Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics

Abstract

In this paper, we revisit one of the prototypical PT-symmetric oligomers, namely the trimer. We find all the relevant branches of "regular" solutions and analyze the bifurcations and instabilities thereof. Our work generalizes the formulation that was proposed recently in the case of dimers for the so-called "ghost states" of trimers, which we also identify and connect to symmetry-breaking bifurcations from the regular states. We also examine the dynamics of unstable trimers, as well as those of the ghost states in the parametric regime where the latter are found to exist. Finally, we present the current state of the art for optical experiments in PT-symmetric trimers, as well as experimental results in a gain-loss-gain three channel waveguide structure.

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• $\mathcal{P}\mathcal{T}$ symmetry breaking in waveguide arrays with competing loss/gain pairs
• $\mathcal{P}\mathcal{T}$ symmetric phase transition and single-photon transmission in an optical trimmer system
• Snakes and ghosts in a parity-time-symmetric chain of dimers
• Exceptional points in oligomer chains
• Parity-time-symmetric closed form optical quadrimer waveguides
• Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity
• Generalized Dimers and their Stokes-variable Dynamics
• Nonlinear Parity-Time (PT) symmetric closed-form optical quadrimer waveguides: Attractor perspective
• Highly Amplified Light Transmission in Parity-Time Symmetric Multilayered Structure
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Non-reciprocal population dynamics in a quantum trimer