# Possible PhD Projects in Physics

Suggested projects for postgraduate research in Physics.

Physics research in the School of Mathematics, Statistics and Physics is concentrated in the following areas:

- Emerging Technologies and Materials (ETM)
- Astrophysical and Geophysical MHD (AG)
- Cosmology and Quantum Gravity (CQG)
- Quantum Matter (QM)

If you choose a PhD project from the areas we've suggested, please provide the titles of your top three projects and list in order of preference. Applicants are invited to apply online.

For further information on theoretical physics projects, please contact Dr Toby Wood, and for further information on experimental physics projects, please contact Dr Pablo Docampo.

#### Renewable energy

Renewable energySunlight is the most abundant energy source in our planet. Our research in this area is centred around “hybrid perovskite” structures as photoabsorbers in photovoltaic devices. These materials can be printed from simple precursor inks and achieve device efficiencies above typical solar materials such as poly-crystalline silicon.

To target more efficient and stable devices you will:

- explore and dig into the physics of these new materials
- elucidate their optoelectronic properties
- utilise them in solar cells

**Supervisor: ** Dr Pablo Docampo

You can find out more information on our group website.

#### Photonics

PhotonicsThe mastery of the photon and its application has become one of the most important innovation drivers for modern society and its economy.

Successful candidates will pursue a research programme in one of the fields of:

- quantum optics
- nonlinear photonics
- materials science
- fundamental physics

The work will be undertaken in a world class photonics laboratory with facilities and lasers that are at the cutting edge of research.

**Supervisor: ** Dr Noel Healy

#### 2D materials and sensing

2D materials and sensingGraphene is just one of a whole class of 2D materials characterised by being only one atom thick.

One property of 2D materials is that they are literally all surface! This makes them ideally suited to us as sensors elements:

- gas sensors
- strain sensors
- electrochemical sensors

We are interested in sensor applications for 2D materials. From research into the mechanism of transduction all the way to solving real world problems such as infrastructure monitoring and health.

**Supervisor: ** Dr Toby Hallam

#### Nanoelectronics technology

Nanoelectronics technologyWe have shown recently that the structure and geometry of nanostructured contacts can enhance electrical conductivity of metal semiconductor junctions compared to standard contacts (see paper doi: 10.1021/acsami.7b06595).

In this project you will characterise the electrical and physical characteristics of these nanostructured contacts using electron microscope and image analysis. This will enable several applications in low temperature electronics, device technology and energy conversion.

#### Materials for low-cost environmental sensing

Materials for low-cost environmental sensingThe government undertakes little monitoring of the North Sea even though there are many mammals (dolphins, whales etc) and other animals who might be affected by plastic pollution and run-off from farm fertilisers.

Activists and agencies lack sufficient resources as current monitoring technology is very expensive.

This project will investigate the possibility of using digital prototyping (eg specialist 3D printing materials to modify commercial electronics) for use as low-cost environmental sensors via field trials in collaboration with local partners.

Supervisor: Prof Nick Wright

#### Materials modelling from first principles

Materials modelling from first principlesReliable theoretical prediction of the properties of materials is of huge importance in the modern world.

Our group employs sophisticated methods and algorithms to model materials based on the fundamental equations of quantum mechanics. We aim to predict such properties without empirical input.

This is a rapidly changing and exciting field of research given continually improving methods coupled with ever more powerful supercomputers. Furthermore, skills obtained in numerical analysis and computational physics are highly transferable.

Projects are available in both methodological development and the application of methods.

**Supervisor:** Dr Mark Rayson and Dr Jon Goss

#### Metamaterials and light-matter interaction

Metamaterials and light-matter interactionMetamaterials (artificial electromagnetic media) can provide full control of light-matter interactions by arbitrarily tailoring the electromagnetic response of matter.

They can be applied at different frequency ranges such as:

- acoustics
- microwave
- Terahertz
- optics

They offer great opportunities in applications such as levitation, invisibility cloaking, plasmonics and quasi-optical devices, to name a few.

