Non-equilibrium phenomena in Rydberg lattice gases with facilitation constraints.

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The exploration of quantum many-body systems far from equilibrium is a topical subject area in physics. In our project we aim to explore new aspects of this wide field, and in particular we will explore quantum analogues of fundamental physical processes underlying glass forming systems. We build on a recently established connection between lattice gases of interacting Rydberg atoms – which are atoms in highly excited states – and the physics of soft-matter models of glass formers. The latter are spin systems with so-called kinetic constraints that mimic excluded volume effects in supercooled liquids and make the relaxation dynamics strongly collective and slow. In Rydberg gases kinetic constraints emerge naturally as a consequence of the strong interatomic interactions. The situation we will focus on in our proposal concerns the so-called facilitation constraint where the excitation probability is enhanced in the vicinity of an excited Rydberg atom. This mechanism is akin to canonical classical glass forming models, such as the Fredrickson-Anderson spin model, which also features such conditional excitation dynamics, i.e. a spin is only flipped if a neighbouring spin is excited. These classical model systems display hallmark features of glassines, such as dynamical heterogeneity as well as ultra-slow relaxation. Rydberg atoms offer the unique advantage to extend and explore these dynamical phenomena in the quantum domain where facilitated spin flips are fully coherent. Very little is known about this regime, as there exist hardly any experiments and state-of-the-art numerical techniques quickly reach their limit of applicability. This is particularly the case when long times and higher dimensions are involved.The goal of the proposed project is to conduct an interlinked experiment-theory research programme that sheds light on the correlated quantum dynamics of lattice spin gases in the presence of facilitation constraints. To this end we will augment an existing experimental platform to allow for the observation and characterisation of Rydberg lattice gases in one- and two-dimensional systems over long times. Furthermore, we will develop theoretical models and numerical approaches to understand the correlated many-body dynamics in close connection to the experiment which will allow us to scrutinise and validate approximations. We expect that our project will shed new light on non-equilibrium phenomena, including metastability, ergodicity breaking as well as the emergence of glassiness, in the largely unexplored quantum regime. Our research will deliver new approaches to experimentally control and monitor many-body quantum systems over long times, we will deliver new theoretical methods and establish a link between cold atomic physics and the physics of soft-matter systems.