PT-symmetric electronic dimer without gain material

Abstract

Abstract In this paper, a way of building an electronic Parity Time (   )-symmetric dimer without gain material is presented. This is achieved by capacitively coupling a pair of LZC circuits, each combining an inductance L, an imaginary resistance Z and a positive/negative capacitance C. We derive the effective Hamiltonian of the system, which commutes with the joint   operator. The eigenspectrum displays spontaneous breaking points, where the system undergoes a transition from real to complex values. The transition points are imposed by the range value of the coupling thanks to the use of a negative capacitance. Temporal charge solutions and energy propagation are also analytically and numerically investigated, and the results are compatible. In the exact phase, these quantities oscillate, whereas in the broken phase, oscillations disappear, giving place to amplification. Our results pave the way to innovative   -symmetric circuits. Applications could include, among others, optics, metamaterials, photonics and sensitive detection.