Quantum simulation of a general anti- -symmetric Hamiltonian with a trapped ion qubit

Non-Hermitian systems satisfying parity-time ( $$ ) symmetry have aroused considerable interest owing to their exotic features. Anti- $$ symmetry is an important counterpart of the $$ symmetry, and has been studied in various classical systems. Although a Hamiltonian with anti- $$ symmetry only differs from its $$ -symmetric counterpart in a global $$ phase, the information and energy exchange between systems and environment are different under them. It is also suggested theoretically that anti- $$ symmetry is a useful concept in the context of quantum information storage with qubits coupled to a bosonic bath. So far, the observation of anti- $$ symmetry in individual quantum systems remains elusive. Here, we implement an anti- $$ -symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence. We characterize the anti- $$ phase transition by mapping out the eigenvalues at different ratios between coupling strengths and dissipation rates. The full information of the quantum state is also obtained by quantum state tomography. Our work allows quantum simulation of genuine open-system feature of an anti- $$ -symmetric system, which paves the way for utilizing non-Hermitian properties for quantum information processing.