Robust many-body Quantum phenomena through Driving and Dissipation

Schoolchildren learn of three phases of matter: Liquid, solid and gas. This list is glaringly incomplete at low temperatures where quantum mechanical principles more markedly determine material properties, leading to a plethora of new states including superconductors and topological phases, many of which have profound practical applications. The theoretical search for phases has implicitly assumed that all such systems come to thermodynamic equilibrium. This seemingly solid assumption underlies all thermodynamics, of which Einstein once said: "It is the only physical theory of universal content, which I am convinced...will never be overthrown". Two important questions arise: 1) is the assumption valid, i.e., do all systems tend to equilibrium and 2) when they do, how do they get there?

"No" is the shocking answer to the first question: some systems do not equilibrate, and a host of new non-equilibrium phases exist beyond the standard thermodynamic paradigm. The realisation was sparked by the discovery of many-body localised (MBL) phases, for which strong disorder prevents the equilibration of, e.g., charge and energy, contrary to the standard assumptions of thermodynamics. As revolutionary as MBL systems are, they do settle in the following sense: left undisturbed, observables settle (are static) at late times. Astonishingly, through a combination of both periodic driving and disorder, one can realise systems that robustly both fail to equilibrate and settle! Many-body localised time crystals (TCs) are a prominent example: for almost any initial state, their local observables eventually oscillate with a period that is an integer multiple (e.g., 2T) of the underlying driving period T, hence the system spontaneously breaks time translation symmetry. A prominent open question is whether the effect can be robust in an open quantum system, i.e., one subject to environmental dissipation.

The second question concerns how strongly correlated systems that do settle generate the dissipation that drives them towards a steady state, as well as quantitative questions of how bulk transport coefficients (conductivity, etc.) depend on the underlying microscopic parameters, how systems respond to external dissipation, and what features of transport are universal and robust. This field has a long history, few controlled results, and is of great practical importance: further progress will aid in the search for new materials with specified transport properties, and clarify existing experimental questions (below).

Our increased understanding of novel quantum phases revolutionised the material world. This project aims to continue the revolution, extending our understanding of the non-equilibrium frontier, searching for new robust---and hence potentially useful---quantum phenomena. Our primary focus will be on a poorly understood class of many-body systems, namely those subject to both environmental dissipation and periodic driving. We will explore various phenomena in this setting, most prominently aiming to: 1) develop the theory behind a new notion of time crystal stable in the presence of dissipation, 2) formulate a theory of quantum information/entanglement spreading and 3) expand our cachet of solvable models with dissipation. We will 4) use our theoretical results in 2) to develop new numerical techniques able to probe the experimentally relevant late time regimes in many-body systems. Finally, we will 6) transform our theoretical progress into experimental proposals pertaining to, amongst other possibilities: a) the exciting prospect that dissipation---rather than being an impediment---can be used to enhance the stability, and hence practical utility, of time crystals; b) exotic transport in interacting systems, e.g., anomalous spin diffusion in 1D quantum magnets; c) a careful assessment of claimed sightings of time crystals in experiments, particularly in Nitrogen vacancy centre platforms.

Industry: While this is a theoretically focussed project, I see two potential impacts on industry.

First, this project was conceived with the following assumption: the most interesting theory is that which pertains to robust phenomena - those which we may actually see in invariably messy experiments. If we are successful in the endeavour of generating new examples of stable quantum phenomena, the technological implications could be significant. A particularly interesting angle is the use of time crystals for metrology; a US based group (Lukin et al., Harvard/Berkeley, http://www.freepatentsonline.com/y2019/0219644.html) has already filed a patent in this direction, but I believe they are not harnessing the full potential of the effect or its generalisation to open systems (which forms the focus of this study). With a combination of my theoretical expertise, and the metrological know-how of the Birmingham based "EPSRC Quantum Technology Hub for Sensors and Timing" (led by Prof. Kai Bongs), I truly believe that the UK can compete with high powered international groups and develop patents of our own, leading to new technologies in the longer term. This is an area where the UK cannot afford to fall behind. While it is true that the UK has made a tremendous investment in quantum technologies, there is currently a shortage of UK-led effort towards harnessing potentially game-changing many-body effects for metrology; this project will go some way to redressing the shortfall.

Second, part of this project aims to develop numerical tools (based on tensor product states/DMRG) for studying dynamics in many-body systems. These tools are applicable to the ab initio modelling of dynamics in 1D quantum systems, including molecules studied in quantum chemistry. Better numerical techniques will eventually enable a better understanding of the dependence of material properties on the underlying microscopic parameters, helping us to systematically search for new materials and states with specified properties. For example, with further development, I believe our methods can be adapted to understand driven-dissipative dynamics in the 2D Hubbard model (a toy model for high-Tc cuprate superconductors). Better simulations of high temperature superconductors, and particularly their response in pump-probe experiments (see e.g., M. Mitrano et al., Nature 530, 461 (2016)), could provide insights into how to increase Tc and hence extend the applicability of superconductors. To facilitate this impact, I will make the code base developed in this project publicly accessible via an institutional server.

UK and regional intellectual environment: this project will establish a world leading centre of theoretical excellence on cutting edge theory topics within the UK, outside the already well established London-Oxbridge triangle. It will benefit the UK and specifically the Midlands by further establishing Birmingham as the place to study quantum many-body physics and technologies. This in turn will facilitate the future attraction of talent to the Midlands, helping to rebalance perceived regional disparities in reputation/excellence.

UK Culture: As evidenced by the flurry of popular press on quantum time crystals, and more recently relating to Google's demonstration of quantum supremacy, the public are interested in the strange and wonderful possibilities presented to us by quantum mechanics. We will make our results accessible to the public via various avenues. 1) As I have done before, I will give interviews with the popular press (previously with Popular Mechanics and ABC Radio Australia) publicising our work. 2) I will also present our results to the local Birmingham public by giving a UoB hosted IOP public lecture. 3) A two minute professionally produced plain-language animation explaining our major results, which will be advertised on our group homepage and group Twitter account.