Dynamics of generalized PT-symmetric dimers with time periodic gain-loss

TL;DR

This paper investigates the dynamics of PT-symmetric dimers with periodically varying gain and loss, revealing conditions for different solution types and the persistence of rotation modes, supported by analytical and numerical analysis.

Contribution

It introduces a generalized analysis of PT-symmetric dimers with time-periodic gain-loss, identifying conditions for various dynamic regimes and the existence of rotation modes.

Findings

Rotation modes can persist under certain conditions.

An approximate threshold for PT-broken phase is provided.

Numerical results support analytical predictions.

Abstract

A Parity-Time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrodinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain-loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results.