Recent progress in various areas of physics has demonstrated our ability to control quantum effects in customized systems and materials, thus paving the way for a promising future for quantum technologies. The emergence of such quantum devices, however, requires one to understand fundamental problems in non-equilibrium statistical physics, which can pave the way towards full control of quantum systems, thus reinforcing new applications and providing innovative perspectives. This project is dedicated to the study and the control of out-of-equilibrium properties of quantum many-body systems which are driven across phase transitions. Among several approaches, it will mainly focus on slow quenches and draw on the understanding delivered by the Kibble-Zurek (KZ) mechanism. This rather simple paradigm connects equilibrium with out-of-equilibrium properties and constitutes a benchmark for scaling hypothesis. It could pave the way towards tackling relevant open questions, which lie at the heart of our understanding of out-of-equilibrium dynamics and are key issues for operating in a robust way any quantum simulator. Starting from this motivation, we will test the limits of validity of the KZ dynamics by analyzing its predictions, thus clarifying its predictive power, and extend this paradigm to quantum critical systems with long-range interactions and to topological phase transitions. We will combine innovative theoretical ideas of condensed-matter physics, quantum optics, statistical physics and quantum information, with advanced experiments with ultracold atomic quantum gases. Quantum gases are a unique platform for providing model systems with the level of flexibility and control necessary for our ambitious goal. Their cleanness and their robustness to decoherence will greatly enhance the efficient interplay between theory and experiments, and provide a platform of studies whose outcomes are expected to have a strong scientific impact over a wide range of disciplines. On the short time scale we will exploit this knowledge to develop viable protocols for quantum simulators. In general, we expect that the results of this project will lay the ground for the development of the next generation of quantum devices and simulators.

The Far infra red (FIR) is defined as the region of electromagnetic spectrum found at wavelengths greater than 15 microns. FIR radiation plays a major role in the Earth's energy balance, accounting for approximately half of the emission to space from the Earth and its atmosphere in the global mean. Fundamental physics implies that FIR radiation will play an even more important role in influencing climate variability and change in the fragile polar regions. The very cold surface temperatures found in these locations means that a greater fraction of the emitted surface energy is found at longer wavelengths. Moreover, the associated very low water vapour concentrations typically found in polar regimes effectively open up 'windows' in the FIR, making it possible to see further into the atmosphere from the ground than would normally be possible at these wavelengths. By the same argument, more of the surface energy emitted at these wavelengths is able to escape to space. Recent work has suggested that assumptions about FIR surface characteristics made in many of the most advanced models that we use to predict climate - termed Earth-system models - mean that they may be missing an important polar climate feedback process. This could lead to an additional Arctic surface warming of up to 2 K by the 2030s which would be expected to affect the rate of ice-melt and sea-level rise. Termed the 'ice-emissivity' feedback, the mechanism depends on the fact that snow and ice emit more energy at FIR wavelengths than sea-water at the same temperature. Current Earth-system models typically assume that all surfaces have the same emissivity in the FIR and so do not include this feedback process. These same models also struggle to match surface observations of the downwelling radiation emitted by the atmosphere in polar regions, a shortcoming that is believed to be principally due to inadequacies in the representation of polar clouds. However, up to now a detailed evaluation of the polar radiation budget has been hampered by a lack of dedicated observations spanning the entire infrared, including the FIR. This project seeks to address this deficiency by bringing together a team of international experts in FIR research and climate modelling to develop a suite of observationally based tools which will be used to assess model performance and drive future improvements. In the course of this work we will derive the first ever assessment of FIR surface emissivity from in-situ airborne observations over the Greenland plateau; characterise the infrared surface radiation budget over Antarctica and assess the meteorological processes driving variability there over a range of time-scales; evaluate approaches used to derive synthetic FIR measurements from space-based observations; and begin the process of quantifying the ice-emissivity feedback in two leading Earth-system models.