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

Abstract

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 experimentally 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.

12 pages, 8 figures

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Topological Origin of Non-Hermitian Skin Effects
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Observation of parity-time symmetry breaking in a single spin system
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
• Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal
• Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins
• Simulating Exceptional Non-Hermitian Metals with Single-Photon Interferometry
• Precision measurement of the lifetime of the 6p 2P_1/2 level of Yb+
• Eigenvalue topology of non-Hermitian band structures in two and three dimensions
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Non-Hermitian Absorption Spectroscopy
• Exceptional Heavy-Fermion Semimetals in Three Dimensions

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