Our group is focused on the theoretical and numerical study of metamaterials and metasurfaces (2D version) from their basic principles and their applications to spatial manipulation of wave propagation.

**Supervisor: ** Dr Victor Pacheco Pena

#### Materials modelling for Nanoscale devices

Materials modelling for Nanoscale devicesAlthough relatively immature, Gallium Nitride is considered a disruptive technology and already finds applications in communications, electric cars and power generation. If we could replace Silicon with Gallium Nitride we could make a saving of £1 Trillion a year in global energy costs alone.

In order to realise these energy savings a number of challenges must be overcome. Our group employs a mix of analytical theory and high performance computer simulation to study the profound changes that occur on the nanoscale in Gallium Nitride aggressively scaled devices.

Projects are available in:

- Monte-Carlo simulation both development and application
- theory of confined electrons and phonons in nanostructures

Supervisor: Dr Angela Dyson

#### Buoyant magnetic fields in the Sun

Buoyant magnetic fields in the SunThe complex magnetic structures (coronal loops and prominences) that appear on the Sun's surface are believed to originate at the bottom of the solar convection zone. This is where the magnetic field is stretched and amplified until it becomes buoyant and rises to the surface. However, the details of this magnetic buoyancy process are poorly understood, and are strongly affected by the Sun's rotation and compressibility.

This project will combine analytical theory with high resolution numerical simulations, to determine how magnetic buoyancy operates under the conditions of the solar interior. We will also address the role that the rising magnetic field structures play in the Sun's overall dynamo process.

We will assume no prior knowledge of solar physics. A good understanding of fluid dynamics is essential.

**Supervisors: **Dr Toby Wood and Dr Paul Bushby

#### Stellar dynamics and evolution

Stellar dynamics and evolutionThe evolution of stars and their ultimate demise is affected by hydrodynamic processes occurring within their interiors throughout their lifetime.

Dynamical processes such as convection, rotation, waves and magnetism all greatly impact how these stars explode, chemically enrich the galactic environment and the properties of the stellar remnant.

This project will involve using multi-dimensional hydrodynamic processes to understand these dynamical processes and how they contribute to stellar evolution. Using this understanding, combined with observational constraints, we will develop one-dimensional prescriptions for use in standard stellar evolution models.

**Supervisor: ** Dr Tamara Rogers

#### Neutron star magnetic fields

Neutron star magnetic fieldsNeutron stars are extremely dense and rapidly rotating objects. They have the strongest magnetic fields in the Universe. Regular stars are powered by nuclear reactions. Neutron stars are powered by their vast reservoirs of rotational and magnetic energy.

A neutron star has a solid outer crust surrounding a superfluid core. Within this core the rotation and magnetic field are "quantised" into thin filaments called vortices and fluxtubes.

This project will develop a model for the dynamics of the vortices in the star's core, and their interaction with the strong magnetic field. We will base our model on suitably modified fluid equations that take account of the superfluid nature of the core.

Basic knowledge of fluid dynamics is required, as well as interest in developing computational skills.

**Supervisors: **Dr Toby Wood and Professor Carlo F Barenghi

#### Observational cosmology in a data-rich era

Observational cosmology in a data-rich eraCosmology is enjoying an era of unprecedented data abundance, with powerful observations already available and next-generation surveys on the immediate horizon. This wealth of data provides an exciting opportunity to pin down the nature of the mysterious dark energy which makes up 70% of the Universe. This PhD project will develop crucial, cutting-edge techniques for the analysis of modern cosmological survey data, and will apply these and other techniques to existing data in order to achieve new insight into the composition, history, and physical laws of our Universe.

**Supervisor:** Dr Danielle Leonard

#### Cosmological Superfluids

Cosmological SuperfluidsOur understanding of dark matter remains elusive despite recent successes. A revolutionary recent idea suggests that dark matter could actually exist in the form of a gigantic cosmic superfluid, whose wave phenomena span thousands of light years. Such studies, still at their infancy, have so far only been conducted in a simple non-interacting condensate picture of scalar dark matter.

