Phase Transitions and Non-equilibrium Dynamics in Homogeneous Quantum Gases

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Atomic gases cooled to less than a millionth of a degree above absolute zero temperature offer flexible experimental systems for fundamental studies of quantum mechanical effects. In particular they offer excellent test-beds for theories of many-body phenomena, such as Bose-Einstein condensation and superfluidity, which arise from the collective behaviour of many interacting particles. Over the past two decades, studies of many-body physics with ultracold atomic gases have been very successful. The resulting improved understanding of the fundamental principles of quantum mechanics is promising to also lead to many practical applications, including the development of novel materials, navigation instruments, and platforms for quantum information processing. A complete understanding of many-body physics, necessary for such developments, must include both equilibrium and non-equilibrium phenomena, and in the latter respect ultracold atomic gases offer some significant experimental advantages. Specifically they feature relatively long characteristic timescales (milliseconds to seconds), which allow for time-resolved studies of non-equilibrium processes.Traditionally, an important difference between "conventional" many-body systems, such as liquid helium and solid-state materials, and ultracold gases has been that the former are usually spatially uniform, while the latter were produced in bowl-like harmonic traps. This difference can sometimes be addressed using the so-called local density approximation (LDA), which assumes that the gas density varies slowly in space. However, for studies of some very important problems this is a serious hindrance. In particular, LDA breaks down close to phase transitions between different states of matter, where the particles become correlated over very large distances, and where some of the most interesting non-equilibrium effects also emerge. Recently, our group has made a major breakthrough in the field of ultracold atoms by creating first quantum gases in an essentially uniform trapping potential of an optical-box trap. This allows for closer connections with both other many-body systems and the theoretical calculations, and has opened up completely new research possibilities. It has already led to an important advance in the studies of non-equilibrium many-body physics, namely the most direct confirmation so far of the Kibble-Zurek theory of the dynamics of continuous phase transitions, which has implications as far reaching as understanding the formation of large structures in the early universe.Under this Fellowship we will focus on fully capitalising on these exciting new developments. We will perform a comprehensive study of non-equilibrium phenomena in a homogeneous Bose gas with dynamically tuneable interactions, and will also collaborate with two other internationally leading groups, at College de France and MIT, to extend these studies to low-dimensional systems and Fermi gases. This will cement the UK's leadership in the emerging field of homogeneous quantum gases and more generally enhance the UK's position in the highly competitive field of ultracold atoms.