Starting from the assumption that the basic building blocks of the quantised electromagnetic field are local bosonic field excitations with a clear direction of propagation and polarisation, we identified their Schrodinger equation and constructed Lorentz covariant electric and magnetic field observables.

Outlook.

In this project we plan to model the interactions of atomic particles with local electromagnetic fields in novel photonic devices in the presence of semi-transparent mirrors using the results of Refs. [4,5] and standard tools from quantum optics. Initially, we plan to have a closer look at the optical quantum sensor for non-invasive continuous glucose monitoring which is currently being developed and tested by the proposed supervisors of this PhD project. For example, calculating spatially-resolved second- and higher-order photon correlation functions, we expect to obtain new tools for extracting even more information from sensor signals. Afterwards, we plan to have a closer look at alternative, highly-improved designs to further enhance the performance and to significantly broaden the applications of non-invasive quantum sensors.

[1] Ultra-broadband entangled photons on a nanophotonic chip, U. A. Javid, et al., arXiv:2101.04877.
[2] Cavity quantum electrodynamics and chiral quantum optics, M. Scheucher, et al., arXiv:2012.06546.
[3] How to administer an antidote to Schrödinger’s cat, J.-R. Alvarez, et al., arXiv:2106.09705.
[4] Quantising the electromagnetic field in position space, D. Hodgson, et al., arXiv:2104.04499.
[5] Locally acting mirror Hamiltonians, J. Southall, et al., J. Mod. Opt. 68, 647 (2021).

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