The aim of this ambitious, interdisciplinary project (supervised by both cosmologists and cold-atom theorists) is to utilise stochastic techniques established in ultracold atomic physics – where they offer precise quantitative agreement with controlled experiments – to understand such cosmic superfluids. We aim to go beyond simple models used to date and include, for example, effects of self-interactions, while also allowing the co-existence of dark matter particles in both a condensed and a gas-like, non-condensed component, separated by a phase transition.

The goal of this ambitious project is to understand Bose-Einstein condensation on cosmological scales, and notably in a setting where the phase transition is actually driven by self-collapse due to gravity. Our numerical simulations will map the relevant parameter space, and could eventually lead to placing constraints, in combination with astrophysical observations.

Supervisors: Dr Gerasimos Rigopoulos (Cosmology) and Professor Nick Proukakis (Cold Atoms)

#### The Big Bang and inflation

The Big Bang and inflationThe main goal of our cosmology programme is to search for direct observational signatures of early universe cosmological models, paying special attention to the role of quantum processes during a period of cosmological inflation. This PhD project covers topical aspects of the very early universe, including:

- the quantum theory of the big bang and the origin of time
- investigations of inflationary models with quantum gravity and Higgs bosons
- models which seek to explain the origin of primordial magnetic fields

**Supervisor:** Professor Ian Moss

#### The large scale structure of the universe

The large scale structure of the universeObservational cosmology has undergone a revolution in recent years due to the availability of high quality data from satellite observations. This makes it possible to attempt to find out what makes up the dominant form of matter in the universe. It also helps us understand the mysterious dark energy which is driving the universe apart. This PhD project attempts to fit models of dark matter and dark energy to observations of large scale structure using new approaches and new theories of dark energy.

**Supervisors: **Professor Ian Moss

#### The early universe as a hologram

The early universe as a hologramResearch in string theory has shown that gravity is holographic. Certain gravitational theories have an equivalent description in terms of a quantum theory, without gravity, living in one spacetime dimensionless.

Holography represents our sharpest understanding of quantum gravity to date. It sheds new light on the fundamental problems of cosmology, from resolving the big bang singularity to explaining the pattern of perturbations visible in the temperature and polarisation of the cosmic microwave background. According to the theory of inflation, these perturbations began as microscopic quantum fluctuations in the matter density and geometry of spacetime. These fluctuations were subsequently stretched to macroscopic scales by the accelerated expansion of the universe. The dynamics of this process can be constrained through measurements of the cosmic microwave background. But it remains poorly understood from a fundamental theoretical perspective.

This project will use holography to recast the four-dimensional early universe as a three-dimensional quantum field theory. We will develop novel holographic approaches to explore the origin and symmetries of the primordial perturbations, building on recent advances in conformal field theory. Ultimately, the goal is to identify distinctive observational signatures of holography that can be tested through future cosmological observations.

**Supervisor**: Dr Paul McFadden and Prof Ian Moss

#### The cosmic large-scale structure

The cosmic large-scale structureThe cosmic large-scale structure is the skeleton of matter on the largest scales in the Universe. Galaxies trace this large-scale skeleton of dark matter and form in large gravitationally bound dark matter structures. With major upcoming galaxy surveys like Euclid and LSST, we will be able to track the growth of structure through time across large volumes. This will provide a cosmic laboratory for testing cosmology, fundamental physics and astrophysics with the large-scale structure. To extract the maximum amount of information from galaxy surveys, we need a) accurate models for the gravitational dynamics of the dominant dark matter component, and b) powerful statistics that capture key aspects of gravitational clustering.

