FOR 2414: Artificial Gauge Fields and Interacting Topological Phases in Ultracold Atoms

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Gauge fields are fundamental for our modern understanding of physics at all scales. From high-energy physics to gravity and condensed matter physics, they constitute a central tool for successfully describing physical phenomena. Recently, the experimental realization of artificial gauge fields for neutral ultracold atoms has opened a door to the quantum simulation of topological quantum effects in novel, unprecedentedly well controlled environments. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials. These systems can mimic the dynamics of electrons moving in a magnetic field, but also, the dynamics of elementary particles in non-Abelian gauge fields. Their versatility and tunability make them ideal platforms for investigating and testing the dynamics of quantum many-body systems in the presence of gauge fields. In this proposal we aim to theoretically investigate and experimentally realize novel topological phases of matter induced by synthetic gauge fields in ultracold atoms in optical lattices. By exploiting the latest developments in experimental, analytical and numerical techniques, we will attempt to characterize, engineer and probe topological phases such as topological insulators and superfluids, designing protocols to test their topological invariants, their exotic transport properties and the intriguing nature of their excitations. Special emphasis will be given to the investigation of the interplay between interactions and external gauge fields, providing routes to the realization and detection of interacting phases, such as topological Mott insulators, fractional Chern insulators and fractional quantum Hall liquids. Moreover, we will investigate out-of-equilibrium dynamics in the presence of gauge fields, exploring paths towards the realization of driven non-equilibrium topological phases. We expect our combined experimental and theoretical effort to bring both the theoretical understanding and the experimental realization of topological matter to a new level, paving the way towards future applications in quantum information processing and spintronics.