$\mathcal{PT}$-symmetric electronics

TLDR

PT‑symmetric electronics provides an experimentally accessible platform that offers new insights into the properties of PT‑symmetric systems, a forefront area of mathematical physics. The authors employ a Liouvillian formulation to define an underlying PT‑symmetric Hamiltonian, enabling a deeper understanding of the system’s behavior. Experimentally, a pair of inductively coupled active LRC circuits—one amplifying, one attenuating—exhibit PT‑symmetric features such as normal modes, temporal evolution, and scattering, and when coupled to transmission lines the device can simultaneously act as an amplifier or absorber depending on wave direction and phase.

Abstract

We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide class of non-Hermitian systems which commute with the joint parity-time PT operator: typical normal modes, temporal evolution, and scattering processes. Utilizing a Liouvilian formulation, we can define an underlying PT-symmetric Hamiltonian, which provides important insight for understanding the behavior of the system. When the PT-dimer is coupled to transmission lines, the resulting scattering signal reveals novel features which reflect the PT-symmetry of the scattering target. Specifically we show that the device can show two different behaviors simultaneously, an amplifier or an absorber, depending on the direction and phase relation of the interrogating waves. Having an exact theory, and due to its relative experimental simplicity, PT-symmetric electronics offers new insights into the properties of PT-symmetric systems which are at the forefront of the research in mathematical physics and related fields.