Condensed Matter Theory
Condensed matter theorists at Lancaster employ quantum-mechanical methods to uncover phenomena in electronic, atomic and photonic systems, and determine the characteristics of novel and artificial materials.
The group is renowned for its comprehensive research portfolio in quantum transport, dynamics and material modelling, ranging from ultracold atoms over low-dimensional electronic structures to photonic and quantum-optical systems.
- First principle studies of low-dimensional materials using Monte Carlo techniques and Density Functional Theory
- Quantum transport in nanostructures including novel materials such as graphene and topological insulators
- Topological phases of matter in nanostructures
- Mesoscopic hybrid systems including superconducting components
- Quantum measurement and control of electronic nanostructures
- Disordered interacting quantum systems
- Superfluids and quantum-Hall liquids
- Ultracold atomic systems and Bose-Einstein condensates
- Quantum optics, light-matter interactions and polaritonics
- Metamaterials and topological photonics
Current PhD Opportunities
Measurement-induced many-body quantum dynamics
Dr Alessandro Romito
Many body quantum dynamics underpin fundamental physical phenomena, from thermalisation to information scrambling, and many aspects of quantum technologies like quantum information processing and transport. A recent breakthrough in the field has been the discovery of entanglement phase transitions induced by local quantum measurements. This new field of Measurement induced Transitions (MIT) has already made surprising connections with condensed matter, statistical mechanics, and quantum information science. Yet, the characterisation and implications of MIT are mainly unexplored, since they can’t be captured by methods developed to date for averaged quantum dynamics.
In this project, you will analyse MITs in different many-body systems and their implications for various quantum resources, from entanglement to topological quantum order. You will develop new numerical, and possibly analytical, methods to describe these new quantum phase transitions.
Topological Thermal Machines
Dr Alessandro Romito
Heat management at the nanoscale is a compelling task, even more now that quantum architectures for computation and transport are a near-future available technology. Exploiting quantum resources for this task is a broadly active research field. The aim of this project is to exploit specific quantum effects, i.e. topologically protected modes present in certain nanostructures. The project will focus on the thermal and thermoelectric performance of superconducting nanocircuits hosting quantum modes protected by topology, particularly when driven by external parameters to make them act at quantum thermal machines.
In this project, you will model superconducting nano-devices and their energy (heat) transport properties adapting the scattering matrix formalisms for time-dependent systems to the. You will develop both numerical simulations and analytical modelling for energy transport in driven topological superconductors.
Topological dynamics of photonic systems
Professor Henning Schomerus
Quantum systems can display robust features related to topological properties. These attain precise values that can only change in phase transitions where the states change their topological properties. While the scope of these effects is well understood for electronic and superconducting systems, a much richer range is accounted for photonic and in general bosonic systems. In these systems particles can be created and annihilated, which results in loss, gain, and nonlinearity. Recent years have seen a surge of activity to tailor these bosonic systems to their electronic counterparts, mostly by eliminating the mentioned differences. Going beyond these efforts, work of the supervisor and collaborators has demonstrated that topological physics extends beyond these mere analogies, leading to experimental demonstrations for laser, microwave resonator arrays, and polaritonic condensates.
What is missing is a detailed understanding of the actual scope of these extensions - how to systematically define the topological invariants, and classify systems in the manner achieved in the electronic context. This project tackles this question both generally, as well as practically by examining specific photonic and polaritonic model systems of experimental interest, and inquiring how to increase their robustness for possible applications. This project develops both analytical skills in quantum mechanics as well as numerical modelling skills.
Statistical descriptions of interacting disordered quantum systems
Professor Henning Schomerus
Quantum systems can encode information, but this information quickly becomes inaccessible if the associated degrees of freedom coupled with the environment. A key recent realization points towards a mechanism whereby quantum information can be localised by combining interactions with the generic disorder. This turns previously undesired artefacts into a highly valuable resource.
In previous work, we developed an efficient description of these so-called many-body localised systems based on a simple single-particle picture. This project aims to transfer this picture to a wider context, such as interacting spins or systems with additional internal degrees of freedom or dimensions. The project develops highly advanced numerical skills, such as DMRG, exact diagonalisation, and tensor network approaches. These will be applied to a range of model systems designed to yield conceptual insights that transfer to a wide range of systems.
Many-body quantum chaos and symmetries
Dr Amos Chan
A fundamental question in theoretical physics is how quantum information gets scrambled in quantum many-body systems. Strongly interacting quantum many-body systems are notoriously difficult to analyse. A recent breakthrough has allowed physicists to make progress by utilising a new family of minimal models, called random quantum circuits, which capture universal signatures of chaos, but yet are analytically tractable since the details of the physical system are abandoned except for unitarity and locality.
This project aims to advance the understanding of many-body quantum chaos, especially in the presence of symmetries, by studying observables like the spectral form factor, entanglement dynamics, and out-of-time-order correlator. This project develops transferable numerical skills and analytical skills when possible.
Dynamics in open quantum many-body systems
Dr Amos Chan
The difficulty of isolating a system from its environment in realistic set-ups motivates the study of open quantum systems, which are systems containing some microscopic regions coupled to external environments. How do open quantum many-body systems relax to its steady state(s) via dissipation? What are the universal signatures of dynamical phases in many-body open quantum systems? And how does the notion of chaos and localisation differ in open systems from isolated ones?
This project aims to advance the understanding of open quantum many-body systems, specifically by studying observables like spectral statistics and entanglement dynamics. This project develops transferable numerical skills and analytical skills when possible.
Theory of interacting quantum many-body system of atoms and photons
Professor Janne Ruostekoski
Cold atomic gases cooperatively coupled with light provide a rich strongly interacting quantum many-body system. The atoms and photons both are treated as quantum fields that can be solved using stochastic simulations and phenomenological approximate models. Long-range interactions between atoms occur through exchange of photons. The atoms can also similarly be considered of mediating interactions between photons. The aim of the project is to study such long-range dipole-dipole interactions between the atoms and their cooperative behaviour. The research can also be related to the effects of continuous quantum measurement processes and non-trivial topologies.
One of the success stories of quantum physics is how individual quantum particles have been controlled and manipulated for quite some time. However, the realisation of a fully controllable, strongly interacting and coherent quantum system, consisting of many particles, is an outstanding challenge. A new frontier of quantum physics has recently emerged utilising photons strongly coupled to quantum atomic gases, such as Bose-Einstein condensates and atoms trapped in optical lattice potentials. Such systems can utilise quantum phenomena for higher precision measurements and for quantum information processing while the interactions between photons and atoms can be engineered and manipulated for applications in quantum technologies.
The Condensed Matter Theory group provides extensive research and training opportunities for postgraduate students, covering subject-specific and general research skills.
Individual training involves supervision and advice that account for the students’ project requirements and the skills needed to make progress in their work.
Your studies are supplemented by weekly group meetings involving PhD students, MPhys/MSci students, postdocs and academics, including formal lectures, informal presentations and dice seminars on new and emerging topics.
Our students also attend the weekly departmental condensed-matter seminars and participate in the North West England Solid State lectures organised in conjunction with Manchester University.
Our students regularly attend national and international summer schools, including the Windsor Summer School Physics by the Lake, and present their work at a variety of scientific conferences. They also have the opportunity to develop their presentation skills via participation in the departmental outreach programme. The Faculty of Science and Technology, Information System Services, and the Library offer additional training.