Zhiyuan Liu

Aharonov-Bohm (AB) caging is a complete localization phenomenon in two-dimensional lattices due to destructive interference induced by the background gauge fields. However, current investigations of AB caging are mostly restricted to the Abelian gauge field case, and the observation of AB caging under non-Abelian gauge fields in a quantum system still remains elusive. Here, we report experimental realization of tunable synthetic non-Abelian SU(2) gauge fields in a rhombic lattice, engineered within the synthetic dimensions of a vibrating trapped ion with multiple levels. We realize AB caging under both Abelian and non-Abelian gauge fields and systematically investigate the distinctive transport properties of the non-Abelian case. In particular, we observe typical emergent quantum dynamics unique to non-Abelian AB caging, including initial-state-dependent dynamics, second-order effects, and asymmetric caging behavior. These observations demonstrate the trapped ion system as a powerful platform for simulating emergent phenomena in high-dimensional quantum systems with exotic synthetic gauge fields.

In the lattice system, when the synthetic flux reaches a $π$ phase along a closed loop under the synthetic gauge field, destructive interference occurs and gives rise to the localization phenomenon. This is known as the Aharonov-Bohm (AB) caging effect. It provides a powerful tool for the study of quantum transportation and dynamical effects. In the system where lattice sites possess internal structure and the underlying gauge field is non-Abelian, localization can also occur, forming the non-Abelian AB caging. Here, we propose an experimental scheme to synthesize non-Abelian gauge fields with a single trapped ion by coupling multiple internal levels and Fock states in its motion via laser fields. In contrast to the Abelian AB caging, we numerically observe that the non-Abelian AB caging occurs either when the interference matrix is nilpotent, or when the initial state is specifically set. Our experimental scheme broadens the study of localization phenomena and provides a novel tool for the study of non-Abelian physics.

Quantum error correction (QEC) is essential for practical quantum computing, as it protects fragile quantum information from errors by encoding it in high-dimensional Hilbert spaces. Conventional QEC protocols typically require repeated syndrome measurements, real-time feedback, and the use of multiple physical qubits for encoding. Such implementations pose significant technical complexities, particularly for trapped-ion systems, with high demands on precision and scalability. Here, we realize autonomous QEC with a logical qubit encoded in multiple internal spin states of a single trapped ion, surpassing the break-even point for qubit lifetime. Our approach leverages engineered spin-motion couplings to transfer error-induced entropy into motional modes, which are subsequently dissipated through sympathetic cooling with an ancilla ion, fully eliminating the need for measurement and feedback. By repetitively applying this autonomous QEC protocol under injected low-frequency noise, we extend the logical qubit lifetime to approximately 11.6 ms, substantially outperforming lifetime for both the physical qubit ($\simeq$0.9 ms) and the uncorrected logical qubit ($\simeq$0.8 ms), thereby beating the break-even point with autonomous protection of quantum information without measurement or post-selection. This work presents an efficient approach to fault-tolerant quantum computing that harnesses the intrinsic multi-level structure of trapped ions, providing a distinctive path toward scalable architectures and robust quantum memories with reduced overhead.