Quantum Matter in and out of Equilibrium

Matter -- substance in the world around us -- is "condensed" when its many pieces act in concert. Examples of condensed matter are virtually limitless, since any material is comprised of many individual atoms. The study of condensed matter on a microscopic scale inevitably involves quantum physics -- the laws of nature that apply to small objects such as individual atoms or electrons. Using quantum theory to study condensed matter lies at the heart of our research.

Quantum condensed matter theory contains some of the most important, most difficult, and most intriguing questions in modern science. The reason is that the effects of quantum mechanics are all the more complex and surprising when many constituent parts of a large system behave collectively. Unexpected phenomena can "emerge" on large scales that bear no similarity to the microscopic properties. For example, many electrons can collectively "superconduct", carrying electrical current over huge distances with absolutely no loss of energy. An even more spectacular emergent behaviour in some systems is electron "fractionalisation", where the electron effectively has split into pieces!

Quantum condensed matter theory is of fundamental academic interest because of the strange and surprising things that occur. It is also essential for the development of a vast range of technologies; it is no exaggeration to say that the computer and communications industries are built upon a foundation of discoveries and understanding in the quantum condensed matter theory of the last century. While our work is mainly academic in nature, our current explorations may very well pave the way for new industries in the years to come.

The Oxford quantum condensed matter theory group use modern tools and techniques to unravel the puzzles of quantum condensed matter, to push forward the boundaries of knowledge, and to lay the groundwork for technologies of the future. The research is motivated by the overarching goal of finding structure and patterns in complex quantum systems, and the particular projects are coherent directions united by both specific motivations and methods. The work is summarized by four themes, all at the forefront of modern research:
(1) Characterisation and Detection of Topological Matter, a particularly promising type of matter for future quantum technologies, only discovered recently, which so far has defied thorough understanding both theoretically and experimentally. One of its specific features is fractionalization.
(2) Non-equilibrium Quantum States of Matter, quantum systems which are not well described by the conventional tools of thermodynamics and statistical mechanics developed in the last century.
(3) Geometric Descriptions of Topological Phases -- the best approach to understanding topological matter from Theme (1) often uses a geometrical language.
(4) Disorder in Correlated Quantum Matter -- some types of matter appear only in systems with many impurities or irregularities in the arrangements of atoms.

The understanding we gain from these explorations will in turn open up new scientific directions.

Many of the technological revolutions of the last century had their primary origins in our increased understanding of quantum condensed matter on a microscopic scale. The modern computer industry, optical communication networks, and magnetic resonance imaging - whose influence on society has been transformative - arose from fundamental breakthroughs in understanding the quantum theory of electrons, light and magnetism in condensed matter. The work proposed here has, in the long term, the potential to benefit society in a similar way. Projects concerned with topological matter, for example, could have direct application in achieving practical quantum information processing - a goal shared by many, including government agencies in the UK and elsewhere, as well as by companies such as Microsoft with whom we work closely (two of us being consultants for their quantum computation effort). Projects advancing our understanding of non-equilibrium quantum physics, which explores systems that are strongly driven and are not well described by the idea of temperature provide another example. As electronic circuits get smaller and faster, they become less and less well characterized by traditional thermal concepts and new techniques will be required to understand the quantum physics that occurs in these systems. Our hope is that the quantum effects currently being studied in our proposal might ultimately be harnessed and functionalized in future technologies of great relevance to the semiconductor industry. Our high profile work in these directions and others, although still in the fundamental research stage, contributes strongly to maintaining the status and reputation of the UK as a highly stimulating environment for the most important scientific and technological developments.

In addition to a large international community of researchers who will be major beneficiaries of our work and its outputs, other direct beneficiaries include students and postdoctoral researchers of the highest international calibre, who come from around the world to work with us and study under our tutelage. We train PDRAs to think independently and critically, and provide them with a sound scientific training and the ability to solve problems using high level reasoning, analytical and computational skills. Our PDRAs will, as they have done in the past, become the university faculty, leaders of industry and commerce and decision makers of the future.

While the main objectives of our proposal are naturally several steps removed from technology at this point, we nonetheless remain keenly aware that some of our advances may be of practical importance in the medium term. For example, as a result of one of our current EPSRC grants, a patent was filed pertaining to near-term advances in quantum technologies. We will continue to review our research for opportunities for technology transfer.

Scientific understanding also has an important role to play in enriching the quality of life, in a way analogous to music or art. It is culturally important to make the general public more aware of the wonders of modern science. Parts of our programme (including the ideas of emergence and topological order that are central to this research) are well suited for such exposure, and as experienced communicators, we are very involved in presenting our work to the wider public. For example, P. Fendley has written several articles for the general public including in Science News and Psychological Inquiry. S. Simon gave a TEDx talk in January 2015 with a live audience of over 1800 with many more expected to watch later on the web. We will also reach out to the public by producing a web site that explains our research and the entire field of "quantum matter" in an engaging way. We hope that this type of activity will also help to inspire the next generation to engage in scientific pursuits.