It is the central theme of the LATIS project to build on the latest developments of optical-lattice technologies in view of revealing exquisite properties of interacting topological matter. While developing our understanding of topological phases from a theoretical perspective, the project will also establish practical methods by which FQH states of neutral atoms can be unambiguously detected in current experimental settings. The ever-growing interest of the scientific community for synthetic topological systems, both for their elegance in addressing fundamental concepts and for their potential applications, highly motivate the LATIS project.
The design of topological band structures in optical-lattice setups has led to the experimental observation of various geometric and topological properties. However, until now, ultracold topological matter has been explored in the non-interacting regime of quantum gases, so that the observed quantities are genuinely associated with single-particle states. While the exploration of (single-particle) topological band theory still constitutes an active field of research, continuously revealing surprising mathematical concepts and novel phenomena in condensed matter, exciting avenues would become accessible upon combining engineered band structures with tunable inter-particle interactions. In particular, this scenario would provide a concrete path towards the experimental realization of strongly-correlated topological states in ultracold gases. Such intriguing phases of matter are reminiscent of the fractional quantum Hall (FQH) states discovered in the solid state, and they are predicted to exhibit remarkable properties, such as emergent fractionally-charged quasiparticles satisfying fractional (anyonic) statistics. The observation and manipulation of these “anyons” represents one of the greatest challenges in condensed-matter physics, motivated by their central role in topological quantum computing.
Activating and controlling interactions between neutral atoms are routine operations in the realm of cold atoms. However, severe complications arise when engineering band structures in the interacting regime of quantum gases. Indeed, the driving schemes that are required to generate topological bands generally lead to heating and instabilities through inevitable interaction processes. A promising strategy to nevertheless load and stabilize interacting atoms in a FQH state would consist in manipulating a very small ensemble of atoms within a few lattice sites of an optical lattice. Such a local addressing of individual atoms is now made possible by quantum gas microscopes, which are currently developed by several groups. This setting not only has the appealing potential to realize FQH states of neutral atoms for the first time, but it would also allow for unprecedented control over these strongly-correlated states of matter through the local addressing and detection tools provided by quantum-gas microscopes. Importantly, this emerging physical framework offers the unique possibility of analyzing topological order, and related notions such as entanglement, in a local and dynamical manner. Altogether, interacting atomic gases in topological band structures offer a unique and promising framework for many-body quantum physics, where theorists and experimentalists join forces to unveil fundamental properties of quantum matter.
