Fig. 1

Schematic diagrams of parity-time and anti-PT symmetric binary systems. a Parity-time (PT)-symmetric coupled oscillators implied by the PT-symmetric Hamiltonian H(PT) in Eq. (1). b Anti-PT (APT)-symmetric binary system derived from the relation H(APT) = ±iH(PT). In the two diagrams, κ denotes inter-resonator coupling constant and vertical arrows indicate directions of energy exchange between the coupled-resonator system and environment