Probing Complex-Energy Topology via Non-Hermitian Absorption Spectroscopy in a Trapped Ion Simulator

Non-Hermitian systems generically have complex energies, which may host topological structures, such as links or knots. While there has been great progress in experimentally engineering non-Hermitian models in quantum simulators, it remains a significant challenge to experimentally probe complex energies in these systems, thereby making it difficult to directly diagnose complex-energy topology. Here, we exper-imentally realize a two-band non-Hermitian model with a single trapped ion whose complex eigenenergies exhibit the unlink, unknot, or Hopf link topological structures. Based on non-Hermitian absorption spectroscopy, we couple one system level to an auxiliary level through a laser beam and then experimentally measure the population of the ion on the auxiliary level after a long period of time. Complex eigenenergies are then extracted, illustrating the unlink, unknot, or Hopf link topological structure. Our work demonstrates that complex energies can be experimentally measured in quantum simulators via non-Hermitian absorption spectroscopy, thereby opening the door for exploring various complex-energy properties in non-Hermitian quantum systems, such as trapped ions, cold atoms, superconducting circuits, or solid-state spin systems.

Automated summary

Non-Hermitian systems with complex energies, hosting topological structures like links or knots, have been experimentally realized using a trapped ion. Through non-Hermitian absorption spectroscopy, the complex eigenenergies of a two-band non-Hermitian model exhibiting unlink, unknot, or Hopf link topological structures are measured, showcasing the possibility of exploring various complex-energy properties in non-Hermitian quantum systems.