Non-equilibrium quantum matter

The understanding of non-equilibrium quantum systems is one of the greatest challenges of modern science, as recognised by the EPSRC Grand Challenges Programme. Its development will have profound effects across different research areas including quantum computation and information, quantum optics, and biology. Theoretical understanding of these systems will form the basis for future development of new generation fast and energy efficient microchips and instruments for precise measurements.

The occurrence of non-equilibrium behaviour is very common in Nature. The simplest example of this can be found when two objects with different temperatures come into contact. Other systems can show various levels of complexity from the physical process that leads to emission of a laser beam to the ultimate case of living organisms. The common characteristic property of these systems is the absence of uniform thermodynamic quantities such as temperature.

Some of the state-of-the-art experiments in this field are made with semiconductor nano-structures in high magnetic fields and very low temperatures. In these systems electrons move in a coherent way similar to photons in a laser beam. Remarkably, because of strong interactions, the electrons in these systems form new strongly-correlated emergent states which exhibit quasi-particles with only a fraction of the electron charge. Similar quasi-particles also occur in quantum magnetic materials in the so-called spin liquid states. In the future it is hoped that these particles will be used as fundamental building blocks of topological quantum computers. The problem of quantum motion of a large number of quasi-particles is in the class of non-equilibrium quantum problems, whose study constitutes one of the main aims of this research programme.

Interestingly, many of these systems show non-equilibrium steady states. Take a piece of metal and connect it on opposite sides to a heater and a refrigerator, a configuration which will result in a steady heat flow. A similar situation occurs in a system of interacting electrons in a quantum wire connected to a battery. The important differences with the former arise from the fact that the motion of particles in the wire obeys the laws of quantum mechanics, which lead to unusual quantum states. Recently it became possible to study these states in experiments, which resulted in a number of unexpected observations e.g. PRL 96, 016804 (2006); PRL 105, 056803 (2010). Next generation experiments will build quantum devices that use and explore the physics of non-equilibrium states based on the new theoretical and experimental insights.

The project is aimed at theoretical understanding of quantum systems which are driven far from equilibrium by, for example, applied voltage or fast switching of external fields. In this setting many physical systems with examples ranging from semiconductor nano-structures and superconductors to quantum magnets and ultra-cold atomic gases show remarkable emergent behaviour (see for example PRL 105, 056803 (2010), arXiv:1308.4336, Science 331, 189 (2011), Nature Physics 8, 325 (2012) etc). This comes as a result of intricate quantum entanglement which occurs in these systems due to motion of interacting particles under non-equilibrium conditions. The properties of these systems cannot be explained using standard theoretical framework, and it is the one of the central tasks of this project to develop this theoretical description.

Condensed matter physics has been the driving force of the tremendous progress that we see today, from the invention of a transistor, that revolutionised our lives, changed the way we think, work, and communicate, to lasers, that brought important advances in medicine, industry and computing. Things such as magnetic resonance imaging (MRI) and levitating trains as well as many remarkable advances in precision measurements came as a result of research in superconductors. The theory of condensed matter systems had profound impacts of its own in many branches of science including biology and particle physics. The concepts of broken symmetry, the theory of phase transitions and the idea of Higgs boson, which originated in superconductor studies, represent some of the most remarkable examples of deep connection between these fields.

From this perspective, being on the leading edge of fundamental research, the proposed programme will provide scientific competitiveness in the immediate future, and in the long term societal impacts and will contribute to UK economic growth. Learning how to create and manipulate the properties of strongly-correlated systems will offer a completely new window of opportunities, which has a potential to overshadow the semiconductor revolution.

This research proposal is in the field of theoretical condensed matter physics and its immediate impact will be in theory and experiment within academia. This includes research groups in the UK and internationally affecting a large number of scientific areas. The project has a potential to stimulate the development of new experimental directions in the UK in the fields of mesoscopic systems and cold atoms. The programme will also contribute to sustainability of condensed matter and cold atom experiments in the UK.

The field of quantum computations will benefit from this research on a number of levels. First, the project will provide theoretical understanding of the properties of electron quantum optics devices, the experimental development of which is one of the first steps on the way to quantum computers. Second, the theory of non-equilibrium edge states in electronic systems and cold atoms is an essential ingredient for understanding how to create and manipulate quantum states in these systems.

The traditional computer industry will start to benefit from this project in the next 10-15 years. With decreasing size, exponentially growing number of components and ultra-fast transistor switching times in modern semiconductor microchips, the industry is fighting increasing problems of heating and occurrence of errors. Without understanding of energy transfer, dissipation, and decoherence on a microscopic scale these problems cannot be solved and it is a task of the project to provide a fundamental basis to make this solution possible.

This programme will also contribute to improving the quality of training of young physicists through discussions, collaborations, seminars; training of PhD students and supervisions of postdocs, and publication of the results in scientific journals. I will use every opportunity to disseminate my research to a general public through the Cambridge University web-site, public lectures organised by the University, and through the Cambridge Science Festival.

The new analytical and numerical toolbox which will be developed in this programme will benefit experimentalists in mesoscopic physics and cold atoms, and the research in the strongly-correlated quantum systems and quantum chemistry.

The theory of quantum systems far-from-equilibrium is in its early age and the aim of this project is to transform this situation, bringing the UK into a world-leading position in this field. This is an extremely hard problem, but the impacts would be huge.