Interactive dynamics of many-body quantum systems

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. They also determine if and how systems of many interacting particles establish an equilibrium or steady state governed by a handful of statistical laws. Physicists are now able to engineer large, tunable collections of interacting quantum particles, both in quantum computing devices and in ultracold atomic gases and solid-state materials. Often, such systems cannot be described by standard techniques that focus on quantum states that have simple structures. In many cases, the routes by which such systems come to equilibrium involve subtle and surprising features of quantum mechanics, necessitating entirely new ways of thinking, or require substantial extensions of older approaches such as hydrodynamics. Another striking new idea that has emerged recently is that quantum mechanical coherence can be preserved even when many-body systems are far from their lowest-energy state. 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, but it is usually washed out as systems achieve equilibrium, which can often be described well using classical physics. Finding routes to evade this equilibrium allows for new and unusual physical phenomena with significant potential utility for quantum technology. Yet a third set of new concepts is motivated by the capabilities of the present-day "noisy, intermediate-scale quantum" (NISQ) devices. In contrast to conventional platforms, these offer the possibility of punctuating the time evolution of a many-body system by measurements, and using the results to shape future evolution - a new form of "quantum interactive dynamics", where the scientist is an active participant rather than a passive spectator. Understanding the new states of matter enabled in this setting and the protocols needed to implement them on NISQ processors is an exciting new frontier. We have organised our research into three themes: (1) What are the mechanisms by which quantum systems approach an equilibrium state? We will develop a better understanding of universal aspects of the equilibrium state in quantum many-body systems. We will also seek to understand certain experimental systems, such as cold atomic gases or solid-state materials, that can be studied using hydrodynamic principles and their generalizations. (2) How can quantum many-body systems evade thermalization to access novel non-equilibrium regimes? We will seek to understand how frozen-in randomness and special symmetries can arrest the approach to equilibrium and allow quantum coherence to persist even in highly excited states. (3) What new possibilities are enabled by "quantum interactive dynamics"? We will clarify how the evolution of quantum systems towards or away from equilibrium can be shaped by measurement and feedback. The answers to these questions are likely to be central in harnessing the full power of quantum mechanics to accomplish complex tasks. Understanding the far-from-equilibrium and interactive dynamics of quantum many-particle systems is likely to play a similar role in the development of future quantum computing devices as the quantum theory of solids did in the technological revolutions of the past century. Thus, while our research is mainly academic in nature, we hope that our discoveries will enable technologies needed to address the challenges of the next century.