The central objectives of the AQuS project are to lay the grounds for experimentally feasible analog quantum simulation, focusing on three promising platforms: Ultracold atoms in optical lattices and in the continuum, as well as cavity polaritons. During the second reporting period strong progress was made both, on the experimental and the theoretical side, while these parts complemented each other, creating synergy in continued close collaborations.
Both, experimental and theoretical efforts were focused on working out measures of certification of quantum simulators, aspects of complexity and robustness, as well as exploring the implications of universal properties. Specific analog quantum simulators, including low-dimensional cold gases in lattices and uniform traps, as well as polariton lattices, were certified by comparing observables with available theory. This helped to build trust for the use of these simulators in extended geometries where no clear theoretical predictions are feasible.
Strong progress was made on the implications of universality for quantum simulators. On the theory side, different avenues have been taken, approaching the scaling properties with analytical field theoretical methods, developing new and more accurate approximation methods, as well as numerical simulations, including the holographic calculations in the first half of the project.
The project further aims at the use of the platforms built to quantum simulate intricate dynamical many-body phenomena. Experiment and theory developed methods to identify universal scaling properties in systems quenched suddenly close to critical configurations, studying in particular the properties of the self-similar dynamical evolution following a quench. Experimental efforts have lead to the identification of metastable non-thermal states as well as non-equilibrium scaling dynamics which can be captured within the theory of non-thermal fixed points. Furthermore, topological band occupations were realised on the out-of-equilibrium polaritonic simulator platforms.
Following up on the demonstration of prethermalisation to states well described by a General Gibbs ensemble in low-dimensional cold gas experiments, cumulants of the phase were read out up to tenth order. This furthermore allowed the quantum simulation of ground-state properties of a quantum sine-Gordon model, and identifying the relevant eigenmodes by means of analysing the measured correlations. The simulator platform furthermore allowed the detection of quantum recurrences in the extremely high coherent evolution of the system as well as the long-time Gaussification of the correlations, contributing new crucial insight into quantum thermalisation dynamics.
New tools for detection and quantification of entanglement correlations across a spatially extended multi-mode continuous cold atomic gas were developed and realised in experiment. These can serve as certification tools for a quantum simulator in that they systematically allow the verification of coherence in the system.
On the basis of the cold-gas lattice platform a first successful realization of many-body localisation within a geometry of uncoupled one-dimensional chains has been achieved. The system allows to study the dimensional crossover to coupled chains and to identify the sources of breakdown of localised states. It also will serve as a quantum simulator towards answering the outstanding question concerning the existence of MBL in higher-dimensional systems.
Polariton systems, in a joint experiment-theory effort were used to realize edge states in the s-wave band as well as the much more complicated p-wave case. Quenches in resonantly and non-resonantly pumped polariton condensates were studied both theoretically and experimentally, as well as quenches in quantum fluids of light in propagating geometries, to quantum simulate Hawking radiation phenomena.
