Bidirectional Wireless Sensing Based on Coexistent PT and Anti-PT Symmetries

External perturbations applied at the exceptional point (EP) of parity-time (PT) or anti-PT (APT) symmetric systems demonstrate the extreme sensitivity of eigenvalues. The phase transition toward the eigenvalue-coalesced state, however, restricts the sensing functionality in a certain perturbation direction. Here, we construct a system with a global Hamiltonian that simultaneously satisfies PT and APT symmetries. By strategically setting coincident EPs of PT and APT symmetries, a bidirectional sensing functionality is realized. Furthermore, the challenge of wired resistive coupling (imaginary coupling) in existing electronic APT-symmetric structures is overcome via substituting it with wireless, cascaded, and inductive couplings (real couplings). After integrating a pair of dual APT-symmetric subsystems into a PT-symmetric system, a fully wireless and bidirectional sensing system is constructed by using coupled RLC resonators. The simulations and experiments are good consistent with the theoretical analysis of the system behavior, following an
$\sim \vert \varepsilon \vert ^{0.5}$
sensitivity for the perturbation
$\varepsilon $
at the EP. Our work lays the groundwork for wireless APT-symmetric systems in electronics and coexistent PT- and APT-symmetric systems in physics as well.