This PhD project will tackle these two intertwined challenges. First, we will use novel techniques to describe gravitational dark matter dynamics, for example using the quantum-classical correspondence. The goal is to develop new analytical and computational tools to solve for the time-evolution of dark matter and hunt for signatures of particular dark matter candidates. Second, we will develop clustering statistics that capture non-Gaussian properties of the late-time matter distribution. The idea is to use a sweet spot of simple statistics that are easy to measure, and can be accurately predicted into the nonlinear regime. With this, we will seek to improve the standard analysis relying on two-point statistics to obtain unique insights into cosmology, fundamental physics and astrophysics.

**Supervisor: Dr Cora Uhlemann**

#### Measuring gravity and accretion using pulsars

Measuring gravity and accretion using pulsarsNeutron stars are extremely dense cinders remaining after stellar explosions. They often have strong magnetic fields and rotate rapidly, and this combination often results in their appearing to pulsate with extreme regularity. We call these objects "pulsars", and their measurable rotation provides an opportunity to take precision measurements in some of the most extreme astrophysical environments accessible to observation.

This project will use existing observations and request and carry out new observations of pulsar systems. These observations will strongly constrain theoretical models of how matter falls onto neutron stars, and in fact probe the details of how gravity works - does it behave as Einstein predicted?

An understanding of the basics of astronomical observation and data analysis is required, as is an interest in understanding models of these phenomena and how to test them.

**Supervisor: Dr Anne Archibald**

#### Quantum droplets

Quantum dropletsLandmark experiments with atomic quantum gases since 2017 have demonstrated a new form of quantum matter - a quantum droplet. These droplets have several unusual properties:

- they are superfluid - meaning that they are free from viscosity and can support eternal flow
- they are self-supporting - like stars under their own gravity
- they also have such high particle density that quantum mechanical fluctuations and correlations, normally negligible in the gas phase, become significant

These unique features bring the droplets to the fore for studying exotic physics, such as laboratory analogs of neutron stars and highly-correlated quantum systems, and developing new technologies, such as ultra-precise sensors.

This timely project will develop computational and/or analytical models of the droplets to explore these state-of-the-art opportunities.

**Supervisors: ** Dr Nick Parker and Dr Tom Billam

#### Ferrofluids go quantum

Ferrofluids go quantumCooling a gas of magnetic atoms down to absolute zero creates a so-called quantum ferrofluid, which combines two of the most extraordinary types of fluid - the quantum fluid and the ferrofluid.

Quantum fluids are fluids in which quantum mechanics takes over. They have no viscosity, can flow forever, and are well-known in the context of superfluid Helium and atomic Bose-Einstein condensates.

Meanwhile, ferrofluids are fluids of magnetic particles which can be controlled and directed by magnetic fields (indeed, they were first created by NASA as a rocket fuel to use in zero-gravity environments), give rise to fascinating patterns (try googling “ferrofluids”) and have found major technological applications.

What strange behaviours emerge when ferrofluids go quantum?

How can we control them using magnetic fields?

And what can they tell us about the fundamentals of magnetism and quantum physics?

These questions and more will be explored with state-of-the-art computational and/or analytic approaches.

Supervisors: Dr Nick Parker and Dr Andrew Baggaley

#### Atomtronics: A Novel Emerging Quantum Technology

Atomtronics: A Novel Emerging Quantum TechnologyImagine circuitry with neutral atomic carriers, instead of electrons and holes. The most evident features that result from such a design would be a reduced decoherence rate due to charge neutrality of the atomic currents, an ability to realise quantum devices with fermionic or bosonic carriers, and a tuneable carrier–carrier interaction from weak-to-strong, from short-to-long range, from attractive-to-repulsive in type. The rapid progress in ultracold atoms and device miniaturisation is spurring this dream to reality.

The newly-emerging field of atomtronics refers to harnessing ultracold atomic matter to produce devices that offer novel opportunities for precision measurements, including rotational sensing. The first prototype atomtronic circuit was experimentally demonstrated in 2014 and the field has rapidly taken off since then. The name atomtronics has been coined by analogy to electronics. It refers to circuits in which ultracold atoms are used to create atomic analogues of electronic components, such as transistors and diodes. Closed atomic circuits are facilitated by doughnut-shaped traps for the atoms, while the atomic dynamics are controlled by moving laser beams that allow for minimal matter transfer across a so-called `Josephson junction’, which acts as a weak link between different parts of the quantum fluid.

