Chanyang Im

Topological phases are governed by discrete symmetries that protect boundary modes against local perturbations. When translational periodicity is absent, the bulk states also become localized, so that a topological edge state can no longer be distinguished from them by spatial localization alone. Here, we investigate the topological edge state (TES) and bulk eigenstates of the anisotropic quantum Rabi model (AQRM) in a trapped-ion quantum simulator. The AQRM hosts a topological phase in a one-dimensional synthetic lattice, whose translational symmetry is broken by the non-uniform couplings scaling with the site index. While both the TES and bulk states show localized distributions, we find that the TES exhibits well-defined chirality and near-complete spin--boson separability as signatures of the topological phase, in contrast to the bulk states. Phase-space tomography further reveals that the bosonic component of the TES is a squeezed vacuum state, with squeezing up to 6.45 dB. These results identify the TES through its intrinsic topological signatures and establish eigenstate-level characterization as a route to probing topological phenomena.

Trapped-ion quantum networks rely on efficient ion-photon interfaces, while objective-based free-space collection systems must balance high photon collection with sufficient working distance for practical integration with ion-trap hardware. Here, we design and characterize an ion-photon interface with a long working distance of 26.15 mm and a high numerical aperture of 0.5. The core of the interface is a photon-collection objective consisting of six commercial spherical lenses with optimized spacing. The interface achieved an overall fiber-coupled photon-detection efficiency of (1.29$\pm$0.09)% from the ion to the detector and maintains fiber coupling over several hours without active realignment, supporting stable operation of the ion-to-fiber interface. Photon-correlation measurements show clear antibunching in the fiber-coupled fluorescence, confirming the preservation of non-classical photon statistics. These results demonstrate a practical implementation of a long-working-distance photon collection interface for trapped-ion quantum network experiments.