${\cal PT}-$Symmetric Dimers with Time-Periodic Gain/Loss Function

TL;DR

This paper investigates ${ m PT}$-symmetric dimers with time-periodic gain/loss functions, analyzing their stability and phase transitions in classical and quantum models through analytical and numerical methods.

Contribution

It provides a comparative analysis of classical and quantum ${ m PT}$-symmetric dimers with time-periodic gain/loss, revealing stability behaviors and phase transition conditions.

Findings

Coupling initially decreases stability in classical dimers but causes re-entrant phase transitions.

Schrödinger dimers behave like single oscillators with periodic gain/loss.

Conditions identified where classical and quantum behaviors coincide.

Abstract

${\mathcal PT}-$symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schr\"{o}dinger dimer representing the coupling of field amplitudes; each system representing a wide class of physical models. Through a thorough analysis of their stability behaviour, we find that turning on the coupling parameter in the classical dimer system, leads initially to decreased stability but then to re-entrant transitions from the exact to the broken ${\mathcal PT}-$phase and vice versa, as it is increased beyond a critical value. On the other hand, the Schr\"{o}dinger dimer behaves more like a single oscillator with time-periodic gain/loss. In addition, we are able to identify the conditions under which the behaviour of the two dimer systems coincides and/or reduces to that of a single oscillator.