Quantum Hall states in synthetic dimension

Ultracold atomic gases can be used to study a wide range of phenomena relevant to quantum matter, including topological states of matter related to the quantum Hall effect. Because of the charge neutrality of atoms, the simulation of the quantum Hall effect relies on the application of an artificial magnetic field, whose generation can be greatly facilitated in systems with synthetic dimensions.

In this talk, I will present an experimental realization of a quantum Hall system using ultracold gases of dysprosium atoms. We use the large spin J = 8 of this atom to encode a synthetic dimension in the magnetic projection states m. We couple the spin to the atomic motion using two-photon optical transitions, which leads to an effective magnetic field. We measure characteristic features of the quantum Hall effect, namely a quantized Hall response and gapless chiral edge modes.

We will then present a more complex experiment probing spatial entanglement properties, by simulating the so-called entanglement Hamiltonian. This experiment relies on the Bisognano-Wichmann theorem, which states that the entanglement Hamiltonian is given by a spatial deformation of the system, which we implement along the synthetic dimension.

Finally, we will present recent work in which we induce a topological phase transition by subjecting the system to an additional lattice potential. We will focus on the properties of the system in the critical regime.