Rigorous Quantum Formulation of Parity-Time Symmetric Coupled Resonators

TL;DR

This paper develops a rigorous quantum Hamiltonian framework for PT-symmetric coupled coil resonators in the RF/microwave regime, enabling precise analysis and design of such systems.

Contribution

It introduces a novel quantum Hamiltonian derivation for coupled LRC resonators using basis transforms, advancing the theoretical understanding of PT symmetry in this context.

Findings

Quantum Hamiltonian for coupled resonators derived

Eigenvalues and eigenvectors obtained analytically

Numerical simulations confirm theoretical accuracy

Abstract

Rigorous quantum formulation of the Parity-Time (PT) symmetry phenomenon in the RF/microwave regime for a coupled coil resonators with lump elements has been presented. The coil resonator is described by the lump-element model that consists of an inductor (L), a resistor (R) and a capacitor (C). Rigorous quantum Hamiltonian for the coupled LRC coil resonators system has been derived through twice basis transforms of the original basis. The first basis transform rotates the original basis such that off-diagonal terms of the governing matrix of the equation system of the coupled coil resonators reduces to constants. Then a second basis transform obtains the quantum Hamiltonian, including the diagonal effective complex frequencies and the off-diagonal coupling terms, together with the transformed basis. With the obtain quantum Hamiltonian, the eigenvalues and eigenvectors of the coupled coil resonators can be obtained as usual as the quantum Hamiltonian. Finally, numerical simulation verifies the correctness of the theory. The quantum formulation of the coupled coil resonators can provide better guideline to design a better PT-symmetric system.