  The exploration of non-Hermitian systems with parity-time (PT) symmetry has
witnessed immense research interest both fundamentally and technologically in a
wide range of subject areas in physics and engineering. One significant example
of the principal emerging fields in this context is the PT symmetric wireless
applications using multiple coils that are spatially separated but mutually
coupled with position-dependent coupling strength. Such a spatial PT
configuration limits the flexibility and miniaturization of the PT symmetric
designs. As far as this is concerned, inspired by scattering induced two
opposite whispering-gallery (WG) modes in an optical resonator, analogously
here we experimentally demonstrate a specially constructed second-order (2-nd
order) PT symmetry in a single coil resonator, whose currents with two
different directions are excited by internal bypass capacitor. Our proposed
structure has the following peculiar feature: First, the bypass capacitor
induces coupling in spectral resonances allow us to observe a 2-nd order phase
transition between symmetry regimes, without the need of a second coil in the
spatial PT case. Under this circumstance, this specially constructed PT
symmetry can be regarded as synthetic PT symmetry, which is enabled by coupling
modes with different directions. Second, by introducing two or more internal
bypass capacitors, the synthetic high-order PT symmetric system bearing such as
third-order exceptional point in a single coil resonator can be realized. These
results will provide a new paradigm to realize higher-order PT symmetry towards
the investigation of non-Hermitian physics in a synthetic perspective, which
can be extended to other physical platforms such as optics and acoustics.
