Realizing the entanglement Hamiltonian of a topological quantum Hall system.

Topological quantum many-body systems are characterized by a hidden order encoded in the entanglement between their constituents. While entanglement is often quantified using the entanglement entropy, its full description relies on the entanglement Hamiltonian, which is commonly used to identify complex phases arising in numerical simulations, but whose measurement remains an outstanding challenge. Here, we map entanglement to spectral properties by realizing a physical system whose single-particle dynamics is governed by the entanglement Hamiltonian of a quantum Hall system.

Realization of an atomic quantum Hall system in four dimensions.

Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted in dimensions > 3. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms.