Developing new approaches to study quantum many-body systems is of fundamental importance in various fields of physics ranging from high energy and condensed matter physics, quantum information and quantum computation. It also holds promise for a better understanding of materials, such as high-Tc superconductors, and fault-tolerant quantum computing which could strongly impact our modern societies. Whereas the equations describing the behaviour of interacting many-body systems are known, they cannot be numerically solved due to the exponential scaling of the Hilbert space with the number of constituents, requiring other approaches. To address problems that classical computers cannot solve, Feynman proposed in 1981 to use a quantum simulator. This machine is a well controlled device whose constituents behave quantum mechanically, allowing to simulate the hamiltonian under study. Various platforms have emerged over the past decade to perform these tasks, such as superconducting qubits, trapped ions or ultracold atoms. A formidable challenge nowadays consists in studying exotic entangled phases of matter with fractional non-local excitations, expected to provide robust storage of quantum information with respect to local decoherence. These excitations mostly occur in flat band systems where the ground state is highly degenerate. Serious candidates under investigation are topologically ordered phases such as fractional quantum Hall states and p- wave superconductors. Highly frustrated spin systems, where energetic constraints cannot be satisfied simultaneously for all spins, also host such robust quantum phases. Similar to Landau levels, the ground state is highly degenerate and strongly correlated phases with fractional excitations can emerge. The underlying topological order of such systems is an outstanding experimental challenge to address with only local observables. Cold atoms platforms with single particle resolution allow to directly measure non-local correlations and are thus highly appealing to study these entangled states of matter.
In FLATBANDS, we are building a novel quantum gas microscope operating with strontium atoms (Obj. 1) to study fractional quantum Hall states (Obj. 2) and frustrated magnetism (Obj. 3).
