Synthetic topological matter with ultracold dysprosium atom

Topological states of matter lie at the heart of our modern understanding of condensed matter systems. For example, in two-dimensional quantum Hall insulators, the non-trivial topology, defined by a topological invariant called the first Chern number in this context, manifests as a quantised Hall conductance and protected ballistic edge modes. Recently, the concept of synthetic dimensions has been experimentally exploited to engineer more exotic systems. It relies on internal degrees of freedom to simulate an additional dimension, which facilitates the realisation of artificial gauge fields for neutral atoms.
In this talk, I will present recent experimental works on integer quantum Hall systems using ultracold samples of atomic dysprosium. We benefit from the large total angular momentum J=8 of dysprosium atoms in their electronic ground state to simulate a synthetic dimension of 2J+1=17 lattice sites. Using optical couplings of different ranges, we encode two synthetic dimensions in a single spin, which we exploit to realise two systems: a quantum Hall cylinder and a four-dimensional quantum Hall system. I will focus on the quantum Hall cylinder and our realisation of Laughlin's topological charge pump. In a set of experiments, we probe the transverse Hall response and observe topological pumping of particles as we thread magnetic flux through the hole of the cylinder. Our measurements are in agreement with the quantisation of the first Chern number of the ground band.
In the last part, I will present some preliminary results on the measurement of the entanglement spectrum, a probe of topological order initially conjectured by Li and Haldane, in an integer quantum Hall system.