EPSRC-SFI: Non-Equilibrium Steady-States of Quantum many-body systems: uncovering universality and thermodynamics (QuamNESS)

QuamNESS will develop novel mathematical tools and powerful simulations to understand the fundamental principles governing the performance of the smallest possible engines. Miniaturised to only handfuls of atoms, these machines hold the promise of offering highly efficient ways of generating power, managing heat flows and recovering wasted energy in wide-ranging technologies, from microprocessors to chemical reactions.

In contrast to conventional engines, the pistons and gears of nanoscale machines are instead the flow of individual particles, such as electrons. By being so small, even a single electron hopping through the engine represents a remarkably disruptive stochastic event. Therefore, the operation of such machines is subject to violent random fluctuations, not dissimilar to a wildly spluttering engine. Moreover, these microscopic constituents of the engine do not behave like everyday objects, but instead obey the laws of quantum mechanics. Both these features make it extremely problematic to define familiar concepts, like heat and temperature, central to the formalism of thermodynamics that so successfully describes conventional engines. Yet such apparently unhelpful complications should rather be seen as unique features of such small machines, presenting a multitude of opportunities to be harnessed. Developing a new framework to unravel these quantum enhancements is of paramount importance and is a core objective of this project.

Quantum systems are well known to possess counterintuitive properties. This includes coherence, namely the idea that a particle can be in many places at once as a superposition. When there are many particles interacting, we can also have entanglement - a superposition of different multi-particle configurations - giving rise to novel correlations and spooky action-at-a-distance. Under the right conditions, these strange quantum effects can compete with and radically alter the usual random jittery thermal motion occurring in a system. This project will sharpen our view of this interplay and how it can be harnessed by reassessing the fundamental concepts of irreversibility and fluctuations.

Useful engines produce a finite power output. This means they are never as efficient as an ideal infinitely slow engine because they inevitably waste energy as friction during a rapid cycle. The trade-off between power output and efficiency relies on quantifying this waste as irreversible entropy production. Our work will reformulate entropy production in new ways best suited to reveal the contributions of quantum coherence and correlations prevalent at the nanoscale. Further to this, for classical machines entropy production is known to bound the fluctuations in time of the power output. Specifically, to make an engine splutter less at a given power output necessitates increasing entropy production. We will determine the highly non-trivial generalization of this relation to the quantum domain. Simultaneous to this, we will develop sophisticated numerical methods for simulating complex quantum machines composed of many interacting constituents, allowing these crucial properties to be predicted.

Our theoretical framework will be high beneficial to current experimental efforts aimed at engineering quantum technologies with super-efficient thermal management. The most pressing applications in this direction will be explored within the scope of this project, including an assessment of novel mechanisms for enhancing quantum thermal machines, the ability to control quantum systems via periodic driving and proposals for experimentally verifying these findings. The bold ambition of this project leverages the synergistic talents of the research team, with PI Clark's expertise in numerical methods complementing the analytical skills of Co-Is Paternostro and Goold.

Quantum thermodynamics is an emerging and expanding field that is experiencing a remarkable growth in output. Important progress is still needed before it can impact significantly on the technological and industrial sector. QuamNESS will contribute to narrowing this knowledge gap by providing an innovative and powerful platform that combines powerful numerics with advanced theoretical tools. Crucially, this mixture of methodologies is both fundamental and practical in nature. The proposed project will deepen our understanding of the conceptual building blocks of quantum thermodynamic processes at the smallest scales at the frontier of future technologies. It will also build sophisticated numerical methods for accurately tracking of the properties of increasingly complex systems relevant for the engineering of real nano-scale devices. The project therefore represents the first systematic merging of these two perspectives within the burgeoning field of quantum thermodynamics. Such a novel combination will spur new analyses of non-equilibrium physics, previously prevented by the inherent difficulty of simulating complex quantum systems and lack of clarity in how to quantify their functional behaviour.

By realizing its objectives, QuamNESS will thus make a substantive impact in our understanding of non-equilibrium steady states in the quantum regime, with immediate benefits for the broadest quantum community. In particular, QuamNESS's deliverables are of relevance for nanotechnology, chemistry, biology and, potentially, industrial applications in magnetic materials and memory devices. At the same time the project will help identify further challenges in the design of quantum devices and will lay the foundations of new thermodynamically inspired approaches.

As outlined in the Pathways to Impact, we will engage in a wide range of activities to initiate and sustain this long-term impact. This begins with a public project website to consolidate and make openly available all our academic outputs, presentations, tutorials, and videos aimed a general audience. Advertising of this project site through social media outlets, specialised and popular press will be enhanced by media production for vlogs and scientific cover art. Moreover, the project workshop will be squarely aimed at framing the project's output at the crucial interface between key scientific beneficiaries and industrial partners, including companies like Thales, IBM, MSquared, ColdQuanta, Google who are already involved with the UK's quantum technology hubs.

To facilitate the widespread adoption of the codes developed in QuamNESS they will all be made freely available by the end of the project on a popular public repository. This will enable both theorists and experimentalists to utilise the project deliverables and help realise broader scientific advances. Beyond this we envisage the code's increasing use in industrial R&D labs, as accurate simulation of quantum processes become critical. Quality, well documented code, adhering to best practices (see e.g. the Software Sustainability Institute) will be essential for the project to entice users of commercial software.

Additionally, the UK academic community will benefit from the enlarged cohort of scientists attaining skills in using and developing high-quality HPC software through their engagement with this project. Further work on algorithms and numerical methods underpinning this project will also carry benefits for other fields of Science, Engineering and Medicine wishing to engage HPC effectively. In the longer-term we anticipate that the inclusion of advanced parallelised stochastic methods into the TNT library will have far-reaching impact for its use in the field of Big Data analysis. Given the huge importance of complex classical systems in natural sciences, operations research and industry, as yet unforeseen applications of hybrid TNT methods could emerge in the near future.