Coherent Many-Body Quantum States of Matter

In our everyday life we rarely think about the effects of quantum mechanics --- and yet they are constantly around us, determining the properties of every material object in our world. The laws of quantum physics define every property of matter, from the behaviour of individual atoms, to how the atoms bind together to form materials, to the characteristics of these resultant materials. Our understanding of this chain of influence is one of the greatest triumphs of modern science. It is only through this understanding that scientists have engineered modern technologies and devices such as computers, mobile phones, and fibre-optic communications.

In the field of quantum condensed matter, we are concerned with materials, and the quantum mechanics of matter, at a very microscopic scale. Our aim is to uncover new principles, predict new behaviours, new types of matter, and enable new applications.

A key concept that we focus on is the idea of quantum mechanical coherence in matter. The word "coherence" here implies that many microscopic objects are acting together in concert. Such behaviour, when it occurs, allows for the effects of quantum physics to be greatly enhanced. A prime example of coherent behaviour occurs in a superconductor, where due to the effects of quantum mechanics, electrons can flow forever with zero resistance and zero energy loss. In the last decades it has become clear in our community that quantum-mechanical coherence in materials is much more common than we previously expected, although its effects are often subtle and well hidden from our view.

Understanding coherent effects in systems made of many particles (i.e., in material substances) is the main aim of the research supported by this grant. We use a combination of modern mathematical and computational tools to investigate the puzzles of our field. The physics we study is highly complex because in such systems, the many constituent particles interact strongly with each other. As a consequence, qualitatively different behaviour emerges. Because of the novelty of these effects, this field of study is both challenging and exciting, attracting some of the best and the brightest young scientists.

We have divided our effort into three main themes:

Understanding Quantum Many-Body Dynamics: the investigation of how quantum mechanics effects the time evolution of material systems on a microscopic scale. We aim to determine new principles for how coherence is created, spreads, and is destroyed, and how this affects the properties of the substance.

Exploring Quantum Behaviour Far From the Ground State: for over a century it was believed that if heat energy is put into a physical system at one point, it will inevitably spread out to other regions. In the last few years, however, it has become clear that due to the effects of quantum coherence in interacting disordered systems, added energy may remain localized in one region in a stable fashion. We aim to understand better the properties of systems that present such stable and/or coherent high energy states.

Identifying Topological Platforms for Quantum Coherent Phenomena: topological matter exhibits subtle long-range patterns of coherence that cannot be understood by local descriptions. Because of these global effects, such materials are believed to be particularly well suited for robust quantum computing applications. The study of these substances therefore has attracted researchers from physics, mathematics, and computer science. We will explore these materials, where they exist in nature, how they might be engineered, and what their applications are.

While our research is mainly academic in nature, we hope that, analogous to discoveries in basic semiconductor physics a century ago, our discoveries may enable technological revolutions of the future.

The underpinnings for much of modern technology lie in our understanding of quantum condensed matter, one of the great accomplishments of twentieth-century physics. Transformative innovations such as the transistor, light-emitting diodes, solar cells, optical communication networks, and magnetic resonance imaging all build on the fundamental understanding of how quantum theory and statistical physics govern the flow of electrons in response to heat, light, and current, and how their interactions can give rise to complex emergent states of matter such as magnets and superconductors. The work proposed here has the potential for similarly beneficial and transformative impacts on society. For example, one set of projects is devoted to the identification of new strongly-correlated topological states of matter that may potentially boost the unusual functionalities of topological matter into new regimes, perhaps more suited to various applications. Another set of projects involves building a deeper understanding of quantum dynamics and of properties of quantum systems that are far from their ground states. Both these aspects may be important in describing strongly driven collections of interacting quantum bits characteristic of many quantum computing protocols. Developing new techniques to study such systems can substantially advance the frontier of this field, which has seen a dramatic recent increase in overlap with industry - as reflected in growing interest from companies internationally, including Google, Microsoft, IBM, Intel, and many others.

Naturally, the large and growing international community of researchers in both academia and industry working on quantum condensed matter will be immediate major beneficiaries of our work and its outputs. Other direct beneficiaries will be the students and top-flight postdoctoral researchers who come to work and study with us since we are a world-leading centre for training the next generation of researchers. We help our PDRAs to grow into sophisticated independent researchers capable of tackling challenging issues, equipping them to become the university faculty, leaders of industry, and decision makers of the future, as evinced by our strong track record in this regard --- for example, no less than 15 junior members from our group have gone on to permanent academic positions in the last 10 years.

Although our primary objectives are some steps removed from immediate technological impact, we nevertheless support links with colleagues in industry, to remain informed about potential practical importance in the medium term. We maintain close ties to collaborators at Microsoft Research, Razorbill Instruments, and Honeywell Technologies. We will continue to review our research for opportunities for technology transfer.

We will ensure our results are disseminated to a broad scientific audience by publishing in leading journals. We, and our PDRAs, are often invited to speak at conferences. We often organize international meetings - for example S. Parameswaran is the lead coordinator for a 13-week program at the Kavli Institute in Santa Barbara that has attracted participants from both industry and academia. We will continue to reach a wider audience by summarizing our work in review articles, summer school lectures, notes and books.

We also recognise a responsibility to make the general public more aware of scientific advances, and of the role of science in enriching the quality of life, both materially and intellectually. To this end we contribute to a range of outreach activities. These include: Oxford's Saturday Mornings of Theoretical Physics lecture series; a website (under construction in summer 2018) to present our research and the entire field of "quantum matter" in an engaging way; a TEDx talk by S. Simon in January 2015 (live audience 1800; 48,000 YouTube hits); and contributions to an online course on emergent phenomena by S. Parameswaran using the Coursera platform.