Topology has stepped into an increasing number of areas in physics, particularly through the concept of topological phases of matter. These states of matter are characterized by the robustness of certain physical quantities under small perturbations of the system. They also exhibit specific transport properties located at the boundary of the system, which are protected by the underlying topology. These unique characteristics are expected to trigger various applications, from the definition of physical standards to the development of robust quantum computing.
In condensed matter physics, electronic systems exhibiting a quantized Hall conductivity constitute the most famous example of topological systems. A wide variety of topological systems have been discovered, from integer and fractional Hall states to topological insulators and superconductors. However, condensed matter systems are often plagued by undesired effects due to disorder or difficulties in accessing and manipulating single electrons. This motivates the need for developing alternative platforms, such as atomic gases or photonic systems.
In the TOPODY project, researchers have developed a new approach using a platform of ultracold dysprosium atoms. The key development was the use of synthetic dimensions encoded in the giant spin of dysprosium atoms, which gave them flexibility to create artificial gauge fields. This allowed them to reproduce the equivalent of a two-dimensional quantum Hall system with local control. They have also generalized the quantum Hall effect to more exotic geometries, including a cylinder and a system effectively evolving in four dimensions, which do not have equivalents in solid-state materials. Additionally, the flexibility of the light-spin coupling used to generate the gauge fields has enabled them to probe entanglement properties, which play a fundamental role in topological quantum systems.
The researchers have also made important steps towards the realization of strongly-correlated topological systems, which involve more complex correlations between particles. These achievements demonstrate the importance of ultracold atomic systems for exploring fundamental questions in condensed matter physics. They may lead to the realization of even more complex systems, such as those exhibiting the emergence of low-energy excitations with anyonic character, which could serve as a starting point for developing new types of quantum computation protocols.
