Optical Energy-Difference Conservation in a Synthetic Anti-PT-Symmetric System.

Anti-parity-time (APT) symmetry is associated with various effects beyond the fundamental limitations implied in the standard Hermitian-Hamiltonian dynamics. Here, we create an optical APT-symmetric system in a synthetic frequency domain using a conventional fiber without intrinsic gain or loss and experimentally reveal photonic APT-symmetric effects, including energy-difference conservation and synchronized power oscillation, which have not yet been confirmed experimentally in the optical domain. The optical fiber-based APT-symmetric system has a long interaction length because of its negligible loss, and the APT-symmetric Hamiltonian is precisely tunable with optical pumping density and phase mismatch. On this basis, we observe the phase transition at exceptional points, energy-difference conservation, and synchronized power oscillation. Our results provide a robust theoretical and experimental framework connecting the emerging non-Hermitian physics with technologically important nonlinear fiber-optic interactions.