Dynamical phase diagram of parity-time symmetry with competing saturable channels

TL;DR

This paper explores the complex dynamical phase diagram of parity-time symmetric systems with competing saturable channels, revealing phases, chaos, and non-reciprocal behaviors relevant for wave-based neural and optical systems.

Contribution

It introduces a detailed analysis of phase transitions and chaos in PT-symmetric systems with saturable nonlinear channels, advancing understanding of their dynamical properties.

Findings

Identification of three distinct dynamical phases.

Revelation of chaos at phase boundaries.

Demonstration of tunable non-reciprocal resonator firing.

Abstract

Nonlinear channels play a critical role in realizing dynamical functions. Neural ionic channels and non-volatile memristors each derive representative biological and electrical functionalities, such as repetitive firing or pinched hysteresis. In electromagnetics, saturable channels of amplification or absorption provide a large nonlinearity for nonequilibrium wave dynamics, from conventional lasing to mode locking to recent achievements of the non-reciprocity in complex potentials. Here, we investigate the dynamical phase diagram of parity-time symmetric systems, governed by competing nonlinear channels of saturable amplification and absorption. Determined by the relative strength and saturation level of the channels, three distinctive phases of fast- and slow-response equilibriums, and an oscillating nonequilibrium are demonstrated. On phase boundaries, we also reveal the chaotic existence of the strong oscillation state, which allows the non-reciprocal realization of repetitive resonator firing with fully tunable time delays. This work will promote the wave-based realization of nonlinear and chaotic temporal functions, toward light-based neural systems.