This project aims to study a range of such currently experimentally-accessible atomtronic devices using in-house state-of-the-art numerical simulations, with findings directly applied to experimental measurements and prototype circuits. Intended outputs include a detailed understanding of an atomtronic quantum interference device, or precision rotation sensor, a rudimentary demonstration of which has already been performed at the Los Alamos Laboratory in the U.S.

Supervisor: Professor Nick Proukakis

#### Quantum Mixtures

Quantum MixturesWe know well what happens when two classical systems interact: they can mix (e.g. milk and water), or phase-separate (e.g. oil and water). What happens then when two quantum fluids overlap? This depends crucially on their interaction strength, with the quantum nature of the many-body system setting new rules for their coupling – critically also depending on whether the atomic system is composed of bosonic, or fermionic, particles.

Motivated by experiments with a plethora of different mixtures of ultracold quantum gases, at temperatures below micro-Kelvin, the aim of this project is to study the static and dynamic properties of such multi-component systems.

Questions to be studied include:

- How do such quantum mixtures emerge from their classical systems across the phase transition?
- What difference does the bosonic, or fermionic, nature of the individual components play, and how does a double superfluid (i.e. a fluid in which both bosonic and fermionic components of a Bose-Fermi mixture are superfluid) differ from other mixtures?
- In particular, how does rotation influence the dynamics of quantum mixtures? (a question of indirect relevance to the cores of neutron stars)
- How does the presence of external (electromagnetic) coupling between different components influence the system’s properties?

Such questions will be addressed in close collaboration with European experimental groups, where such experiments are underway.

Supervisor: Professor Nick Proukakis

#### Atomtronic devices

Atomtronic devicesExperimental advances over the last decade are beginning to usher in an age of quantum devices, such as sensors and interferometers. They have the potential to surpass their classical predecessors in terms of:

- sensitivity
- reliability
- miniaturization

One paradigm for constructing such devices involves using ultracold atoms as the quantum element. This has led to the creation of "atomtronic" analogs of electronic (and optical) devices in which the electrons (or light) are replaced with a superfluid current of ultracold atoms. This atomic superfluid can be made to flow without viscosity through carefully shaped channels in a similar way to electricity flowing through circuits, and light travelling through photonic media such as optical fibres or nonlinear crystals. Owing to many-body quantum effects inherent in the atomic superfluid, atomtronics has possible applications in making ultra-sensitive, quantum-enhanced sensors and interferometers.

This project will develop computational and analytical models of novel atomtronic quantum interference devices. In particular, we will connect with recent developments in quantum electronics to generate and develop new proposals for atomtronic devices that exhibit quantum-enhanced performance.

S**upervisors:** Dr Tom Billam and Dr Clive Emary

#### Cosmological Superfluids

Cosmological SuperfluidsOur understanding of dark matter remains elusive despite recent successes. A revolutionary recent idea suggests that dark matter could actually exist in the form of a gigantic cosmic superfluid, whose wave phenomena span thousands of light years. Such studies, still at their infancy, have so far only been conducted in a simple non-interacting condensate picture of scalar dark matter.

The aim of this ambitious, interdisciplinary project (supervised by both cosmologists and cold-atom theorists) is to utilise stochastic techniques established in ultracold atomic physics – where they offer precise quantitative agreement with controlled experiments – to understand such cosmic superfluids. We aim to go beyond simple models used to date and include, for example, effects of self-interactions, while also allowing the co-existence of dark matter particles in both a condensed and a gas-like, non-condensed component, separated by a phase transition.

