Exceptional point in a trimer chain of oscillators with a quadratic driving

TL;DR

This paper investigates exceptional points in a dissipative trimer chain of coupled oscillators driven by quadratic photons, revealing unique spectral features and a method to estimate coupling strength.

Contribution

It demonstrates the emergence of exceptional points in a quadratic-driven trimer chain and links spectral peak behavior to the system's coupling strength.

Findings

Optical spectrum splits into two peaks at the exceptional point

Peak positions relate to the natural frequency of a closed system

Post-exceptional point, peak positions remain unchanged, aiding coupling estimation

Abstract

Exceptional points of a dissipative chain of three coupled oscillators (trimer), which is driven by quadratic photon, are investigated. The exceptional points emerge from the coalescence of both eigenvalues and eigenvectors of the dynamical matrix that describes the first moments of the trimer. At the exceptional point, we found that the optical spectrum is split into two peaks, instead of a conventional single peak, as in the case of a single oscillator. In particular, the positions of these peaks correspond to the natural frequency of the trimer in a \textit{closed system}, which depends only on the coupling strength. Furthermore, after passing the exceptional point, the peak positions do not change, which can be used to estimate the coupling strength between oscillators.