The goal of this ambitious project is to understand Bose-Einstein condensation on cosmological scales, and notably in a setting where the phase transition is actually driven by self-collapse due to gravity. Our numerical simulations will map the relevant parameter space, and could eventually lead to placing constraints, in combination with astrophysical observations.

Supervisors: Dr Gerasimos Rigopoulos (Cosmology) and Professor Nick Proukakis (Cold Atoms)

#### Is turbulence knotted?

Is turbulence knotted?Mathematicians, physicists and engineers have studied turbulence for more than a century. Almost all investigations into this fundamental problem of the natural sciences have concentrated the attention on two aspects:

- the geometry
- the dynamics of turbulence

Little attention has been paid, in comparison, to a third equally important aspect: the topology.

This is despite the fact that 19th century pioneers of fluid dynamics such as Kelvin and Helmholtz were already aware of the possibility of vortices becoming twisted, linked and knotted. Unfortunately, until recently, the only vortex structures which could be created in the laboratory were either very simple (such as vortex rings) or utterly complex (such as turbulence): the 'hydrogen atom' of topological complexity was missing. This situation suddenly changed in 2013, when Kleckner and Irvine, at the University of Chicago, showed that it is possible to create trefoil vortex knots under controlled and reproducible laboratory conditions. This breakthrough is now driving a great interest in the study of the topology of vortices and turbulence.

The project aims to:

- perform a numerical investigation of turbulent flows by solving the governing Euler or Navier-Stokes equations
- look for evidence of knotted structures.

The objectives are to:

- define and quantify the topological complexity of turbulence
- to explore the possibility of scaling laws

You should have an interests in fluid dynamics and methods of computational mathematics. You should be willing to learn tools from other relevant disciplines such as knot theory.

**Supervisors: **Professor Carlo F Barenghi and Dr Andrew Baggaley

#### Vortex lines as topological defects at phase transitions: micro big-bangs in superfluid helium

Vortex lines as topological defects at phase transitions: micro big-bangs in superfluid heliumThe progress of cosmology is limited as it cannot be studied in the laboratory. This remark motivates attempts to find physical systems which model some of the fundamental properties of the universe but are also experimentally accessible. One of such systems is the formation of topological defects at phase transitions. Below the temperature of approximately a milliKelvin, superfluid helium 3 exhibits a phase transition to a superfluid state characterised by the breaking of various symmetries that are good analogues to those broken after the Big Bang.

The experimental set up is the following. Superfluid helium 3 is locally heated by neutrons, creating a hot spot of normal liquid which expands and quickly cools back down to the superfluid state. Coherent superfluid regions of the liquid grow simultaneously, and, when they come in contact, the mismatch of the order parameter creates linear topological defects called vortex lines. It is thought that this process, called the Kibble-Zurek mechanism, in the context of cosmology, may be responsible for the formation of inhomogeneous large-scale structures, such as super clusters of galaxies. In liquid helium, the Kibble-Zurek mechanism has been observed experimentally at Helsinki and Grenoble.

To make better connection with theory, it is necessary to understand how the small region of vortex lines, a turbulent spot, diffuses in space and time: this is what we plan to do numerically. In particular, we want to find how strongly nonlinear processes such as vortex reconnections, which occur when two vortex lines collide with each other, affect the diffusion. Preliminary numerical experiment suggest that vortex rings evaporate away from the turbulent spot.

**Supervisor: **Professor Carlo F Barenghi

#### Vortex motion in atomic condensates

Vortex motion in atomic condensatesCurrent experiments with atomic condensates are concerned with the motion of vortices confined in a small geometry (typically discs or spheres). The small size of these systems means that this motion is affected by the boundaries.

The aim of this project is to gain more understanding of the behaviour of vortices and vortex clusters and possibly make connections with experiments. In particular, we shall use the point vortex method of classical Euler fluid dynamics and the nonlinear Gross-Pitaevksii equation to determine vortex trajectories and to study the chaotic properties of these vortex systems.

**Supervisor: **Professor Carlo F Barenghi